Secondary-flow-aided single-train elastic-inertial focusing in low elasticity viscoelastic fluids

Elastic-inertial focusing has attracted increasing interest in recent years due to the three-dimensional (3D) single-train focusing ability it offers. However, multi-train focusing, instead of single-train focusing, was observed in viscoelastic fluids with low elasticity as a result of the competition between inertia effect and viscoelasticity effect. To address this issue, we employed the secondary flow to facilitate single-train elastic-inertial focusing in low elasticity viscoelastic fluids. A three-section contraction-expansion channel was designed to induce the secondary flow to pinch the multiplex focusing trains into a single one exactly at the channel centerline. After demonstrating the focusing process and mechanism in our device, we systematically explored and discussed the effects of particle diameter, operational flow rate, polymer concentration, and channel dimension on particle focusing performances. Our device enables single-train focusing of particles in viscoelastic fluids with low elasticity, and offers advantages of planar single-layer structure, and sheathless, external-field free operation.     

A Mellin transform approach to pricing barrier options under stochastic elasticity of variance

This article considers a problem of evaluating barrier option prices when the underlying dynamics are driven by stochastic elasticity of variance (SEV). We employ asymptotic expansions and Mellin transform to evaluate the option prices. The approach is able to efficiently handle barrier options in a SEV framework and produce explicitly a semi-closed form formula for the approximate barrier option prices. The formula is an expansion of the option price in powers of the characteristic amplitude scale and variation time of the elasticity and it can be calculated easily by taking the derivatives of the Black–Scholes price for a barrier option with respect to the underlying price and computing the one-dimensional integrals of some linear combinations of the Greeks with respect to time. We confirm the accuracy of our formula via Monte-Carlo simulation and find the SEV effect on the Black–Scholes barrier option prices.     

Zn(NCN)单轴的负热膨胀性及机理研究

负热膨胀(NTE)是一种反常的物理现象, 已在合金和框架结构化合物等材料中被观察到, 但NTE材料的种类仍然有限. 本文合成了一种单轴NTE材料Zn(NCN), 该材料在c轴方向及在100~475 K下的热膨胀系数为-3.35×10^?6 K^?1, 而a轴和b轴方向则呈低热膨胀性, 体积具有低的热膨胀系数[6.13×10^?6 K^?1(100~475 K)]. 通过同步辐射X射线衍射、 扩展X射线吸收精细结构和拉曼光谱等方法, 研究了Zn(NCN)的NTE机理. 结果表明, Zn—N键具有明显的横向振动, 一些低频振动模Grüneisen参数为负值. 直接的实验证据表明, N=C=N的横向振动以及准刚性ZnN₄四面体的耦合旋转和扭摆导致了c轴方向的NTE.     

Reactions of a Four-Membered Borete with Carbon,Silicon, and Gallium Donor Ligands: Fused and Spiro-Type Boracycles

Donor-acceptor cyclopropanes or cyclobutanes are dipolar reagents, which are widely used in the synthesis of complex organic (hetero)cycles in ring expansion reactions. Applying this concept to boron containing heterocycles, the four-membered borete cyclo-iPr₂N-BC₁₀H₆ reacted with the carbon donor ligands 2,6-xylylisonitrile and the carbene IMes :C(NMesCH)₂ with ring expansion and ring fusion, respectively. In particular, the tetracyclic structure formed with IMes displays zwitterionic character and absorption in the visible region. In contrast to the carbene IMes, the heavier carbenoids :Si(NDippCH)₂ and :Ga(AmIm) with a two-coordinate donor atom afford spiro-type bicyclic compounds, which display four-coordinate geometry at silicon or gallium. (TD-)DFT calculations provide deeper insight into the mechanism of formation and the absorption properties of these new compounds.     

Three-Dimensional Dynamic Contact Problem for an Elliptic Crack Interacting with a Normally Incident Harmonic Compression–Expansion Wave

The paper deals with the three-dimensional dynamic problem for an elliptic crack interacting with a normally incident harmonic compression–expansion wave, considering the contact interaction of the crack faces. An asymmetric solution is obtained using an iteration algorithm developed earlier. Numerical results are presented     

Analytical Solutions to Expansion of Cylindrical Cavity in Linear Softening Soil

Based on the results of conventional triaxial compression tests for a soil, a trilinear elasto-plastic model is proposed to simulate the stress-strain softening curve. According to this curve, the constitutive relation between the bulk strain and two pr…     

Periodic Solutions of Delay Differential Equations with a Small Parameter: Existence,Stability and Asymptotic Expansion

We consider a scalar delay differential equation with a small parameter, and employ Walthers method to obtain a result on the existence and stability of a slowly oscillatory periodic solution that represents a refinement of the estimate for the Lipschitz constant of a returning map. We also develop a matching method and obtain asymptotic expansions of the slowly oscillatory periodic solution and its minimal period.Dedicated to Professor Shui-Nee Chow on the occasion of his 60th birthdayAMS subject classifications: 34K15; 34K20; 34C25.     

Weak Nonlinear Analysis of Moderate Stefan Number Oscillatory Convection in Rotating Mushy Layers

We consider the solidification of a binary alloy in a mushy layer subject to Coriolis effects. A near-eutectic approximation and large far-field temperature is employed in order to study the dynamics of the mushy layer with a Stefan number of unit order of magnitude. The weak nonlinear theory is used to investigate analytically the Coriolis effect in a rotating mushy layer for a new moderate time scale proposed by the author. It is found that increasing the Taylor number favoured the forward bifurcation.     

Special cases in a control problem

A number of control problems for mechanical systems with feedback are reduced to a matrix algebraic Riccati equation. The exact solutions of matrix algebraic Riccati equations with singularities are presented. These singularities do not permit the use of standard solution procedures. Asymptotic solutions of these equations are found in the neighborhood of the singular points. These results can be used as test examples in developing new solution algorithms for matrix algebraic Riccati equations __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 113–120, February 2006.