A Kolmogorov-type competition model with multiple coexistence states and its applications to plant competition for sunlight

It is demonstrated that a Kolmogorov-type competition model featuring species allocation and gain functions can possess multiple coexistence states. Two examples are constructed: one in which the two competing species possess rectangular allocation functions but distinct gain functions, and the other in which one species has a rectangular allocation function, the second species has a bi-rectangular allocation function, and the two species share a common gain function. In both examples, it is shown that the species nullclines may intersect multiple times within the interior of the first quadrant, thus creating both locally stable and unstable equilibrium points. These results have important applications in the study of plant competition for sunlight, in which the allocation functions describe the vertical placement of leaves for two competing species, and the gain functions represent rates of photosynthesis performed by leaves at different heights when shaded by overlying leaves belonging to either species.     

Conception of a new technique in cell cultivation using a lab-on-chip aided miniaturised device with calibratable electrochemical sensors

Continuous electrochemical sensing is often carried out in order to track the growth of cells as an alternative to optical monitoring. Planar sensors and multi-sensor chips are applied in case of adhered growing cells, and usually introduced into lab-on-chip systems. Repeated recalibration is necessary with most chemosensors so far and this limits the operational lifetime of such lab-on-chip systems to a few days. An assembly is presented here that eliminates this disadvantage and enables the monitoring of a long-term cultivation of tissue. Cell cultures and sensor are arranged such that they can be separated or contacted at variable times without having an impact on the growth of the cells. The use of a biocompatible nano-porous membrane is especially important. A multi-well system is described where each well is supplied with a planar multi-sensor chip below the adhered cells to determine (a) pH, (b) glucose, (c) oxygen, and—optionally—impedance, for example during the cultivation of cartilage tissue.     

Non-destructive bulk analysis of the Buggenum sword by neutron resonance capture analysis and neutron diffraction

Two neutron based techniques, neutron resonance capture analysis (NRCA) and time-of-flight neutron-diffraction (TOF-ND) have been used to determine the elemental composition and structure of a precious and very well preserved all-metal sword from the Bronze Age. This Buggenum sword was on loan from the National Museum of Antiquities (NMA) in Leiden (NL). NRCA and TOF-ND experiments have been carried out at a number of more or less identical positions of the sword. The tin-bronze ratio and the relative amounts of some minor elements (Sb, As, Ag, In) have been determined. The results of neutron diffraction measurements showed considerable tin-segregation, and clear indications of hardening on the edges of the blade. In addition, radiographs using Bremsstrahlung revealed the construction of the hilt–blade connection. The work was carried out at the EC Joint Research Centre IRMM in Geel (B) and at the ISIS facility of the Rutherford Appleton Laboratory (UK).     

Approximation numbers of Sobolev embeddings—Sharp constants and tractability

We investigate optimal linear approximations (approximation numbers) in the context of periodic Sobolev spaces H^s(T^d)$H^s\left({\mathbb{T}}^d\right)$ of fractional smoothness s>0$s>0$ for various equivalent norms including the classical one. The error is always measured in _L2(T^d)$L_2\left({\mathbb{T}}^d\right)$. Particular emphasis is given to the dependence of all constants on the dimension d$d$. We capture the exact decay rate in n$n$ and the exact decay order of the constants with respect to d$d$, which is in fact polynomial. As a consequence we observe that none of our considered approximation problems suffers from the curse of dimensionality. Surprisingly, the square integrability of all weak derivatives up to order three (classical Sobolev norm) guarantees weak tractability of the associated multivariate approximation problem.     

A novel approach to the determination of the crosslink density in rubber materials with the dipolar correlation effect in low magnetic fields

We present a novel NMR approach to the determination of crosslink densities in rubber materials. The method is based on the dipolar correlation effect (DCE) on the stimulated echo examined in a series of rubber samples and linear polyisoprene. The parameter evaluated from the echo attenuation curves is the mean‐squared dipolar fluctuation associated with anisotropic reorientations of macromolecular backbones. The contributions to the DCE of the constraints due to excluded volume effects and chemical crosslinks are estimated. A strong dependence of the mean‐squared dipolar fluctuation on the crosslink density of rubber combined with the simplicity of performing the measurements with inexpensive low‐field instruments suggests that the DCE is a useful tool for routine applications. The potential and problems of performing DCE measurements in low‐magnetic‐field conditions are discussed in detail. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2207–2216, 2001