Ursell operators in statistical physics of dense systems: the role of high order operators and of exchange cycles

The purpose of this article is to discuss cluster expansions in dense quantum systems as well as their interconnection with exchange cycles. We show in general how the Ursell operators of order 3 or more contribute to an exponential which corresponds to a mean-field energy involving the second operator U2, instead of the potential itself as usual. In a first part, we consider classical statistical mechanics and recall the relation between the reducible part of the classical cluster integrals and the mean-field; we introduce an alternative method to obtain the linear density contribution to the mean-field, which is based on the notion of tree-diagrams and provides a preview of the subsequent quantum calculations. We then proceed to study quantum particles with Boltzmann statistics (distinguishable particles) and show that each Ursell operator Un with n greater or equal to 3 contains a ``tree-reducible part'', which groups naturally with U2 through a linear chain of binary interactions; this part contributes to the associated mean-field experienced by particles in the fluid. The irreducible part, on the other hand, corresponds to the effects associated with three (or more) particles interacting all together at the same time. We then show that the same algebra holds in the case of Fermi or Bose particles, and discuss physically the role of the exchange cycles, combined with interactions. Bose condensed systems are not considered at this stage. The similarities and differences between Boltzmann and quantum statistics are illustrated by this approach, in contrast with field theoretical or Green's functions methods, which do not allow a separate study of the role of quantum statistics and dynamics.Comment: 31 pages, 7 figure

GIS modelling of forest wood residues potential for energy use based on forest inventory data: Methodological approach and case study application

This paper presents an approach to perform geo-referenced estimations of forest wood residues availability for energy use based on forest inventory data integration into a GIS. Three different estimation methods are described. The first one evaluates biomass availability based on the application of biomass expansion factors to stem volume data of the forest inventories. The method accounts for forest dynamics and assigns management treatments in function of forest properties. The second method estimates available forest wood residues applying biomass production by tree, derived from field studies, to the inventoried tree species. The third method links inventory data with national statistics of final cuttings of commercial tree species. Useful biomass potential is then estimated based on ecological, logistic and economic constraints. The methods were tested in a case study in Northern Spain where optimal facilities location based on marginal delivery costs and resources competition between facilities were found. Results are presented for three different scenarios. Biomass resources estimations under the different methods result in significant differences. GIS maps of useful biomass availability estimations are presented giving an idea of the optimal locations for bioenergy facilities based on resource availability

Detecting filaments in the ultra-high energy cosmic ray distribution

We propose and test new statistical tools to study the distribution of cosmic rays based on the use of the Minimal Spanning Tree. The method described is particularly sensitive to filamentary structures, as those expected to arise from strong sources of charged cosmic rays which get deflected by intervening magnetic fields. We also test the method with data available from the AGASA and SUGAR surface detector arrays.Comment: minor changes, matching the published version in Astroparticle Physic

(1+1)-dimensional turbulence

A class of dynamical models of turbulence living on a one-dimensional dyadic-tree structure is introduced and studied. The models are obtained as a natural generalization of the popular GOY shell model of turbulence. These models are found to be chaotic and intermittent. They represent the first example of (1+1)-dimensional dynamical systems possessing non trivial multifractal properties. The dyadic structure allows to study spatial and temporal fluctuations. Energy dissipation statistics and its scaling properties are studied. Refined Kolmogorov Hypothesis is found to hold.Comment: 18 pages, 9 figures, submitted to Phys.of Fluid

Calorific values and ash contents of different organs of Masson pine (Pinus massoniana) in southern China

Calorific values of plants are important indices for evaluating and reflecting material cycle and energy conversion in forest ecosystems. Based on the data of Masson Pine (Pinus massoniana) in southern China, the calorific values (CVs) and ash contents (ACs) of different plant organs were analyzed systematically using hypothesis test and regression analysis in this paper. The results show: (i) the CVs and ACs of different plant organs are almost significantly different, and the order by AFCV (ash-free calorific value) from the largest to the smallest is foliage (23.55 kJ/g), branches (22.25 kJ/g), stem bark (21.71 kJ/g), root (21.52 kJ/g) and stem wood (21.35 kJ/g); and the order by AC is foliage (2.35%), stem bark (1.44%), root (1.42%), branches (1.08%) and stem wood (0.33%); (ii) the CVs and ACs of stem woods on top, middle and lower sections are significantly different, and the CVs are increasing from top to lower sections of trunk while the ACs are decreasing; (iii) the mean GCV (gross calorific value) and AFCV of aboveground part are larger than those of belowground part (roots), and the differences are also statistically significant; (iv) the CVs and ACs of different organs are related, to some extent, to diameter, height and origin of the tree, but the influence degrees of the factors on CVs and ACs are not the same