Thermal analysis and X-ray studies of chiral ferroelectric liquid crystalline materials and their binary mixtures

Summary Thermal properties of a homologous series of ferroelectric liquid crystals S-(-)-[4-(2-n-alkoxy-propionyloxy)]biphenyl-4'-[n-alkoxy-(3,5-dimethyl)]benzoate have been investigated by polarizing optical microscopy and differential scanning calorimetry. The mesophases were identified and confirmed by X-ray too. Three binary mixtures were prepared from the individual homologues. In one of the mixtures (Mix1), the ferroelectric SmC* phase has broadened and became enantiotropic. This mesophase remained monotropic in the other two mixtures (Mix2, Mix3). The chiral nematic N* phase did not appear in Mix1, but remained monotropic for the other two mixtures. Two molecular parameters, the layer spacing and the average intermolecular distance have been calculated from the X-ray results for the homologues and their mixtures. An intercalated tail-to-tail packing of molecules was found both in the single compounds and their mixtures resulting in the layer spacing about half of the molecular length of the single compounds.     

Wave chaos in quantum systems with point interaction

We study perturbations of the quantized version ₀ of integrable Hamiltonian systems by point interactions. We relate the eigenvalues of to the zeros of a certain meromorphic function . Assuming the eigenvalues of ₀ are Poisson distributed, we get detailed information on the joint distribution of the zeros of and give bounds on the probability density for the spacings of eigenvalues of . Our results confirm the wave chaos phenomenon, as different from the quantum chaos phenomenon predicted by random matrix theory.SFB 237 Essen-Bochum-Düsseldorf     

Quantitative analysis of mixed self-assembled monolayers using ToF-SIMS

The spacing of chemical functional groups on self-assembled monolayers (SAMs) plays an important role in controlling the density of biomolecules in biochips and biosensors. In this sense, a mixed SAM made of two different terminal groups is a useful organic surface since spacing can be easily controlled by changing a relative mole fraction in a mixture solution. In this study, an acetylene-OCH₂O(EG)₃(CH₂)₁₁S-S(CH₂)₁₁(EG)₃OCH₂O-propene (Eneyne) SAM and mixed SAMs made by a mixture of (S(CH₂)₁₁(EG)₃OCH₂O-acetylene)₂ (Diyne) and (S(CH₂)₁₁(EG)₃OCH₂O-propene)₂ (Diene) were produced on gold substrates and measured by using ToF-SIMS. The secondary ion yield ratio of [Au·S(CH₂)₁₁(EG)₃OCH₂O-acetylene]⁻ to [Au·S(CH₂)₁₁(EG)₃OCH₂O-propene]⁻ was measured for each mixed SAM and plotted as a function of the mole fraction of Diyne to Diene in a SAM solution. The ion yield ratio of a mixed SAM produced from a solution with a mole fraction of 0.5 (i.e., 1:1 mixture) was 0.3, which corresponded well to the ion yield ratio measured from an Eneyne SAM. A time-dependent experiment of Eneyne SAM formation and immersion experiment of Eneyne SAM into Diyne solution or into Diene solution were performed. The relative ion yield ratio of 0.3 was due to a different secondary ion formation and not due to the difference in the amount of adsorbates on the surface, nor to the different binding strengths onto the gold surface. Our study shows that a mixed SAM with well-controlled spacing can be produced and quantified by using the ToF-SIMS technique.     

A widely tunable dual-wavelength erbium-doped fiber ring laser operating in single longitudinal mode

A new mechanism to induce polarization hole burning effect in Er-doped fiber ring lasers is presented. By using this effect, incorporating with the counter-propagation of the two light beams, the inhomogeneous in the gain medium broadening was significantly increased, and thus a stable dual-frequency Er-doped fiber ring laser operating in single longitudinal mode and single-frequency was demonstrated. Frequency spacing was tunable from 0.47 GHz to THz.     

激光主动干涉条纹间距识别光学目标口径

利用物理光学相关知识及Collins衍射积分公式和硬边光阑的复高斯函数分解法,推导得到目标处干涉图样条纹间距与光学目标反射光时间分布关系的解析表达式.从原理分析、仿真计算和实验研究等方面研究了干涉场的条纹间距、光学目标口径参数和反射光时间分布包络的峰峰数、峰峰间距和峰峰比之间定量关系.结果表明,当条纹间距的大小约为目标的口径尺寸时,反射光时间分布包络的峰峰数由单峰向多峰过渡,峰峰间距和峰峰比曲线会出现极大值,根据这一变化规律可以估测出光学目标的口径参数,其估测精度受条纹间距可调节范围的影响.     

Growth of tertiary dendritic arms during the transient directional solidification of hypoeutectic Pb–Sb alloys

Despite the importance of a complete characterization of dendritic patterns in castings, the availability of studies on the development of tertiary dendrite arms is scarce in the literature. In the present study, the tip cooling rate, local solidification time, primary and tertiary dendrite arm spacings have been determined in Pb–Sb alloys castings directionally solidified under unsteady-state heat flow conditions. The alloys compositions experimentally examined are widely used in the as-cast condition for the manufacture of positive and negative grids of lead-acid batteries. The initial growth of tertiary dendritic arms from the secondary branches was found to occur only for a Pb–3.5 wt% Sb alloy at cooling rates in the range 0.4–0.2?K/s, with no evidence of this spacing pattern for Pb–Sb alloys having lower solute content. Tertiary dendritic branches have been observed along the entire casting lengths for alloys of the Pb–Sb hypoeutectic range having compositions higher than 4.0 wt% Sb. It is shown that a power function experimental law with a characteristic ?0.55 exponent is able to characterize the tertiary spacing evolution with the solidification cooling rate for alloys compositions ≥4.0 wt% Sb. The only exception was the Pb–3.5 wt% Sb alloy for which λ ₃ exhibited significant lower values when compared with the experimental values obtained for the other Pb–Sb alloys for a same solidification cooling rate.     

Averaging principle for equation driven by a stochastic measure

ABSTRACT

Equation with the symmetric integral with respect to stochastic measure is considered. For the integrator, we assume only σ-additivity in probability and continuity of the paths. It is proved that the averaging principle holds for this case, the rate of convergence to the solution of the averaged equation is estimated.     

On a Class of Random Variational Inequalities on Random Sets

We study a class of random variational inequalities on random sets and give measurability, existence, and uniqueness results in a Hilbert space setting. In the special case where the random and the deterministic variables are separated, we present a discretization technique based on averaging and truncation, prove a Mosco convergence result for the feasible random set, and establish norm convergence of the approximation procedure.     

Cramér's asymptotics in systems with fast and slow motions

This paper is devoted to the averaging principle for stochastic systems with slow and intermixing fast motions. Here we (i) prove the existence of the Cramér type asymptotics for the probabilities of large deviations from an averaged motion, which implies the central limit theorem, and (ii) develop an analytic procedure for computation of this asymptotics. We use general apparatus of superregular perturbations of fiber ergodic semigroups to investigate two systems in the same way. The first of them is a cascade in which slow motions are determined by a vector field depending both on slow and fast variables, and fast motions compose a Markov chain depending on the slow variable. The second is a process defined by a system of two stochastic differential equations.     

具有分布偏差变元的二阶中立型方程的振动准则(英文)

利用Riccati变换及积分平均技巧,建立一类具有非线性中立项及分布偏差变元的二阶中立型方程的振动准则,我们的结果推广并改进了一些已有的结果.