Micro-Electro-Elastic Modeling of Electric Field- and Stress-Driven Domain Wall Motion

Recently, increasing interest in functional materials such as piezoceramics has been shown. Such materials are characterized by properties, which can be significantly changed by external stimuli, such as stress, electric or magnetic fields. We outline a micro-electro-elastic model for the evolution of electrically and mechanically poled domains incorporating the surrounding free space. To this end, recently developed incremental variational principles (Miehe & Rosato [1]) for local dissipative response need to be extended to gradient-type phase-field models, including an embedding into the free space. The variational setting serves as a natural starting point for a compact and symmetric finite element implementation, considering the mechanical displacement, the electric polarization treated as an order parameter, and the electric potential induced by the polarization as the primary variables. The latter is defined on both the solid domain as well as the surrounding free space. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Classification of Lagrangian fibrations over a Klein bottle

This paper completes the classification of regular Lagrangian fibrations over compact surfaces. Mishachev (Diff Geom Appl 6:301–320, 1996) classifies regular Lagrangian fibrations over \mathbbT²{\mathbb{T}^2}. The main theorem in Fried et al. (Comment Math Helv 56(4):487–523, 1981) is used to in order to classify integral affine structures on the Klein bottle K ² and, hence, regular Lagrangian fibrations over this space.     

Cardanol Based Matrix for Jute Reinforced Pipes

The aim of this work is the development of composite pipes using renewable resources. The pipes, manufactured by filament winding technology, were obtained using an epoxy resin crosslinked with a cardanol based novolac as matrix and jute fibres as reinforcement. Cardanol is a natural oil extracted from the shell of the cashew (Anacardium occidentale L.) nut. An amount of natural materials higher than 50% by weight was achieved in the final composites. Tensile and parallel plate compression tests were carried out on the composite pipes.     

Intermolecular interactions of substituted benzenes on multi-walled carbon nanotubes grafted on HPLC silica microspheres and interaction study through artificial neural networks

Purified multi-walled carbon nanotubes (MWCNTs) grafted onto silica microspheres by gamma-radiation were applied as a HPLC stationary phase for investigating the intermolecular interactions between MWCNTs and substituted benzenes. The synthetic route, simple and not requiring CNTs derivatization, involved no alteration of the nanotube original morphology and physical–chemical properties. The affinity of a set of substituted benzenes for the MWCNTs was studied by correlating the capacity factor (k′) of each probe to its physico-chemical characteristics (calculated by Density Functional Theory). The correlation was found through a theoretical approach based on feedforward neural networks. This strategy was adopted because today these calculations are easily affordable for small molecules (like the analytes), and many critical parameters needed are not known. This might increase the applicability of the proposed method to other cases of study. Moreover, it was seen that the normal linear fit does not provide a good model. The interaction on the MWCNT phase was compared to that of an octadecyl (C18) reversed phase, under the same elution conditions. Results from trained neural networks indicated that the main role in the interactions between the analytes and the stationary phases is due to dipole moment, polarizability and LUMO energy. As expected for the C18 stationary phase correlation, is due to dipole moment and polarizability, while for the MWCNT stationary phase primarily to LUMO energy followed by polarizability, evidence for a specific interaction between MWCNTs and analytes. The CNT-based hybrid material proved to be not only a chromatographic phase but also a useful tool to investigate the MWCNT-molecular interactions with variously substituted benzenes.     

Does thermophoretic mobility depend on particle size?

Thermophoresis is particle drift induced by a temperature gradient. By measuring the full temperature dependence of this effect for polystyrene latex suspensions, we show that the thermophoretic mobility (or "thermal diffusion coefficient") D(T) is basically independent on particle size, in particular, when the interfacial properties of the colloidal particles are carefully standardized by adsorbing a surfactant layer on the particle surface. Even more, all investigated systems show values of D(T) which are very close to those measured for simple micellar solutions of the adsorbed surfactant. Our findings could be of relevance for downsizing microfluidics to the nanometric range.     

