Derivations and Dirichlet forms on fractals

We study derivations and Fredholm modules on metric spaces with a local regular conservative Dirichlet form. In particular, on finitely ramified fractals, we show that there is a non-trivial Fredholm module if and only if the fractal is not a tree (i.e. not simply connected). This result relates Fredholm modules and topology, and refines and improves known results on p.c.f. fractals. We also discuss weakly summable Fredholm modules and the Dixmier trace in the cases of some finitely and infinitely ramified fractals (including non-self-similar fractals) if the so-called spectral dimension is less than 2. In the finitely ramified self-similar case we relate the p-summability question with estimates of the Lyapunov exponents for harmonic functions and the behavior of the pressure function.Comment: to appear in the Journal of Functional Analysis 201

Smooth cutoff formulation of hierarchical reference theory for a scalar phi4 field theory

The phi4 scalar field theory in three dimensions, prototype for the study of phase transitions, is investigated by means of the hierarchical reference theory (HRT) in its smooth cutoff formulation. The critical behavior is described by scaling laws and critical exponents which compare favorably with the known values of the Ising universality class. The inverse susceptibility vanishes identically inside the coexistence curve, providing a first principle implementation of the Maxwell construction, and shows the expected discontinuity across the phase boundary, at variance with the usual sharp cutoff implementation of HRT. The correct description of first and second order phase transitions within a microscopic, nonperturbative approach is thus achieved in the smooth cutoff HRT.Comment: 8 pages, 4 figure

Assessment Of Environmental Impact From Renewable And Non-renewable Energy Sources

The scientific studies show that the greatest amount of CO2 emissions, in the European Union, results from the production of electricity and heat (for example, the production of coal-based energy in the EU Member States generates an amount of approximately one billion tons of CO2 emissions, that is about 1/4 of total CO2 emissions in the EU). The waste sector is a significant contributor to greenhouse gas (GHG) emissions accountable for approximately one twentieth of the global greenhouse budget. This contribution consists of CH4 emission from waste anaerobic decomposition and CO2 from thermal treatments. This study presents some district heating preliminary considerations through thermo-chemical conversion of renewable and non-renewable sources. Three locations are virtually analyzed, two counties from Romania and one from Italy. A comparison is made between using different potential types of fuel: wood, coal, MSW, residual municipal solid waste (RMSW), bio-dried waste (BD) and solid-recovered fuel (SRF). The lower heating values (LHVs) of the two types of studied lignite (coal from Romania and Italy) are higher in comparison with the LHV of MSW, similar to the ones of RMSW and BD waste, but lower to the ones of SRF and wood, with some exceptions. Data suitable for preliminary global environmental balances and local impact considerations from atmospheric emissions were carried out for the quantity of primary fuel as presented. Results demonstrate that, even from the preliminary considerations, the environmental performances of district heating are strongly affected by the choice of the fuel.This paper work has been partially funded by Erasmus+ under financial agreement 2014-1-RO01-KA203-002986