The exact numerical simulation of piezoelectric transducers requires the knowledge of all material tensors that occur in the piezoelectric constitutive relations. To account for mechanical, dielectric and piezoelectric losses, the material parameters are assumed to be complex. The issue of material tensor identification is formulated as an inverse problem: As input measured impedance values for different frequency points are used, the searched-for output is the complete set of material parameters. Hence, the forward operator F mapping from the set of parameters to the set of measurements, involves solutions of the system of partial differential equations arising from application of Newton's and Gauss' law to the piezoelectric constitutive relations. This, via two or three dimensional finite element discretisation, leads to an indefinite system of equations for solving the forward problem. Well-posedness of the infinite dimensional forward problem is proven and efficient solution strategies for its discretized version are presented. Since unique solvability of the inverse problem may hardly be verified, the system of equations we have to solve for recovering the material tensor entries can be rank deficient and therefore requires application of appropriate regularisation strategies. Consequently, inversion of the (nonlinear) parameter-to-measurement map F is performed using regularised versions of Newton's method. Numerical results for different piezoelectric specimens conclude this paper.

The paper focuses on the matrix differential equation \[ \dot y(t)=A(t)y(t)+\sum_{j=1}^{m}B_j(t)y(\tau_j(t))+f(t),\quad t\in I=[t_0,\infty)\vspace*{-3pt} \] with continuous matrices $A$, $B_j$, a continuous vector $f$ and continuous delays $\tau_j$ satisfying $\tau_k\circ\tau_l =\tau_l\circ\tau_k$ on $I$ for any pair $\tau_k,\tau_l$. Assuming that the equation \[ \dot y(t)=A(t)y(t)\] is uniformly exponentially stable, we present some asymptotic bounds of solutions $y$ of the considered delay equation. A system of simultaneous Schröder equations is used to formulate these asymptotic bounds.

Motivated generally by potential applications in the liquid crystal display industry [8,35], and specifically by recent experimental, theoretical and numerical work [6,7,13,14,21,25,30,31], we consider a thin film of nematic liquid crystal (NLC), sandwiched between two parallel plates. Under certain simplifying assumptions, laid out in £2, we find that for monostable surfaces (i.e. only a single preferred director anchoring angle at each surface), two optically-distinct, steady, stable (equal energy) configurations of the director are achievable, that is, a bistable device. Moreover, it is found that the stability of both of these steady states may be destroyed by the application of a sufficiently large electric field, and that switching between the two states is possible, via the flexoelectric effect. Such a phenomenon could be used in NLC display devices, to reduce power consumption drastically. Previous theoretical demonstrations of such (switchable) bistable devices have either relied on having bistable bounding surfaces, that is, surfaces at which there are two preferred director orientations at the surface [7,14]; on having special (nonplanar) surface morphology within the cell that allows for two stable states (the zenithal bistable device (ZBD) [4,21], or, in the case of the Nemoptic BiNem technology [11,19], on flow effects and a very carefully applied electric field to effect the switching.

The continuing down-scaling trend of CMOS technology has brought serious deterioration in the accuracy of the SPICE (Simulation Program with Integrated Circuit Emphasis) device models used in the design of chip functions. This is due to in part to hot electron and quantum effects that occur in modern nano-scale MOSFET devices [13, 25, 28, 33, 34]. The focus of this paper is on modeling quantum confinement effects based on the Density-Gradient (DG) model [6, 9, 14], for application in SPICE. Analytic 1-D quantum mechanical (QM) effects correction formulae for the MOSFET inversion charge and electrostatic potential are derived from the DG model using matched asymptotic expansion techniques. Comparison of these new models with numerical data shows good results.