On the crack-tip stress singularity of interfacial cracks in transversely isotropic piezoelectric bimaterials

In this paper, characteristics of the interface crack-tip stress and electric displacement fields in transversely isotropic piezoelectric bimaterials are studied. The authors have proven, within the framework of the generalized Stroh formalism for piezoelectric bimaterials, that there is no coexistence of the parameters (oscillating) and κ (non-oscillating) in the interface crack-tip generalized stress field for all transversely isotropic piezoelectric bimaterials. This leads to the classification of piezoelectric bimaterials into one group that exhibits the oscillating property in the interface crack-tip generalized stress field and the other that does not. Fifteen (15) pair-combinations of six (6) piezoelectric materials PZT-4, PZT-5H, PZT-6B, PZT-7A, P-7, and BaTiO₃, which are commonly used in practice, are numerically analyzed in this study, and the results backup the above theoretical conclusions. Moreover, the associated eigenvectors for such material systems (with either =0 or κ=0) are also obtained numerically, and the result show that there still exist four linear independent associate eigenvectors for each bimaterial.     

Weissenberg-Rabinowitsch-Auswertung der mit dem Platte-Platte-Rotationsrheometer gemessenen Fließkurve mittels eines Fließgesetzes vom Carreauschen Typ

Zusammenfassung Basierend auf dem das Fließverhalten strukturviskoser Fluide sehr genau beschreibenden sogenannten Carreau-Ansatz wird eine Näherungsformel für die Drehmoment-Schergeschwindigkeit-Charakteristik (scheinbare Fließkurve) des Platte-Platte-Rotationsrheometers (PPR) im stationären Versuch vorgeschlagen. Die gewonnenen Resultate können in die Auswertungseinheit des Platte-Platte-Systems leicht integriert werden und damit das Anwendungsgebiet des PPR-Systems für konzentrierte Polymerlösungen und Polymerschmelzen beträchtlich erweitern.

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A new simplified, but very accurate, formula is proposed for the torque-rate characteristic (apparent flow curve) of the parallel-disk rotational rheometer (PDR) in steady-shear mode, based on the Carreau formula for the viscosity of pseudoplastic fluids. The results can easily be incorporated into the evaluation of the parallel-disk system and therefore the application field of the PDR-system can be extended considerably for concentrated polymer solutions and polymer melts.

     

不可压缩二维流动Navier—Stokes方程的有限元解

对不可压缩流体沿二维后台阶流动的Ｎ－Ｓ方程的流函数－涡量式用有限元方法加以求解，固壁上的涡量用时间迭代法加以确定。分别计算Ｒｅ＝２００，４００，８００和１０００时流动区域的流函数和涡量值，并在Ｒｅ＝８００时与有关文献的结果相比较，基本吻合。且在此基础上讨论了出口条件对计算结果的影响。本文的方法对分析流经液压阀口等流动问题具有借鉴意义。     

Stochastic systems with memory and jumps

Stochastic systems with memory naturally appear in life science, economy, and finance. We take the modelling point of view of stochastic functional delay equations and we study these structures when the driving noises admit jumps. Our results concern existence and uniqueness of strong solutions, estimates for the moments and the fundamental tools of calculus, such as the Itô formula. We study the robustness of the solution to the change of noises. Specifically, we consider the noises with infinite activity jumps versus an adequately corrected Gaussian noise. The study is presented in two different frameworks: we work with random variables in infinite dimensions, where the values are considered either in an appropriate $L^p$-type space or in the space of càdlàg paths. The choice of the value space is crucial from the modelling point of view, as the different settings allow for the treatment of different models of memory or delay. Our techniques involve tools of infinite dimensional calculus and the stochastic calculus via regularisation.     

Singular p-Laplacian equations with superlinear perturbation

We consider a nonlinear Dirichlet problem driven by the p-Laplace operator and with a right-hand side which has a singular term and a parametric superlinear perturbation. We are interested in positive solutions and prove a bifurcation-type theorem describing the changes in the set of positive solutions as the parameter $\lambda >0$ varies. In addition, we show that for every admissible parameter $\lambda >0$ the problem has a smallest positive solution ${\stackrel{￣}{u}}_{\lambda }$ and we establish the monotonicity and continuity properties of the map $\lambda \to {\stackrel{￣}{u}}_{\lambda }$.     

Vertex correction and conductivity in 2D Dirac-like systems with non-conserving spin disorder

We determine the classical diffusion of two dimensional Dirac-like quasiparticles, in the presence of conserving spin disorder (scattering off electric impurities) and non-conserving spin disorder (scattering off magnetic impurities). We use the Kubo formula for the conductivity tensor and employ diagrammatic perturbation theory to calculate the vertex correction and the renormalisation of the current operator for both electric and magnetic scattering. Scattering off electric impurities is isotropic and the current operator renormalised to two times the bare current operator irrespective of the direction of the dynamics, as usual for Dirac-like fermions. For magnetic scattering the renormalisation of the current operator depends on the direction of the dynamics and on the polarisation of the magnetic impurities, making the system anisotropic. We calculate the anisotropic magnetoresistance (AMR) and analyse it as a function of the ratio of the strength of the electric to the magnetic scattering potentials, for short range Gaussian correlation.