A direct method for the Boltzmann equation based on a pseudo-spectral velocity space discretization

A deterministic method is proposed for solving the Boltzmann equation. The method employs a Galerkin discretization of the velocity space and adopts, as trial and test functions, the collocation basis functions based on weights and roots of a Gauss-Hermite quadrature. This is defined by means of half- and/or full-range Hermite polynomials depending whether or not the distribution function presents a discontinuity in the velocity space. The resulting semi-discrete Boltzmann equation is in the form of a system of hyperbolic partial differential equations whose solution can be obtained by standard numerical approaches. The spectral rate of convergence of the results in the velocity space is shown by solving the spatially uniform homogeneous relaxation to equilibrium of Maxwell molecules. As an application, the two-dimensional cavity flow of a gas composed by hard-sphere molecules is studied for different Knudsen and Mach numbers. Although computationally demanding, the proposed method turns out to be an effective tool for studying low-speed slightly rarefied gas flows

A second-order slip model for arbitrary accomodation at the wall

This paper was presented at the 3rd Micro and Nano Flows Conference (MNF2011), which was held at the Makedonia Palace Hotel, Thessaloniki in Greece. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, Aristotle University of Thessaloniki, University of Thessaly, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute.We present a kinetic-theory derivation of second-order slip boundary conditions for a plane isothermal pressure driven gas owing through a microchannel. In the proposed approach, the distribution function is expanded in terms of orthogonal polynomials and the system of moment equations in the expansion coefficients is analytically solved. The velocity slip coefficients, as well as their Knudsen layer corrections, are obtained by evaluating the solution in the near continuum limit. In comparison with other methods, the present approach is accurate and easy to implement. The results are presented for the Bhatnagar-Gross-Krook-Welander (BGKW) kinetic model equation and Maxwell's boundary conditions, but can be extended to more general collision integral and different scattering kernels.Fondazione Cariplo within the framework of the project Surface interactions in micro/nano device

Flessibilit? di rete, flessibilit? di scuola

abstract not availabl

Anatomical variants of sphenoid sinuses pneumatisation: a CT scan study on a Northern Italian population

Sphenoid bone may be affected by different variants of pneumatisation, which have a relevant importance from a clinical and surgical point of view. The description of such variants in different populations may give useful information. However, few articles describe the variability of sphenoid pneumatised structures and none of them focuses on Northern Italian population. Variants of pneumatisation of sphenoid bone were described in a sample of 300 Northern Italian patients who underwent a CT scan. More than fifty-seven percent of patients showed a form of anatomical variant: the most common form was the pneumatised pterygoid processes (39.6%), followed by dorsum sellae (32.9%) and clinoid processes (20.3%), without statistically significant differences between males and females (p\ua0>\ua00.01). In 26.3% of patients, a combined pneumatisation of these three structures was observed, being the combination pterygoid processes-dorsum sellae the most frequent (11.3%). In 9.3%, all the three sphenoid structures were affected. This article is the first description of the prevalence of different variants of pneumatisation in a Northern Italian population: the occurrence of such forms has to be acknowledged for their possible clinical and surgical consequences

Behavioral Human Crowds and Society

This chapter provides an introduction to the contents of this edited volume. In keeping with the style of the previous edited volumes, we also consider research perspectives. The first part of this chapter contributes to the selection of some key perspectives that take into account not only the technical interest of modeling and simulation, but also the impact that this research activity can have on the well-being of society. The second part provides a brief introduction to the contents of the chapters that follow this editorial introduction. The contents of the chapter refer both to the aforementioned key topics and to the contents of the preceding edited volumes (Bellomo and Gibelli, Behavioural human crowds, recent results towards new research frontiers. In: Bellomo, Gibelli (eds) Crowd dynamics, Volume 3 - Modeling and social applications in the time of COVID 19. Birkhäuser, New York, pp 1–9, 2021; Bellomo et al., Behavioural human crowds. In: Gibelli (ed) Crowd dynamics, Volume 2 - Theory, models, and applications. Birkhäuser, New York, pp 1–10, 2020; Gibelli and Bellomo, Behavioral human crowds. In: Crowd dynamics, Volume 1 - Theory, models, and safety problems. Birkhäuser, New York, pp 1–14, 2018).</p