Fast Legendre spectral method for computing the perturbation of a gradient temperature field in an unbounded region due to the presence of two spheres

The temperature distribution around two spheres is considered when the main field has a constant gradient at infinity. Bispherical coordinates are used, together with a transformation of the dependent variable that leads to separation of variables. Then the solution can be sought in Legendre series with respect to one of the bispherical coordinates. An important element of the proposed work is the effective way to reduce an essentially 3D problem to a set of three 2D problems. The Legendre spectral method is shown to have an exponential convergence which is confirmed by the computations. The efficiency is so high that even for the hard cases of two closely situated spheres, an accuracy of 10^?10 is achieved with as few as 20 terms in the expansion. Solutions with both longitudinal and transverse gradients at infinity are obtained, and the contour lines of the temperature field are presented graphically. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010     

老化反应对高碱度烷基水杨酸钙胶体结构及抗磨性的影响

采用冷冻蚀刻电镜（ＦＥ－ＥＭ）,傅立叶红外光谱（ＦＴ－ＩＲ）及钙分布测定等研究了高碱度烷基水杨酸钙的老化过程,并探讨了老化机理,老化反应高碱度烷基水杨酸钙胶体粒子变小,胶体中氢氧化钙的相对含量增加,粘度降低,总碱值（ＴＢＮ）升高;老化后样品的清净性及抗磨性明显提高;水、甲醇及氢氧化钙等影响老化效果。     

Dynamic melt flow of nanocomposites based on poly-ɛ-caprolactam

 The dynamic flow behavior of polyamide-6 (PA-6) and a nanocomposite (PNC) based on it was studied. The latter resin contained 2 wt% of organoclay. The two materials were blended in proportions of 0, 25, 50, 75, and 100 wt% PNC. The dynamic shear rheological properties of well-dried specimens were measured under N₂ at T=240 °C, frequency ω=0.1–100 rad/s, and strains γ=10 and 40%. At constant T, γ, and ω the time sweeps resulted in significant increases of the shear moduli. The γ and ω scans showed a complex rheological behavior of all clay-containing specimens. At γ=10% the linear viscoelasticity was observed for all compositions only at ω>1 rad/s, while at γ=40% only for 0 and 25 wt% of PNC. However, the effect was moderate, namely decreasing G′ and G′′ (at ω=6.28 rad/s; γ=50%) by 15 and 7.5%, respectively. For compositions containing >25 wt% PNC two types of non-linearity were detected. At ω≤ω_c=1.4 ± 0.2 rad/s yield stress provided evidence of a 3-D structure. At ω > ω_c, G′ and G′′ were sensitive to shear history – the effect was reversible. From the frequency scans at ω > ω_c the zero-shear relative viscosity vs concentration plot was constructed. The initial slope gave the intrinsic viscosity from which the aspect ratio of organoclay particles, p=287 ± 9 was calculated, in agreement with the value calculated from the reduced permeability data, p=286. Received: 24 May 2001 Accepted: 27 August 2001     

Rheology of poly(methyl methacrylate-<Emphasis Type="Italic">co</Emphasis>-styrene) particles suspended in water: effects of electrostatic surface layer

 Linear and nonlinear viscoelastic properties were examined for aqueous suspensions of monodisperse poly(methyl methacrylate-co-styrene) (MS) particles having the radius a ₀ =45 nm and the volume fractions φ=0.428−0.448. These particles had surface charges and the resulting electrostatic surface layer (electric double layer) had a thickness of t_s=5.7 nm. At low frequencies in the linear viscoelastic regime, the MS particles behaved approximately as the Brownian hard particles having an effective radius a _eff=a ₀ + t_s, and the dependence of their zero-shear viscosity η₀ on an effective volume fraction φ_eff (={a _eff/a ₀}³φ) agreed with the φ dependence of η₀ of ideal hard-core silica suspensions. In a range of φ_eff < 0.63, this φ_eff dependence was well described by the Brady theory. However, the φ_eff dependence of the high-frequency plateau modulus was weaker and the terminal relaxation mode distribution was narrower for the MS suspensions than for the hard-core suspensions. This result suggested that the electrostatic surface layer of the MS particles was soft and penetrable (at high frequencies). In fact, this “softness” was more clearly observed in the nonlinear regime: the nonlinear damping against step strain was weaker and the thinning under steady shear was less significant for the MS suspension than for the hard-core silica suspensions having the same φ_eff. These weaker nonlinearities of the concentrated MS particles with φ_eff∼ 0.63 (maximum volume fraction for random packing) suggested that the surface layers of those particles were mutually penetrating to provide the particles with a rather large mobility. Received: 10 July 2001 Accepted: 2 November 2001     

Field-induced phase transitions and reversible field-induced inversion of chirality in tilted smectic phases of bent-core mesogens

Three homologous achiral five-ring bent-core mesogens are presented where 4-chlororesorcinol is the central core and the aromatic rings are linked by ester groups. These compounds form smectic phases with a tilted arrangement of the molecules (tilt angle ≈ 45^°). On cooling the isotropic liquid this phase adopts a fan-like texture which shows for two homologues at relatively high electric fields ( 25-35V μm^-1) an antiferroelectric electro-optical response based on the collective rotation of the molecules around their long axes. At lower temperature the application of a sufficiently high electric field leads to a continuous transition into a non-birefringent texture which exhibits randomly distributed domains of opposite handedness. These domains can be reversibly switched into a state of opposite chirality by reversal of the field polarity. This switching is bistable and shows a current response typical for a ferroelectric ground state. The possible mechanism of the field-induced phase transition, of the ferroelectric switching and of the field-induced inversion of the chirality is discussed on the base of XRD, ¹³C- and ¹H-NMR investigations, dielectric and electro-optical measurements.     

