Compositional evolution with mass transfer in closed systems

Evolution of compositions in time, space, temperature or other covariates is frequentin practice. For instance, the radioactive decomposition of a sample changes its composition with time. Some of the involved isotopes decompose into other isotopes of thesample, thus producing a transfer of mass from some components to other ones, butpreserving the total mass present in the system. This evolution is traditionally modelledas a system of ordinary di erential equations of the mass of each component. However,this kind of evolution can be decomposed into a compositional change, expressed interms of simplicial derivatives, and a mass evolution (constant in this example). A rst result is that the simplicial system of di erential equations is non-linear, despiteof some subcompositions behaving linearly.The goal is to study the characteristics of such simplicial systems of di erential equa-tions such as linearity and stability. This is performed extracting the compositional differential equations from the mass equations. Then, simplicial derivatives are expressedin coordinates of the simplex, thus reducing the problem to the standard theory ofsystems of di erential equations, including stability. The characterisation of stabilityof these non-linear systems relays on the linearisation of the system of di erential equations at the stationary point, if any. The eigenvelues of the linearised matrix and theassociated behaviour of the orbits are the main tools. For a three component system,these orbits can be plotted both in coordinates of the simplex or in a ternary diagram.A characterisation of processes with transfer of mass in closed systems in terms of stability is thus concluded. Two examples are presented for illustration, one of them is aradioactive decay

Effects of riparian vegetation removal on nutrient retention in a Mediterranean stream

We examined the effects of riparian vegetation removal on algal dynamics and stream nutrient retention efficiency by comparing NH4-N and PO4-P uptake lengths from a logged and an unlogged reach in Riera Major, a forested Mediterranean stream in northeastern Spain. From June to September 1995, we executed 6 short-term additions of N (as NH4Cl) and P (as Na2HPO4) in a 200-m section to measure nutrient uptake lengths. The study site included 2 clearly differentiated reaches in terms of canopy cover by riparian trees: the first 100 m were completely logged (i.e., the logged reach) and the remaining 100 m were left intact (i.e., the shaded reach). Trees were removed from the banks of the logged reach in the winter previous to our sampling. In the shaded reach, riparian vegetation was dominated by alders (Alnus glutinosa). The study was conducted during summer and fall months when differences in light availability between the 2 reaches were greatest because of forest canopy conditions. Algal biomass and % of stream surface covered by algae were higher in the logged than in the shaded reach, indicating that logging had a stimulatory effect on algae in the stream. Overall, nutrient retention efficiency was higher (i.e., shorter uptake lengths) in the logged than in the shaded reach, especially for PO4-P. Despite a greater increase in PO4-P retention efficiency relative to that of NH4-N following logging, retention efficiency for NH4-N was higher than for PO4-P in both study reaches. The PO4-P mass-transfer coefficient was correlated with primary production in both study reaches, indicating that algal activity plays an important role in controlling PO4-P dynamics in this stream. In contrast, the NH4-N mass-transfer coefficient showed a positive relation-ship only with % of algal coverage in the logged reach, and was not correlated with any algal-related parameter in the shaded reach. The lack of correlation with algal production suggests that mechanisms other than algal activity (i.e., microbial heterotrophic processes or abiotic mechanisms) may also influence NH4-N retention in this stream. Overall, this study shows that logging disturbances in small shaded streams may alter in-stream ecological features that lead to changes in stream nutrient retention efficiency. Moreover, it emphasizes that alteration of the tight linkage between the stream channel and the adjacent riparian zone may directly and indirectly impact biogeochemical processes with implications for stream ecosystem functioning.

Numerical simulation of combined heat transfer phenomena (conduction, convection, and radiation). Application to he optimisation of thermal systems

Thermal systems interchanging heat and mass by conduction, convection, radiation (solar and thermal ) occur in many engineering applications like energy storage by solar collectors, window glazing in buildings, refrigeration of plastic moulds, air handling units etc. Often these thermal systems are composed of various elements for example a building with wall, windows, rooms, etc. It would be of particular interest to have a modular thermal system which is formed by connecting different modules for the elements, flexibility to use and change models for individual elements, add or remove elements without changing the entire code. A numerical approach to handle the heat transfer and fluid flow in such systems helps in saving the full scale experiment time, cost and also aids optimisation of parameters of the system. In subsequent sections are presented a short summary of the work done until now on the orientation of the thesis in the field of numerical methods for heat transfer and fluid flow applications, the work in process and the future work.

Efficiency of informational transfer in regular and complex networks

We analyze the process of informational exchange through complex networks by measuring network efficiencies. Aiming to study nonclustered systems, we propose a modification of this measure on the local level. We apply this method to an extension of the class of small worlds that includes declustered networks and show that they are locally quite efficient, although their clustering coefficient is practically zero. Unweighted systems with small-world and scale-free topologies are shown to be both globally and locally efficient. Our method is also applied to characterize weighted networks. In particular we examine the properties of underground transportation systems of Madrid and Barcelona and reinterpret the results obtained for the Boston subway network.