Ergodicity of scalar stochastic differential equations with Hölder continuous coefficients

It is well-known that for a one dimensional stochastic differential equation driven by Brownian noise, with coefficient functions satisfying the assumptions of the Yamada–Watanabe theorem (Yamada and Watanabe, 1971, [31,32]) and the Feller test for explosions (Feller, 1951, 1954), there exists a unique stationary distribution with respect to the Markov semigroup of transition probabilities. We consider systems on a restricted domain $D$ of the phase space $\mathbb{R}$ and study the rate of convergence to the stationary distribution. Using a geometrical approach that uses the so called free energy function on the density function space, we prove that the density functions, which are solutions of the Fokker–Planck equation, converge to the stationary density function exponentially under the Kullback–Leibler divergence, thus also in the total variation norm. The results show that there is a relation between the Bakry–Émery curvature dimension condition and the dissipativity condition of the transformed system under the Fisher–Lamperti transformation. Several applications are discussed, including the Cox–Ingersoll–Ross model and the Ait-Sahalia model in finance and the Wright–Fisher model in population genetics.     

High pressure-induced structural effects in plastic packaging

Today, flexible vacuum packages are predominantly used for products to be subjected to high pressure treatment. However, tray packages with a modified atmosphere are in demand, which provide a high failure rate with respect to gas and water vapour permeability and packaging integrity. Methods to follow permeation processes under high pressure were developed and used together with optical microscopy, confocal scanning laser microscopy, Raman spectroscopy and atomic force microscopy to identify the mechanisms for changes in permeability and damage to the packaging materials. Single film samples and pouch packages filled with model products were studied. Results indicate a reversible decrease in the coefficients of diffusion and permeation under the impact of high pressure, due to the compression of the polymeric bulk. Irreversible changes in the polymeric materials are associated with gases in the packaging head space, which cause high local temperatures and create damage due to rapid deliberation upon the pressure drop at the end of the high pressure cycle.     

How should complexity scale with system size?

We study how statistical complexity depends on the system size and how the complexity of the whole system relates to the complexity of its subsystems. We study this size dependence for two well-known complexity measures, the excess entropy of Grassberger and the neural complexity introduced by Tononi, Sporns and Edelman. We compare these results to properties of complexity measures that one might wish to impose when seeking an axiomatic characterization. It turns out that those two measures do not satisfy all those requirements, but a renormalized version of the TSE-complexity behaves reasonably well.     

Sequential Voltammetric Determination of Uranium,Cadmium and Lead by Using the ex situ Bismuth Film Electrode: Application to Phosphate Fertilizers

A sequential voltammetric procedure for the determination of uranium, cadmium and lead was investigated at an ex situ bismuth film electrode (BiFE). First, the adsorptive stripping voltammetry was applied to assay the U(VI)‐cupferron complex in the differential pulse mode (detection limit of 1.0 µg L^?1, 200 s accumulation time). Through the manipulation of the same aliquot of the sample, efforts were made to quantify cadmium and lead by square wave anodic stripping voltammetry. Detection limits of 2.03 µg L^?1 for Cd (II) and 2.43 µg L^?1 for Pb (II) were calculated (100 s accumulation time). The methodology was successfully applied to phosphate fertilizer samples after open vessel wet decomposition (HNO₃/H₂O₂). The following value ranges were evaluated: U (VI) 37.2–150 mg kg^?1, Pb (II) 78.3–204 mg kg^?1 and Cd (II) 44.1–71.6 mg kg^?1. Validation was performed by using the standard reference materials SRM‐695 – phosphate fertilizer – and SRM‐1643e – water.     

Catalyst volume to surface area constraints for nucleating carbon nanotubes

In this Article, we describe a carbon nanotube formation model in which sp2 carbon hemispheres form the embryonic caps from which a nanotube can grow. This requirement leads to a single wall carbon nanotube formation window concomitant with our systematic experimental findings, which show upper and lower diameter limits. Further, the successful formation of a nucleation cap (hemisphere) is governed by catalyst particle volume to surface area considerations. Single wall carbon nanotubes are only obtained when both the nanotube formation window and the precipitating catalyst size distribution cross over. The extent to which these two windows overlap establishes the mean diameter and diameter distribution of the obtained single wall carbon nanotubes.     

Multiplicity results for the two-vortex Chern-Simons Higgs model on the two-sphere

We consider a Ginzburg-Landau type functional on S ² with a 6 ^th order potential and the corresponding selfduality equations. We study the limiting behavior in the two vortex case when a coupling parameter tends to zero. This two vortex case is a limiting case for the Moser inequality, and we correspondingly detect a rich and varied asymptotic behavior depending on the position of the vortices. We exploit analogies with the Nirenberg problem for the prescribed Gauss curvature equation on S ². Received: December 3, 1997     

Energy identities and blow-up analysis for solutions of the super Liouville equation

In this paper, we study the super Liouville equations, a natural generalization of the Liouville equation. We establish energy identities and a precise blow-up analysis for solutions of the super Liouville equations.     

Randomness,chaos, and structure

We show how a simple scheme of symbolic dynamics distinguishes a chaotic from a random time series and how it can be used to detect structural relationships in coupled dynamics. This is relevant for the question at which scale in complex dynamics regularities and patterns emerge. © 2009 Wiley Periodicals, Inc. Complexity 2009