An Extremal Eigenvalue Problem for a Two-Phase Conductor in a Ball

The pioneering works of Murat and Tartar (Topics in the mathematical modeling of composite materials. PNLDE 31. Birkhäuser, Basel, 1997) go a long way in showing, in general, that problems of optimal design may not admit solutions if microstructural designs are excluded from consideration. Therefore, assuming, tactilely, that the problem of minimizing the first eigenvalue of a two-phase conducting material with the conducting phases to be distributed in a fixed proportion in a given domain has no true solution in general domains, Cox and Lipton only study conditions for an optimal microstructural design (Cox and Lipton in Arch. Ration. Mech. Anal. 136:101–117, 1996). Although, the problem in one dimension has a solution (cf. Kre?n in AMS Transl. Ser. 2(1):163–187, 1955) and, in higher dimensions, the problem set in a ball can be deduced to have a radially symmetric solution (cf. Alvino et al. in Nonlinear Anal. TMA 13(2):185–220, 1989), these existence results have been regarded so far as being exceptional owing to complete symmetry. It is still not clear why the same problem in domains with partial symmetry should fail to have a solution which does not develop microstructure and respecting the symmetry of the domain. We hope to revive interest in this question by giving a new proof of the result in a ball using a simpler symmetrization result from Alvino and Trombetti (J. Math. Anal. Appl. 94:328–337, 1983).     

Simultaneous Determination of Acetylsalicylic Acid and Caffeine in Pharmaceutical Formulation by First Derivative Synchronous Fluorimetric Method

A sensitive, rapid, and specific assay has been developed for the simultaneous determination of acetylsalicylic acid and caffeine in commercial tablets based on their natural fluorescence. The mixture of these drugs was resolved by first derivative synchronous fluorimetric technique using two scans. At Δλ=106 nm, using first derivative synchronous scanning, only acetylsalicylic acid yields a detectable signal at 316 nm (peak to zero method) which is unaffected by caffeine. At Δλ=30 nm, the signal of caffeine at 288 nm (peak to zero method) is not affected by acetylsalicylic acid. The range of application is between 0.021 and 41.62 μg ml⁻¹ (correlation coefficient, R=0.9995) for acetylsalicylic acid and between 0.4486 and 44.86 μg ml⁻¹ (correlation coefficient, R=0.99786) for caffeine. The recovery range of 98.40–102% for acetylsalicylic acid and 90–100.5% for caffeine from their synthetic mixture was reported. Overall recovery of both compounds about 97–99% for acetylsalicylic acid and 97–98% for caffeine was obtained from real sample analysis. The detection limits are 0.0013 μg ml⁻¹ and 0.0306 μg ml⁻¹ for acetylsalicylic acid and caffeine, respectively. The relative standard deviation (n=10) for 20 μg ml⁻¹ of acetylsalicylic acid is 2.75% and for 2.2 μg ml⁻¹of caffeine is 1.7%.     

测地极坐标下空间形式的度量特征

将R3中Gauss曲率为常数k0的常曲率曲面S的度量特征推广到了一般的空间形式,主要工作是利用活动标架法和测地极坐标的理论,通过对结构方程的微分,找到了关于度量的一个内在方程,由此给出了定理的一个证明。     

Stable High-Energy Density Super-Atom Clusters of Aluminum Hydride

With the concept of super-atom, first principles calculations propose a new type of super stable cage clusters Al_nH_3n that are much more energetic stable than the well established clusters, Al_nH_n+2. In the new clusters, the aluminum core-frame acts as a super-atom with n vertexes and 2n Al-Al edges, which allow to adsorb n hydrogen atoms at the top-site and 2n at the bridge-site. Using Al₁₂H₃₆ as the basic unit, stable chain structures, (Al₁₂H₃₆)m, have been constructed following the same connection mechanism as for (AlH₃)_n linear polymeric structures. Apart from high hydrogen percentage per molecule, calculations have shown that these new clusters possess large heat of formation values and their combustion heat is about 4.8 times of the methane, making them a promising high energy density material.     

