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Dichotomy results for delay differential equations with negative Schwarzian derivative

We gain further insight into the use of the Schwarzian derivative to obtain new results for a family of functional differential equations including the famous Wright’s equation and the Mackey-Glass type delay differential equations. We present some dichotomy results, which allow us to get easily computable bounds of the global attractor. We also discuss related conjectures, and formulate new open problems.     

Effect of reduced cooperativity on growth-induced polarity formation: a comparison between different growth models

We investigate the influence of the growth process on macroscopic polarity formation in molecular crystals consisting of polar molecules with two directional states. Specifically, layer-by-layer growth is compared with growth along surface steps, and growth at kink sites. Idealized models for these growth processes are presented, being characterized by the thermal equilibrium formation of a domain of molecules on the surface, ranging from an entire adlayer to a single molecule only (reduced cooperativity). Longitudinal and lateral Ising-type nearest neighbour interactions are taken into account. Formerly attached and thermalized molecules are kept frozen upon growth and therefore, bulk polarity results. Growth models are studied by means of Monte Carlo simulations. Results show that a reduced cooperativity between neighbouring molecules on the crystal surface increases the probability of orientational disorder. However, in the asymptotic limit of infinite growth and for sufficiently strong longitudinal couplings, phenomenologically, evolution of polarity for step and kink growth remains the same as for layer-by-layer growth, being mainly a thermodynamically driven process. Despite their strong out-of-equilibrium character, step and kink growth processes feature a continuous phase transition as layer-by-layer growth and are reasonably well described by an effective lateral coordination number within a mean field approach.     

Harns?urebestimmung

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Zur Analyse von Eisen und Stahl

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