G. Guerra | Searcharxiv

arXiv2021

Non Conservative Products in Fluid Dynamics

Fluid flow in pipes with discontinuous cross section or with kinks is described through balance laws with a non conservative product in the source. At jump discontinuities in the pipes' geometry, the physics of the problem suggests how to single out a solution. On this basis, we present a definition of solution for a general BV geometry and prove an existence result, consistent with a limiting procedure from piecewise constant geometries. In the case of a smoothly curved pipe we thus justify the appearance of the curvature in the source term of the linear momentum equation. These results are obtained as consequences of a general existence result devoted to abstract balance laws with non conservative source terms.

math.AP↗

arXiv2016

Effect of thermal annealing on the heat transfer properties of reduced graphite oxide flakes: a nanoscale characterization via scanning thermal microscopy

This paper reports on the thermal properties of reduced graphite oxide (RGO) flakes, studied by means of scanning thermal microscopy (SThM). This technique was demonstrated to allow thermal characterization of the flakes with a spatial resolution of the order of a few tens of nanometers, while recording nanoscale topography at the same time. Several individual RGO flakes were analyzed by SThM, both as obtained after conventional thermal reduction and after a subsequent annealing at 1700°C. Significant differences in the thermal maps were observed between pristine and annealed flakes, reflecting higher heat dissipation on annealed RGO flakes compared with pristine ones. This result was correlated with the reduction of RGO structure defectiveness. In particular, a substantial reduction of oxidized groups and sp3 carbons upon annealing was proven by X-ray photoelectron and Raman spectroscopies, while the increase of crystalline order was demonstrated by X-ray diffraction, in terms of higher correlation lengths both along and perpendicular to the graphene planes. Results presented in this paper provide experimental evidence for the qualitative correlation between the defectiveness of graphene-related materials and their thermal conductivity, which is clearly crucial for the exploitation of these materials into thermally conductive nanocomposites.

cond-mat.mtrl-sci↗

arXiv2008

Modeling and Optimal Control of Networks of Pipes and Canals

This paper deals with the optimal control of systems governed by nonlinear systems of conservation laws at junctions. The applications considered range from gas compressors in pipelines to open channels management. The existence of an optimal control is proved. From the analytical point of view, these results are based on the well posedness of a suitable initial boundary value problem and on techniques for quasidifferential equations in a metric space.

math.AP↗