Energy principle of ferroelectric ceramics and single domain mechanical model

Many physical experiments have shown that the domain switching in a ferroelectric material is a complicated evolution process of the domain wall with the variation of stress and electric field. According to this mechanism, the volume fraction of the domain switching is introduced in the constitutive law of ferroelectric ceramic and used to study the nonlinear constitutive behavior of ferroelectric body in this paper. The principle of stationary total energy is put forward in which the basic unknown quantities are the displacement u (i) , electric displacement D (i) and volume fraction rho (I) of the domain switching for the variant I. Mechanical field equation and a new domain switching criterion are obtained from the principle of stationary total energy. The domain switching criterion proposed in this paper is an expansion and development of the energy criterion. On the basis of the domain switching criterion, a set of linear algebraic equations for the volume fraction rho (I) of domain switching is obtained, in which the coefficients of the linear algebraic equations only contain the unknown strain and electric fields. Then a single domain mechanical model is proposed in this paper. The poled ferroelectric specimen is considered as a transversely isotropic single domain. By using the partial experimental results, the hardening relation between the driving force of domain switching and the volume fraction of domain switching can be calibrated. Then the electromechanical response can be calculated on the basis of the calibrated hardening relation. The results involve the electric butterfly shaped curves of axial strain versus axial electric field, the hysteresis loops of electric displacement versus electric filed and the evolution process of the domain switching in the ferroelectric specimens under uniaxial coupled stress and electric field loading. The present theoretic prediction agrees reasonably with the experimental results given by Lynch.

Calibrating the Gaussian multi-target tracking model

We present novel batch and online (sequential) versions of the expectation-maximisation (EM) algorithm for inferring the static parameters of a multiple target tracking (MTT) model. Online EM is of particular interest as it is a more practical method for long data sets since in batch EM, or a full Bayesian approach, a complete browse of the data is required between successive parameter updates. Online EM is also suited to MTT applications that demand real-time processing of the data. Performance is assessed in numerical examples using simulated data for various scenarios. For batch estimation our method significantly outperforms an existing gradient based maximum likelihood technique, which we show to be significantly biased. © 2014 Springer Science+Business Media New York.

Evaluation of nonlinear chromatographic performance by frontal analysis using a simple multi-plate mathematical model

A multi-plate (NIP) mathematical model was proposed by frontal analysis to evaluate nonlinear chromatographic performance. One of its advantages is that the parameters may be easily calculated from experimental data. Moreover, there is a good correlation between it and the equilibrium-dispersive (E-D) or Thomas models. This shows that it can well accommodate both types of band broadening that is comprised of either diffusion-dominated processes or kinetic sorption processes. The MP model can well describe experimental breakthrough curves that were obtained from membrane affinity chromatography and column reversed-phase liquid chromatography. Furthermore, the coefficients of mass transfer may be calculated according to the relationship between the MP model and the E-D or Thomas models. (C) 2004 Elsevier B.V. All rights reserved.