Homoclinic bifurcation in a Hodgkin-Huxley model of thermally sensitive neurons

We study global bifurcations of the chaotic attractor in a modified Hodgkin-Huxley model of thermally sensitive neurons. The control parameter for this model is the temperature. The chaotic behavior is realized over a wide range of temperatures and is visualized using interspike intervals. We observe an abrupt increase of the interspike intervals in a certain temperature region. We identify this as a homoclinic bifurcation of a saddle-focus fixed point which is embedded in the chaotic attractors. The transition is accompanied by intermittency, which obeys a universal scaling law for the average length of trajectory segments exhibiting only short interspike intervals with the distance from the onset of intermittency. We also present experimental results of interspike interval measurements taken from the crayfish caudal photoreceptor, which qualitatively demonstrate the same bifurcation structure. (c) 2000 American Institute of Physics.     

Interpolation on Sparse Grids and Tensor Products of Nikol'skij–Besov Spaces

We investigate the order of convergence of periodic interpolation on sparse grids (blending interpolation) in the framework of tensor products of Nikol'skij–Besov spaces. To this end, we make use of the uniformity of the considered tensor norms and provide a unified approach to error estimates for the interpolation of univariate periodic functions from Nikol'skij–Besov spaces.     

Multiple Eigenvalues in Spectral Analysis for Solving QBD Processes

A number of authors have recently suggested solving quasi birth-and-death (QBD) processes through the use of eigenvalue-based methods. These methods take on a special form when there are multiple eigenvalues present. We investigate this problem in a general setting as well as in the context of a specific preemptive priority queueing model.      

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).