Dynamic frictionless contact with adhesion

A model for the dynamic, adhesive, frictionless contact between a viscoelastic body and a deformable foundation is described. The adhesion process is modeled by a bonding field on the contact surface. The contact is described by a modified normal compliance condition. The tangential shear due to the bonding field is included. The problem is formulated as a coupled system of a variational equality for the displacements and a differential equation for the bonding field. The existence of a unique weak solution for the problem is established, together with a partial regularity result. The existence proof proceeds by construction of an appropriate mapping which is shown to be a contraction on a Hilbert space.     

Effect of Pressure on Fluid Damping in MEMS Torsional Resonators with Flow Ranging from Continuum to Molecular Regime

High quality factor of dynamic structures at micro and nano scale is exploited in various applications of micro electro-mechanical systems (MEMS) and nano electro-mechanical system. The quality factor of such devices can be very high in vacuum. However, when vacuum is not desirable or not possible, the tiny structures must vibrate in air or some other gas at pressure levels that may vary from atmospheric to low vacuum. The interaction of the surrounding fluid with the vibrating structure leads to dissipation, thus bringing down the quality factor. Depending on the ambient fluid pressure or the gap between the vibrating and the fixed structure, the fluid motion can range from continuum flow to molecular flow giving a wide range of dissipation. The relevant fluid flow characteristics are determined by the Knudsen number which is the ratio of the mean free path of the gas molecule to the characteristic flow length of the device. This number is very small for continuum flow and reasonably big for molecular flow. In this paper, we study the effect of fluid pressure on the quality factor by carrying out experiments on a MEMS device that consists of a double gimbaled torsional resonator. Such devices are commonly used in optical cross-connects and switches. We only vary fluid pressure to make the Knudsen number go through the entire range of continuum flow, slip flow, transition flow, and molecular flow. We experimentally determine the quality factor of the torsional resonator at different air pressures ranging from 760 Torr to 0.001 Torr. The variation of this pressure over six orders of magnitude ensures required rarefaction to range over all flow conditions. Finally, we get the variation of quality factor with pressure. The result indicates that the quality factor, Q, follows a power law, Q ∝P ^–r , with different values of the exponent r in different flow regimes. In the second part of the paper, we propose the use of effective viscosity for considering velocity slip conditions in solving Navier–Stokes equation numerically. This concept is validated with analytical results for a simple case and then compared with the experimental results presented in this paper. The study shows that the effective viscosity concept can be used effectively even for the molecular regime if the air-gap to length ratio is sufficiently small (h ₀/L<0.01). As this ratio increases, the range of validity decreases.     

Q-正则Loewner空间中的拟对称映射

本文在Q-正则Loewner空间中用环模不等式刻划了拟对称映射.另外,在 Q-维Ahlfors-David正则空间中建立了拟对称映射作用下的Grotzsch-Teichmuller型 模不等式,它是通过伸张系数的积分平均来表示.     

采用Authorware 5制作现代光学实验多媒体课件

我们采用目前最流行的多媒体制作软件Authorware 5开发工具，把现代光学实验原理，公式推导，实验内容，步骤等字材料，以及用CCD采集的干涉图像，优美的背景音乐及解说词等多种数学信息，制作成多媒体课件，可直接用于远程教育，有较大的实用价值。     

A study of electrostatic spring softening for dual-axis micromirror

Electrostatic spring softening is an important characteristic of electrostatically actuated dual-axis micromirror, since it lowers the resonant frequencies. This paper presents an approach based on approximating the electrostatic forces by the first-order Taylor's series expansion to investigate this characteristic. The dual-axis micromirror studied in this paper has three motion modes, two torsional (about x- and y-axis, respectively) and one translational (about z-axis). The stiffnesses of all these modes are softened by a DC bias voltage applied to the mirror plate. The resonant frequencies are lowered with the increment of the bias voltage. The relationship of the bias voltage and the resonant frequencies of all the motion modes is derived. The analytical results show that the resonant frequency curves are affected by the capacitor geometries, i.e. the gap between the mirror plate and the electrodes and the electrodes size. The lowering curves drop slowly when the bias voltage is small. While for large bias voltage, the lowering curves drop rapidly. The experiment results are consistent with those obtained by the analytical approach.     

