Second order parabolic equations in Banach spaces with dynamic boundary conditions

In this paper, we exhibit a unified treatment of the mixed initial boundary value problem for second order (in time) parabolic linear differential equations in Banach spaces, whose boundary conditions are of a dynamical nature. Results regarding existence, uniqueness, continuous dependence (on initial data) and regularity of classical and strict solutions are established. Moreover, several examples are given as samples for possible applications.

     

Ergodicity for the Dissipative Boussinesq Equations with Random Forcing

We study the stationary measure for the two-dimensional Boussinesq equation with random forcing. We prove the ergodicity for the two-dimensional stochastically forced Boussinesq equation. We also study the Galerkin truncations of the three-dimensional Boussinesq equations under degenerate stochastic forcing. We follow closely the previous results on the stochastically forced Navier–Stokes equations.     

质子化丙酮分子团簇的结构和振动光谱

用密度泛函B3LYP/ 6 3 1G(d)方法 ,对质子化丙酮分子团簇 (CH3COCH3) nH+ (n =1～ 7)弱相互作用体系进行了全自由度能量梯度优化 ,得到了该系列团簇的稳定结构及其对应的体系能量 .通过对构型的分析得出了质子化丙酮分子团簇 (CH3COCH3) nH+ (n =1～ 7)的生长规律 .计算了中性丙酮分子团簇体系的质子亲合能并总结出其变化趋势 .分析讨论了质子化团簇的红外振动光谱 ,发现质子化团簇的振动光谱普遍较中性环型团簇的振动光谱复杂 ,最强的振动峰来源于质子在溶剂壳中两个氧原子之间的振动 ,而且随着团簇尺寸的增加羰基的伸缩振动峰的数目也随之增多     

Investigation of the Li1+xV3O8 electrode–organic electrolyte interface by scanning photoelectron microscopy

To investigate the formation of a solid electrolyte interface (SEI) on the Li_1+xV₃O₈ electrode surface in the thermodynamic stability range of the organic electrolyte, we applied scanning photoelectron microscopy (SPEM) to a pristine electrode and to an electrode after ten cycles. The F K-edge absorption spectrum of the cycled electrode showed that LiF forms on the electrode surface during the lithium insertion–extraction process in the Li_1+xV₃O₈/Li cell. The photoelectron spectrum for the cycled electrode showed intense spectral features corresponding to Li 1s, F 2s, F 2p, and P 2p electron signals, whereas these spectral features were of negligible intensity for the pristine electrode. The above results give strong support for the formation of an SEI that consists of LiF and compounds containing phosphorus during operation of the battery. The SPEM images also revealed that the fluorine distribution on the surface of the cycled electrode was inhomogeneous.     

Applying a Mode Selector to Improve the Pulse-Compression Performance of Asymmetric-Coupled-Waveguide-Based Dispersion Compensators

An InGaAsP slab-type asymmetric-coupled-waveguide-based dispersion compensator with a mode selector has been designed and fabricated. The mode selector is necessary to select either a symmetric [with a positive group-velocity dispersion (GVD)] or antisymmetric (with a negative GVD) supermode. These supermodes exist simultaneously in the dispersion-compensation region of the device. Pulse-compression experiments were used to test the dispersion compensator, evaluating the function of the mode selector. A theoretical study of the experimental results shows that the mode selector obtains a very strong selectivity (nearly 100%) for the antisymmetric supermode.     

Study of period number effect in the superlattice infrared photodetector

Superlattices have been demonstrated previously by our group in the design of the multicolor infrared photodetector. In general, the period number of the superlattice may be up to several dozens. In this paper, we have investigated the performance of the infrared photodetectors especially with 3, 5 and 15 periods. The detector structure contains a thick blocking barrier embedded between two superlattices with different period numbers but with the same well and barrier widths. This double-superlattice structure shows switchable spectral responses between two spectral regions by the voltage polarities. The photoresponse in each spectral region is also tunable by the magnitude of the applied voltage. The voltage-dependent behavior reveals the photoelectron relaxation and transport mechanism in the superlattice miniband. Superlattice with few periods has high electron group velocity, less relaxation effect and less collection efficiency. Therefore the superlattice with few periods may have better responsivity and narrower photoresponse range than the one with many periods. Based on the experimental results of our devices, it is observed that the superlattice with fewer periods has better detectivity, responsivity, wider range of the operational temperature, and more flexible miniband engineering than the conventional multiple quantum well infrared photodetector.     

Structural optimization design for large mirror

The system design must be started from the concept with low cost and high performance. In this point, the topological shape of the structure is very important in the view of the structural rigidities and light-weight design.In this paper, the optimization methodology is presented in the design stage of the large optical mirror. We obtain the optimal layout through the topology optimization and then design the details through the size or shape optimization for structural rigidity.     

Two-dimensional autocorrelation function analysis of smoked foil patterns

Digital image processing techniques have been applied to the analysis of cellular smoked foil patterns from gaseous detonations. In particular, the two-dimensional autocorrelation function is applied to digital cell pattern images and an orientational correlation parameter is calculated. Taking line profiles along the directions of highest correlation provides an unbiased method of determining the mean cell size in each of the two principal directions. By analyzing the width, amplitude and angular position of the orientational correlation plots, information can be extracted concerning the cellular pattern regularity, the relative angular correlation between two sets of transverse waves in two directions, and the mean shape or elongation of the cells within the pattern. The technique is applied to smoked foils from oxyacetylene mixtures with argon dilutions ranging from 0 to 75% to quantify the increase in regularity with argon dilution. This method provides a simple and useful way of analyzing cellular patterns and constitutes a promising technique for improving smoked foil diagnostics.