Online research in philosophy

A new model of bioturbation has been developed to describe short term sediment reworking induced by macrobenthic communities. The design of the model had to consider the mixing processes, firstly, at the organism level, and secondly, at community level. This paper describes the mixing mode of the four types of bioturbators defined by the authors: the biodiffusors, the upward-conveyors, the downward-conveyors and the regenerators. The mathematical formulation of these sub-models consists of ordinary differential equations. They take into account the size (...) of the bioturbated zone, the output fluxes to the water column, tracer decay, physical mixing due to local currents and the type and intensity of the bioturbation processes. These sub-models make it possible to describe correctly the mixing events that have occurred in cores with each type of bioturbator. They also provide the basis for general bioturbation model, that will take into account the respective degrees of involvement of (i) the different bioturbation processes and their characteristics, (ii) the interference between the different processes, and (iii) make possible to predict the particle reworking in order to include it in studies of organic matter in early diagenesis. (shrink)

The aim of this work is to present aggregation methods of hierarchically organized systems allowing one to replace the initial micro-system by a macro-system described by a few global variables. We also study the relations between the fast micro-dynamics and the slow macro-dynamics which can produce global properties. Emergence corresponds to a bottom-up coupling that is the result effected by a micro-level at a macro-level. As an example, we present prey-predator models with different time scales in an heterogeneous environment. A (...) fast time scale is associated to the migration process on spatial patches and a slow time scale is associated to growth and interactions between the populations. Preys must go on spatial patches where resources are located and where predators can attack them. The efficiency of the predators to catch preys is patch dependent. Perturbation methods allow us to aggregate the initial system of differential equations for the patch sub-populations into a macro-system of two differential equations governing the total population densities. We study the case of density independent and density dependent migrations. In the latter case, we show that different functional responses can emerge in the macro prey-predator model as a result of the coupling between the slow and fast systems. (shrink)

The complexity and the variability of parameters occurring in ecological dynamical systems imply a large number of equations.Different methods, more or less successful, have been described to reduce this number of equations. For instance, in the paper of Auger and Roussarie (1993), the authors describe how to obtain a reduction by considering different time-scales. They consider a system which can be sub-divided into sub-systems such that the strengths of the intra-sub-systems interactions are much larger than those of the inter-sub-systems interactions. (...) Using the Central Manifold Theorem, they obtain on the slow-manifold, a perturbation of the external dynamics by the internal dynamics. (shrink)