Of Dogs and Fleas: The Dynamics of N Uncoupled Two-State Systems

The historical Ehrenfest model dating back to 1907 describes the process of equilibration together with fluctuations around the thermal equilibrium. This approach represents a special case in the dynamics of N uncoupled two-state systems. In this article we present a generalization of the original model by introducing an additional parameter p which denotes the probability of a single state change. Analytical solutions for the probability distribution of the system's state as well as the fluctuation distribution are derived. Interestingly, close inspection of the fluctuation distribution reveals an intrinsic time scale. Sampling the system's state at much slower rates yields the familiar macroscopic exponential distribution for equilibrium processes. For faster measurements a power law extends roughly over log₁₀ N orders of magnitude followed by an exponential tail. At some point, further increases of the sampling rate merely result in a shift of the fluctuation distribution towards higher values leaving plateau at small fluctuation sizes behind. Since the generic solution is rather unwieldy, we derive and discuss simple and intuitive analytical solutions in the limit of small p and large N. Furthermore, we relax the quantization of time by considering a complementary approach in continuous time. Finally we demonstrate that the fluctuation distributions resulting from the two different approaches bear identical characteristic features.     

Surface chemistry and optimization of focused ion beam iodine-enhanced etching of indium phosphide

Focused ion beam physical sputtering and iodine-enhanced etching of indium phosphide (InP) were performed. Up to 15× enhanced etching rates over sputtering were measured at room temperature, due to the addition of iodine to the sputter-process. Reaction mechanisms and products are discussed and characterized. The reaction is limited by the desorption of indium triiodide (InI₃) at room temperature. InI₃ has to be removed by sputtering, which simultaneously amorphizes the underlying substrate. Surface roughness and stoichiometry of InP are compared for sputtering and etching. Gallium-contamination and the damaged zone in InP are significantly reduced by iodine-enhanced etching. Based on the reaction mechanisms, an optimum beam scanning strategy is proposed which allows precise microfabrication in reduced time and minimizes damage to the substrate. The method is also applicable for other halide gas etching processes of III-V semiconductors.     

Preparation and properties of phenylene oxide–aryl ether sulphone block copolymers and their blends

We have prepared triblock copolymers of poly(phenylene oxide) (PPO) and polysulphone (PSF) of the form PPO–PSF–PPO in order to assess their intrinsic mechanical properties and their potential as interfacial compatibilizers in polystyrene/PSF blends. For sufficiently long polysulphone block lengths, we observed microphase separation both in the triblock copolymers and in their blends with polystyrene. The triblock polymers, nevertheless, showed very similar microdeformation behavior to the PPO homopolymer, suggesting the phase separation to play a minor role. On the other hand, the compatibility of the poly(phenylene oxide) blocks and polystyrene ensured a high degree of interphase adhesion in blends containing both polystyrene and free PSF, even for relatively high homopolymer molecular weights. © 1996 John Wiley & Sons, Inc.     

Coevolutionary dynamics: from finite to infinite populations

Traditionally, frequency dependent evolutionary dynamics is described by deterministic replicator dynamics assuming implicitly infinite population sizes. Only recently have stochastic processes been introduced to study evolutionary dynamics in finite populations. However, the relationship between deterministic and stochastic approaches remained unclear. Here we solve this problem by explicitly considering large populations. In particular, we identify different microscopic stochastic processes that lead to the standard or the adjusted replicator dynamics. Moreover, differences on the individual level can lead to qualitatively different dynamics in asymmetric conflicts and, depending on the population size, can even invert the direction of the evolutionary process.     

Preparation and characterization of cationic nanofibrillated cellulose from etherification and high-shear disintegration processes

Oat straw cellulose pulp was cationized in an etherification reaction with chlorocholine chloride. The cationized cellulose pulp was then mechanically disintegrated in two process steps to obtain trimethylammonium-modified nanofibrillated cellulose (TMA-NFC). The materials thus obtained were analyzed by elemental analysis, X-ray photoelectron spectroscopy (XPS), X-ray diffraction (XRD), scanning electron microscopy (SEM) and other techniques. A higher nitrogen content of TMA-NFC samples was found by XPS analysis than by elemental analysis, which indicates that the modification occurred mainly on the surface of cellulose fibrils. XPS also confirmed the existence of ammonium groups in the samples. SEM provided images of very fine network structures of TMA-NFC, which affirmed the positive effect of ionic charge on mechanical disintegration process. According to XRD and SEM results, no severe degradation of the cellulose occurred, even at high reaction temperatures. Because of the different properties of the cationic NFC compared to negatively charged native cellulose fibers, TMA-NFC may find broad applications in technical areas, for instance in combination with anionic species, such as fillers or dyes. Indeed, TMA-NFC seems to improve the distribution of clay fillers in NFC matrix.