The Dissipative Spectral Methods for the First Order Linear Hyperbolic Equations

In this paper, we introduce the dissipative spectral methods (DSM) for the first order linear hyperbolic equations in one dimension. Specifically, we consider the Fourier DSM for periodic problems and the Legendre DSM for equations with the Dirichlet boundary condition. The error estimates of the methods are shown to be quasi-optimal for variable-coefficients equations. Numerical results are given to verify high accuracy of the DSM and to compare the proposed schemes with some high performance methods, showing some superiority in long-term integration for the periodic case and in dealing with limited smoothness near or at the boundary for the Dirichlet case.     

第一壁材料用纳米结构氧化物弥散强化钢制备工艺及其性能研究进展

近年来发展起来的纳米结构氧化物弥散强化钢(ODS钢),因其有优异的耐高温、抗辐照及力学性能,满足聚变堆第一壁结构材料的要求。本文主要简述了纳米结构ODS钢制备工艺及其性能的研究进展。     

Non-equilibrium effects in chaperone-assisted translocation of a stiff polymer

Chaperone-assisted biopolymer translocation is the main model proposed for translocation in vivo. A dynamical Monte Carlo method is used to simulate the translocation of a stiff homopolymer through a nanopore driven by chaperones. Chaperones are proteins that bind to the polymer near the wall and prevent its backsliding through Cis side. The important parameters include binding energy, size and the local concentration of the chaperones. The profile of these local concentrations, build up the chaperones distribution. Here we investigate the effects of binding energy, size and the exponential distribution of chaperones in their equilibration in each step of the polymer translocation needed for stable translocation time. The simulation results show that in case of chaperones with the size of a monomer ($\lambda =1$) and/or positive effective binding energy and/or uniform distribution, the chaperones binding equilibration rate/frequency is less than 5 times per monomer. However, in some special cases in the exponential distribution of chaperones with size $\lambda >1$ and negative effective binding energy the equilibration rate will diverge to more than 20 times per monomer. We show that this non-equilibrium effect results in supper diffusion, seen before. Moreover, we confirm the equilibration process theoretically.     

Penta-SiC5 monolayer: A novel quasi-planar indirect semiconductor with a tunable wide band gap

In this paper, by using of the first principles calculations in the framework of the density functional theory, we systematically investigated the structure, stability, electronic and optical properties of a novel two-dimensional pentagonal monolayer semiconductors namely penta-SiC₅ monolayer. Comparing elemental silicon, diamond, and previously reported 2D carbon allotropes, our calculation shows that the predicted penta-SiC₅ monolayer has a metastable nature. The calculated results indicate that the predicted monolayer is an indirect semiconductor with a wide band gap of about 2.82 eV by using Heyd–Scuseria–Ernzerhof (HSE06) hybrid functional level of theory which can be effectively tuned by external biaxial strains. The obtained exceptional electronic properties suggest penta-SiC₅ monolayer as promising candidates for application in new electronic devices in nano scale.     

First order transition to oscillation death through an environment

The emergence of dynamical abrupt transitions for the first time in an ensemble of identical limit-cycle and chaotic oscillators coupled via a common environment is reported. The transition from the oscillatory state to the death state and vice versa, in these networks of oscillators are found not only discontinuous as well as irreversible in the parameter space. This first order phase transition in these systems is termed as Explosive Death. The occurrence of such transition is studied in details by using an appropriate order parameter for both limit-cycle and chaotic oscillators, in particular, Stuart–Landau and Rössler oscillators. The backward transition point for this phenomenon is obtained analytically using linear stability analysis and is found to be consistent with the numerical results.     

The first principle study of the electronic structure of SixGe(1−x) alloy films

First principles calculation based on density functional theory (DFT) with the generalized gradient approximation (GGA) are carried out to investigate the electronic band structures of ${\text{Si}}_x{\text{Ge}}_{(1?x)}$ alloys nanofilms. The calculation results show that the band gaps of (100), (110) and (111) surfaces ${\text{Si}}_x{\text{Ge}}_{(1?x)}$ alloy films with different thickness first increase with the increase of Si content, then flatten out, and finally decrease. At the same time, the transformation of direct band gap and indirect band gap occurs when the thickness of films and Si content of the three surface ${\text{Si}}_x{\text{Ge}}_{(1?x)}$ alloy films changes to a certain critical condition. It will be a good way to obtain direct-gap band emission in ${\text{Si}}_x{\text{Ge}}_{(1?x)}$ alloys materials.