Identification of rain cells from radar and stochastic modelling of space-time rainfall

We discuss two problems related to the utilization of weather radar: the automated identification of rain cells and the extension of cluster models to include the random variability of space-time rainfall within and between cells. The need for such extension emerges from visual inspection and formal analysis of radar reflectivity images. The algorithm proposed for the identification of cells is based on statistical techniques for the estimation of probability density mixtures. The algorithm does not assign pixels to cells deterministically; rather, it calculates the probability with which each pixel belongs to the different cells. Through an iterative procedure, the cell parameters and pixel probabilities are updated until the final identification of cells is reached. The second part of the paper deals with a generalization of cluster rainfall models in space and time. The models studied here combine an arbitrary birth point process with arbitrary random fields generated by the cells. Second-moment properties of these processes are derived.

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Sommario Vengono descritti i primi risulati di un lavoro in corso su due problemi legati all'uso del radar meteorologico: l'identificazione automatica delle celle di pioggia e l'estensione dei modelli a cluster per includere la variabilità casuale delle precipitazioni nello spazio e nel tempo all'interno e fra le celle. La necessità di tale estensione sorge sia dall'esame visivo, sia da un'analisi formale delle immagini della riflettività radar. L'algoritmo proposto per l'identificazione delle celle è basato sulle tecniche statistiche per la stima delle miscele di distribuzioni di densità di probabilità. L'algoritmo non assegna in maniera deterministica i singoli pixels alle celle, bensì calcola la probabilità con cui ogni pixel appartiene alle diverse celle. Attraverso una procedura iterativa si calcolano di volta in volta i parametri delle celle e le probabilità dei pixels, fino a che si raggiunge un assetto finale e le celle vengono identificate. Nella seconda parte del lavoro si tratta della generalizzazione dei modelli a cluster nello spazio e nel tempo. I modelli qui studiati combinano un processo arbitrario di occorrenza delle celle con un campo casuale arbitrario generato dalle celle. In particolare, sono derivate le proprietà generali dei secondi momenti di tali processi.

     

A Variational Homogenization Approach to Electromechanical Hystereses Caused by Domain Wall Movement

In recent years, increasing interest in so-called smart materials such as ferroelectric polymers and ceramics has been shown. Those materials are used in various actuators, sensors, and also in medical devices. In this paper, we outline a micro-macro approach to the modeling of macroscopic hystereses which directly takes into account the microstructural evolution of electrically poled domains. To this end, an incremental variational formulation for a gradient-type phase field model is developed and exploited for the simulation of electromechanically coupled problems. The formulation determines the hysteretic response of the material in terms of an energy-enthalpy and a dissipation function which both depend on the microscopic remanent polarization treated as an order parameter. The gradient-type balance law for the phase field can be considered as a generalization of Biot's equation for standard dissipative materials and may be related to the classical Ginzburg-Landau equation. Furthermore, the variational formulation serves as natural starting point for a compact and symmetric finite element implementation of the coupled micromechanical problem covering the displacement, the electric potential, and the microscopic polarization vector. For this three-field scenario we develop a variational-based homogenization method which determines the overall macroscopic hysteretic properties of a polycrystalline aggregate. The proposed computational method can be used as a numerical laboratory for the improvement of microstructural properties. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Hardy–Rellich inequalities with boundary remainder terms and applications

We prove a family of Hardy–Rellich inequalities with optimal constants and additional boundary terms. These inequalities are used to study the behavior of extremal solutions to biharmonic Gelfand-type equations under Steklov boundary conditions.     

Singularities of functions of one and several bicomplex variables

In this paper we study the singularities of holomorphic functions of bicomplex variables introduced by G. B. Price (An Introduction to Multicomplex Spaces and Functions, Dekker, New York, 1991). In particular, we use computational algebra techniques to show that even in the case of one bicomplex variable, there cannot be compact singularities. The same techniques allow us to prove a duality theorem for such functions.     

On the WGSC Property in Some Classes of Groups

The property of quasi-simple filtration (or qsf) for groups has been introduced in literature more than 10 years ago by S. Brick. This is equivalent, for groups, to the weak geometric simple connectivity (or wgsc). The main interest of these notions is that there is still not known whether all finitely presented groups are wgsc (qsf) or not. The present note deals with the wgsc property for solvable groups and generalized FC-groups. Moreover, a relation between the almost-convexity condition and the Tucker property, which is related to the wgsc property, has been considered for 3-manifold groups.