Frustrated structure of an anticlinic-like smectic-C phase

We present a polarising optical microscopy study of the low-temperature anticlinic-like tilted mesophase of the liquid-crystal compound octylphenyl-2-chloro-4-(p-cyano-benzoyloxy) (DB₈Cl). This mesophase has been described as a bilayer smectic structure in which the molecules within each layer are organised in an anticlinic way. The optical textures observed in samples with planar orientation show a double stripe pattern, with the lines aligned parallel to the rubbing direction, characteristic of a double periodic modulation of the refractive index of the material. The long-period modulation is temperature dependent and disappears for thin sample cells (< 5μm). The short-period modulation is nearly independent of the thickness of the cells. The experimental results are analysed in terms of a model which considers that there is a special distribution of the principal optical axis which may be in or out of the polariser-analyser plane. The observed periodic variation of the principal optical axis could not be interpreted in terms of the original structure proposed for this phase. DB₈Cl presents a structure formed by dimers that can be viewed as flexible bent-core-like molecules, showing similarities with phases found in banana-like systems, but exhibiting a much more complex structure.     

Application of inertia-induced excitation theory for nonlinear acoustic modes in colloidal plasma equilibrium flow

Application of inertia-induced acoustic excitation theory offers a new resonant excitation source channel of acoustic turbulence in the transonic domain of plasma flow. In bi-ion plasmas like colloidal plasma, two well-defined transonic points exist corresponding to the parent ion and the dust grain-associated acoustic modes. As usual, the modified ion acoustic mode (also known as dust ion-acoustic (DIA) wave) dynamics associated with parent ion inertia is excitable for both nanoscale-and micronscale-sized dust grains. It is found that the so-called (ion) acoustic mode (also known as dust-acoustic (DA) wave) associated with nanoscale dust grain inertia is indeed resonantly excitable through the active role of weak but finite parent ion inertia. It is interestingly conjectured that the same excitation physics, as in the case of normal plasma sound mode, operates through the active inertial role of plasma thermal species. Details of the nonlinear acoustic mode analyses of current interest in transonic domains of such impure plasmas in hydrodynamic flow are presented.      

A study of the evaporative deposition process: Pipes and truncated transport dynamics

We consider contact line deposition of an evaporating thin drop. Following Dupont’s proposal (unpublished), we focus on transport dynamics truncated by a maximal concentration as the single deposition mechanism. The truncated transport process, formalized as the “pipe model”, admits a characteristic shock front that has a robust functional form and depends only on local hydrodynamic properties. By applying the pipe model, we solve the density profile in different asymptotic regimes. In particular, we find that near the contact line the density profile follows a scaling law that is proportional to the square root of the concentration ratio defined as the initial solute volume concentration divided by the maximal concentration. The maximal deposit density occurs at about 2/3 of the total drying time for uniform evaporation and 1/2 for diffusion-controlled evaporation. Away from the contact line, areal density decays exponentially with the radial distance to the power of -3 for the uniform evaporation and -7 for the diffusion-controlled evaporation.     

Bridging Two Worlds: Colloidal versus Epitaxial Quantum Dots

An overview is given of two distinct classes of semiconductor quantum dots, epitaxial and colloidal structures that have been studied intensely for more than 30 years by now, however, without large interconnection between the two involved research communities. The largely parallel and independent evolution of the two structure classes may be partly related to the origin of colloidal systems from chemistry, while epitaxial quantum dots have been addressed mostly by the physics community. These independent evolutions are somewhat surprising because the interest in optics‐related applications is shared by both communities. Here, a short summary of the development of the two structure classes, the present status of activities, and some perspectives for future developments are presented.     

二维氧化锌纳米阵列的制备及光学吸收特性研究

采用漂移法,在玻璃衬底上制备出粒径分别为117,350和500 nm单层、大面积的聚苯乙烯胶体球掩膜板,在已制得的掩膜板上用射频磁控溅射的方法沉积一层氧化锌薄膜,最后用有机溶液四氢呋喃(THF)浸泡去除聚苯乙烯胶体球,获得不同粒径的二维氧化锌纳米团簇。通过扫描电子显微镜和能量色散X射线光谱仪对样品的形貌及成份进行表征,表明所制得样品为有序分布的蜂窝网状氧化锌纳米阵列。在室温下,通过吸收光谱仪测试样品在300～800 nm波长范围内的吸收光谱,结果表明对于具有不同尺寸晶粒的氧化锌纳米团簇样品,随着所采用的聚苯乙烯胶体球粒径的增大,即氧化锌纳米团簇粒径的增加,光吸收峰出现了宽化和红移;随着溅射时间的延长,即氧化锌薄膜膜厚的增加,光吸收率提高。此外,对氧化锌纳米团簇阵列的光吸收特性进行了基于离散偶极子近似的理论计算从而获得任意形状和尺寸粒子的吸收。目前,文献报道中用此理论计算各种形状的纳米金、银等金属的结果与实验结果相符,但是应用离散偶极子的近似理论计算氧化锌纳米颗粒的报道很少。应用此理论计算三角棱台形状的氧化锌光学吸收特性,根据氧化锌薄膜介电常数和膜厚的变化进行光吸收特性的模拟,并解释了实验结果。