Backward Clusters, Hierarchy and Wild Sums for a Hard Sphere System in a Low-Density Regime

We study the statistics of backward clusters in a gas of hard spheres at low density. A backward cluster is defined as the group of particles involved directly or indirectly in the backwards-in-time dynamics of a given tagged sphere. We derive upper and lower bounds on the average size of clusters by using the theory of the homogeneous Boltzmann equation combined with suitable hierarchical expansions. These representations are known in the easier context of Maxwellian molecules (Wild sums). We test our results with a numerical experiment based on molecular dynamics simulations

On The Weak-Coupling Limit for Bosons and Fermions

In this paper we consider a large system of Bosons or Fermions. We start with an initial datum which is compatible with the Bose-Einstein, respectively Fermi-Dirac, statistics. We let the system of interacting particles evolve in a weak-coupling regime. We show that, in the limit, and up to the second order in the potential, the perturbative expansion expressing the value of the one-particle Wigner function at time $t$, agrees with the analogous expansion for the solution to the Uehling-Uhlenbeck equation. This paper follows in spirit the companion work [\rcite{BCEP}], where the authors investigated the weak-coupling limit for particles obeying the Maxwell-Boltzmann statistics: here, they proved a (much stronger) convergence result towards the solution of the Boltzmann equation

Particle Approximation of the BGK Equation

In this paper we prove the convergence of a suitable particle system towards the BGK model. More precisely, we consider an interacting stochastic particle system in which each particle can instantaneously thermalize locally. We show that, under a suitable scaling limit, propagation of chaos does hold and the one-particle distribution function converges to the solution of the BGK equation

An algorithm for operational flood mapping from Synthetic Aperture Radar (SAR) data using fuzzy logic

Abstract. An algorithm developed to map flooded areas from synthetic aperture radar imagery is presented in this paper. It is conceived to be inserted in the operational flood management system of the Italian Civil Protection and can be used in an almost automatic mode or in an interactive mode, depending on the user's needs. The approach is based on the fuzzy logic that is used to integrate theoretical knowledge about the radar return from inundated areas taken into account by means of three electromagnetic scattering models, with simple hydraulic considerations and contextual information. This integration aims at allowing a user to cope with situations, such as the presence of vegetation in the flooded area, in which inundation mapping from satellite radars represents a difficult task. The algorithm is designed to work with radar data at L, C, and X frequency bands and employs also ancillary data, such as a land cover map and a digital elevation model. The flood mapping procedure is tested on an inundation that occurred in Albania on January 2010 using COSMO-SkyMed very high resolution X-band SAR data

A hydrodynamic model arising in the context of granular media

AbstractIn this note, we propose a formal argument identifying the hydrodynamic limit of a Fokker-Planck model for granular media appearing in [1]. More precisely, in the limit of large background temperature and vanishing friction, this hydrodynamic limit is described by the classical system of isentropic gas dynamics with a nonstandard pressure law (specifically, the pressure is proportional to the cube root of the density). Finally, some qualitative properties of the hydrodynamic model are studied

Life Cycle Assessment of a Lithium-Ion Battery Pack Unit Made of Cylindrical Cells

Saving energy is a fundamental topic considering the growing energy requirements with respect to energy availability. Many studies have been devoted to this question, and life cycle assessment (LCA) is increasingly acquiring importance in several fields as an effective way to evaluate the energy demand and the emissions associated with products’ life cycles. In this work, an LCA analysis of an existent lithium-ion battery pack (BP) unit is presented with the aim to increase awareness about its consumption and offering alternative production solutions that are less energy intensive. Exploiting the literature data about cradle-to-grave and cradle-to-gate investigations, and after establishing reasonable approximations, the main BP sub-elements were considered for this study, such as the plastic cells support, the Li-ion cells brick, the PCBs for a battery management system (BMS), the liquid-based battery thermal management system (BTMS) and the BP container. For each of these components, the impacts of the extraction, processing, assembly, and transportation of raw materials are estimated and the partial and total values of the energy demand (ED) and global warming potential (GWP) are determined. The final interpretation of the results allows one to understand the important role played by LCA evaluations and presents other possible ways of reducing the energy consumption and (Formula presented.) emissions

Integrating physical and topographic information into a fuzzy scheme to map flooded area by SAR

A flood mapping procedure based on a fuzzy sets theory has been developed. The method is based on the integration of Synthetic Aperture Radar (SAR) measurements with additional data on the inundated area, such as a land cover map and a digital elevation model (DEM). The information on land cover has allowed us to account for both specular reflection, typical of open water, and double bounce backscattering, typical of forested and urban areas. DEM has been exploited to include simple hydraulic considerations on the dependence of inundation probability on surface characteristics. Contextual information has been taken into account too. The proposed algorithm has been tested on a flood occurred in Italy on November 1994. A pair of ERS-1 images, collected before and after (three days later) the flood, has been used. The results have been compared with the data provided by a ground survey carried out when the flood reached its maximum extension. Despite the temporal mismatch between the survey and the post-inundation SAR image, the comparison has yielded encouraging results, with the 87% of the pixels correctly classified as inundated

2-D constrained Navier-Stokes equation and intermediate asymptotics

We introduce a modified version of the two-dimensional Navier-Stokes equation, preserving energy and momentum of inertia, which is motivated by the occurrence of different dissipation time scales and related to the gradient flow structure of the 2-D Navier-Stokes equation. The hope is to understand intermediate asymptotics. The analysis we present here is purely formal. A rigorous study of this equation will be done in a forthcoming paper

Experimental Investigation on Latent Thermal Energy Storages (LTESs) Based on Pure and Copper-Foam-Loaded PCMs

In this work, a commercial paraffin PCM (RT35) characterized by a change range of the solid-liquid phase transition temperature Ts−l=29–36 °C and the low thermal conductivity λSL=0.2 W/m K is experimentally tested by submitting it to thermal charging/discharging cycles. The paraffin is contained in a case with a rectangular base and heated from the top due to electrical resistance. The aim of this research is to show the benefits that a 95% porous copper metal foam (pore density PD=20PPI) can bring to a PCM-based thermal storage system by simply loading it, due to the consequent increase in the effective thermal conductivity of the medium (λLOAD=7.03 W/m K). The experimental results highlight the positive effects of the copper foam presence, such as the heat conduction improvement throughout the system, and a significant reduction in time for the complete melting of the PCM. In addition, the experimental data highlight that in the copper-foam-loaded PCM the maximum temperature reached during the heating process is lower than 20K with respect to the test with pure PCM, imposing the same heat flux on the top (P=3.5 W/m2)