Many Sets Of Parameters Research Articles

Behaviour of the current in a membrane-covered disc microelectrode under steady-state conditions

The inlaid disc electrode covered with a membrane can be modelled as a system with axial symmetry containing several parallel layers with different permeabilities. A recent solution of the steady state under diffusion limited conditions of an electroactive species in such a system is implemented with Mathematica. Computation of the theoretical current becomes an easy and fast procedure, capable of being implemented on any personal computer or workstation. The effects of the membrane permeability, the thickness of the membrane, the electrode radius and the electrolyte layer thickness on the current are analysed. We define an index of edge-effect contribution of each layer to the overall flux, providing their formulae together with the physical interpretation. For many sets of parameters, the edge-effect is responsible for an important contribution of the radial diffusion within the electrolyte and membrane. More accurate determination of the permeabilities of the different media is now possible experimentally, as the functional dependence of the current on the physical parameters is readily available for fitting procedures.

Sex and population dynamics

Chaos has been found in many mathematical models of population dynamics. This suggests that it should be a common feature of natural populations, quite in contrast to the scarcity of systems where it has been demonstrated. We suggest in this paper that the reason for this contrast may lie in the reproductive system. Whereas ecological modelling traditionally deals with asexual organisms, we introduce sexual reproduction (and thus explicit population genetics) into the population dynamic models. As specific examples, we describe the effect of sexual reproduction on two models (a host-parasite model and a predator-prey model) which exhibit chaotic behaviour for many sets of parameters. The results show that sexual reproduction generally reduces the complexity of the system, leading to a stable equilibrium or other forms of simple dynamics, or at least reducing the fluctuations of the system. Thus the chaotic behaviour predicted by many population dynamic models may be restricted to systems with asexual reproduction.

The effective α-nucleon interaction in nuclei

The microscopic model for elastic α-particle scattering from nuclei makes use of a parametrization of the effective α-nucleon interaction in nuclei. In this paper many sets of parameters have been considered in detail. Since the interaction takes place in the low-density region of the nucleus, each parametrization has been studied in relation to the free a-nucleon scattering, and the ability of some forms derived for the free α-nucleon interaction to describe the scattering of α-particles from nuclei has been checked. The results indicate that a consistent picture can be obtained and the effective interaction is quite well determined.