Construction of a Lyapunov functional for a class of controlled population balance models

In this paper, we consider a class of controlled population balance equations describing granulation processes in chemical engineering. Such a control system admits an equilibrium which is not asymptotically stable in general. In order to stabilize this equilibrium, we consider the perturbed system and introduce a Lyapunov functional candidate as a weighted L²-norm. It is shown that the weight function for this construction may be defined in terms of solutions to a certain differential inequality. We present a solution of this differential inequality in a particular case and discuss possible extensions of this approach for multidimensional hyperbolic systems. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

BAMLSS: Bayesian Additive Models for Location,Scale, and Shape (and Beyond)

Bayesian analysis provides a convenient setting for the estimation of complex generalized additive regression models (GAMs). Since computational power has tremendously increased in the past decade, it is now possible to tackle complicated inferential problems, for example, with Markov chain Monte Carlo simulation, on virtually any modern computer. This is one of the reasons why Bayesian methods have become increasingly popular, leading to a number of highly specialized and optimized estimation engines and with attention shifting from conditional mean models to probabilistic distributional models capturing location, scale, shape (and other aspects) of the response distribution. To embed many different approaches suggested in literature and software, a unified modeling architecture for distributional GAMs is established that exploits distributions, estimation techniques (posterior mode or posterior mean), and model terms (fixed, random, smooth, spatial,…). It is shown that within this framework implementing algorithms for complex regression problems, as well as the integration of already existing software, is relatively straightforward. The usefulness is emphasized with two complex and computationally demanding application case studies: a large daily precipitation climatology, as well as a Cox model for continuous time with space-time interactions. Supplementary material for this article is available online.     

Small-angle X-ray scattering studies of zinc stearate-filled sulfonated poly(ethylene-co-propylene-co-ethylidene norbornene) ionomers

The crystallization, melting, and dissolution behavior of zinc stearate (ZnSt) in ZnSt-filled sulfonated poly(ethylene-co-propylene-co-ethylidene norbornene) (SEPDM) ionomers was studied by synchrotron small-angle X-ray scattering (SAXS). The melting temperature of ZnSt in the ionomer was considerably lower than in the pure state, which was consistent with the existence of very small ZnSt crystalline domains and a specific interaction between the metal sulfonate groups of the SEPDM and the metal carboxylate groups of ZnSt. Temperature-resolved SAXS showed that, on melting, some or all of the ZnSt rapidly dissolved into the ionomer. Ionic aggregates in the neat ionomer persisted up to 300°C. Microphase separation was also observed at elevated temperatures for the ZnSt-filled ionomers, but the composition of the microdomains was believed to be quite different than that of the microdomains in the neat SEPDM. The time and temperature dependence of the ZnSt crystallization in the filled ionomers was characterized by time-resolved SAXS experiments following a temperature quench from the melt. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 3141–3150, 1999