AD-HOC principles of minimum energy expenditure as corollaries of the constructal law the cases of river basins and human vascular systems

In a recent paper [1] Reis showed that both the principles of extremum of entropy production rate, which are often used in the study of complex systems, are corollaries of the Constructal Law. In fact, both follow from the maximization of overall system conductivities, under appropriate constraints. In this way, the maximum rate of entropy production (MEP) occurs when all the forces in the system are kept constant. On the other hand, the minimum rate of entropy production (mEP) occurs when all the currents that cross the system are kept constant. In this paper it is shown how the so-called principle of "minimum energy expenditure" which is often used as the basis for explaining many morphologic features in biologic systems, and also in inanimate systems, is also a corollary of Bejan's Constructal Law [2]. Following the general proof some cases namely, the scaling laws of human vascular systems and river basins are discussed as illustrations from the side of life, and inanimate systems, respectively.

A symbolic approach to nonlinearly perturbed heat equation

We consider a system described by the linear heat equation with adiabatic boundary conditions which is perturbed periodicaly. This perturbation is nonlinear and is characterized by a one-parameter family of quadratic maps. The system, depending on the parameters, presents very complex behaviour. We introduce a symbolic framework to analyze the system and resume its most important features.