锰(Ⅱ)-高碘酸钾-灿烂绿体系测定水中痕量锰

在 HAc- Na Ac环境中 ,锰 ( )对于高碘酸钾氧化灿烂绿的反应具有很强的催化作用。据此 ,建立了催化动力学光度法测定痕量锰 ( )的新方法。该方法的检出限为 2 .2 2× 10 -11g/ m L ,测定线性范围为0 .1— 12 ng/ m L。直接用于环境水样中锰的测定 ,获得满意的结果     

Spectroscopic evidence for triplet excitation energy transfer among carotenoids in the LH2 complex from photosynthetic bacterium <Emphasis Type="Italic">Rhodopseudomonas palustris</Emphasis>

The LH2 complex from Rhodopsudomonas (Rps.) palustris is unique in the heterogeneous carotenoid compositions. The dynamics of triplet excited state Carotenoids (³Car* has been investigated by means of sub-microsecond time-resolved absorption spectroscopy both at physiological temperature (295 K) and at cryogenic temperature (77K). Broad and asymmetric T _n ←T ₁ transient absorption was observed at room temperature following the photo-excitation of Car at 532 nm, which suggests the contribution from various carotenoid compositions having different numbers of conjugated C=C double bonds (N_c=c). The triplet absorption bands of different carotenoids, which superimposed at room temperature, could be clearly distinguished upon decreasing the temperature down to 77 K. At room temperature the shorter-wavelength side of the main T_n04T₁ absorption band decayed rapidly to reach a spectral equilibration with a characteristic time constant of ∽1 μs, the same spectral dynamics, however, was not observed at 77 K. The aforementioned spectral dynamics can be explained in terms of the triplet-excitation transfer among heterogeneous carotenoid compositions. Global spectral analysis was applied to the time-resolved spectra at room temperature, which revealed two spectral components peaked at 545 and 565 nm, and assignable to the T_n04 T₁ absorption of Cars with Nc=c=11 and Nc=c=13, respectively. Surprisingly, the decay time constant of a shorter-conjugated Car, i.e. 0.72 ώs (aerobic) and 1.36 ώs (anaerobic), is smaller than that of a longer-conjugated Car, i.e. 2.12 us (aerobic) and 3.75 ώs (anaerobic), which is contradictory to the general rule of carotenoids and relative polyenes. The results are explained in terms of triplet-excitation transfer among different types of Cars. It is postulated that two Cars with different conjugation lengths coexist in an α, β-subunit in the LH2 complex.     

有机溶剂与水溶液引入电感耦合等离子体电子密度和电子温度轴向分布的比较

为了研究有机ICP最佳分析条件与水溶液ICP明显不同的原因,本文在不同的等离子体操作条件下测量了Hβ486.133nm Stark变宽,分别计算了有机溶剂和水溶液引入1CP轴向的n_e和Te值,并进行了比较。有机溶剂引入ICP时,在固定的功率,观测高度及载气流量下其轴向ne和Te均比用水溶液引入时低一些。有机ICP的优异分析性能只有在比水溶液ICP有较高的入射功率和较低的载气流量条件下才能展现出来。     

Synthesis and photoinduced memory effect of poly[2-N-carbazolylethyl acrylate-co-2-(3,5-dinitrobenzoyloxy) ethyl methacrylate]

Copolymers containing an intramolecular electron donor-acceptor (EDA) complex were synthesized by free radical copolymerization of 2-N-carbazolylethyl acrylate and 2-(3,5-dinitrobenzoyloxy)ethyl methacrylate. Glass transition temperatures show a positive deviation from the weight-average values of copolymers, indicating the presence of the specific EDA interaction in copolymers in the solid state. Photoinduced “memory effect,” which is defined as the percentage of the difference of the surface potential given by corona charging before and after irradiation of light on polymer films, was 30% for the copolymer with 5 mol% of acceptor content. Memory effect increased to 70% for a 8 μm film by doping with 2 wt% of trichloroacetic acid (TCAA), and leveled off at 5 wt% of TCAA content. Memory effect was also enhanced by increasing the thickness of polymer films and irradiation time. The largest value of memory effect (85%) was obtained from the film of the copolymer with 5 mol% acceptor content doped with 1 wt% TCAA and with thickness larger than 14 μm.