Discrete Multiscale Analysis: A Biatomic Lattice System

We discuss a discrete approach to the multiscale reductive perturbative method and apply it to a biatomic chain with a nonlinear interaction between the atoms. This system is important to describe the time evolution of localized solitonic excitations. We require that also the reduced equation be discrete. To do so coherently we need to discretize the time variable to be able to get asymptotic discrete waves and carry out a discrete multiscale expansion around them. Our resulting nonlinear equation will be a kind of discrete Nonlinear Schr\"odinger equation. If we make its continuum limit, we obtain the standard Nonlinear Schr\"odinger differential equation

Crystallization in Confinement

Many crystallization processes of great importance, including frost heave, biomineralization, the synthesis of nanomaterials, and scale formation, occur in small volumes rather than bulk solution. Here, the influence of confinement on crystallization processes is described, drawing together information from fields as diverse as bioinspired mineralization, templating, pharmaceuticals, colloidal crystallization, and geochemistry. Experiments are principally conducted within confining systems that offer well‐defined environments, varying from droplets in microfluidic devices, to cylindrical pores in filtration membranes, to nanoporous glasses and carbon nanotubes. Dramatic effects are observed, including a stabilization of metastable polymorphs, a depression of freezing points, and the formation of crystals with preferred orientations, modified morphologies, and even structures not seen in bulk. Confinement is also shown to influence crystallization processes over length scales ranging from the atomic to hundreds of micrometers, and to originate from a wide range of mechanisms. The development of an enhanced understanding of the influence of confinement on crystal nucleation and growth will not only provide superior insight into crystallization processes in many real‐world environments, but will also enable this phenomenon to be used to control crystallization in applications including nanomaterial synthesis, heavy metal remediation, and the prevention of weathering

MICROSCOPIC POLARIZABILITY MODEL OF FERROELECTRIC SOFT MODES

A simplified version of a recent microscopic model of ferroelectric soft modes1 is studied. It is shown that the compensation of long-range and short-range forces2 which induces the soft mode behaviour of ferroelectric systems can be expressed in terms of a simple linear chain model with a non-linear polarizability at the chalcogenide ion lattice site3. This polarizability is equivalent to an on-site electron-two-phonon coupling. The four different temperature regimes which result from the model equations are discussed. The model is applicable to completely different systems such as perovskites, SbSI4, IV-VI5 semiconductors and K2SeO46,7

Variantenuntersuchung zur geplanten A26 Stade-Hamburg Textband. Anlagenband

TIB: AC 9647+(Anl) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman