197,764 research outputs found
A BGK model for mixtures of monoatomic and polyatomic gases with discrete internal energy
No full textWe generalize the BGK model proposed in Bisi and Cáceres (2016) to a mixture constituted by both monoatomic and polyatomic gas species with each polyatomic one being characterized by its own number of discrete internal energy levels, to model its non-translational degrees of freedom. We prove that all disposable parameters appearing in the Maxwellian attractors may be determined in terms of the actual macroscopic fields in such a way that correct Maxwellian equilibria and collision invariants are preserved, as well as the validity of the H-theorem. Evolution equations for species densities, velocities and temperatures are also derived, and some numerical examples are shown in space homogeneous conditions
PROCEEDINGS OF SIMAI 2020+21: THE XV BIANNUAL CONGRESS OF SIMAI 30 August - 3 September 2021 Parma, Italy
No full textThe book collects the abstracts of the bi-annual congress of the Italian Society of Applied and Industrial Mathematics (SIMAI) held from August 30 to September 3, 2021 at the University of Parma. The Congress met together about 500 researchers from academia and industry active in the study of mathematical and numerical models as well as in their applications to industrial and real life problems. The aim of this traditional event is to stimulate interdisciplinary research in Applied Mathematics and to foster interactions of the scientific community with industry. The content of this book is made by the contributions of: 6 Plenary Speakers; 63 Minisymposia and some other individual contributions; the "Industrial Session", a special event gathering together academic and industrial representatives to work on mathematical problems encountered in Research & Development areas; "EDU-SIMAI session", the event dedicated to the relationship with Secondary Schools on the subject of applied mathematics teaching
Kinetic model for international trade allowing transfer of individuals
No full textWe propose a kinetic model to describe trade among different populations, living in different countries. The interaction rules are assumed depending on the trading propensity of each population and also on non-deterministic (random) effects. Moreover, the possible transfers of individuals from one country to another are also taken into account, by means of suitable Boltzmann-type operators. Consistent macroscopic equations for number density and mean wealth of each country are derived from the kinetic equations, and the effects of transfers on their equilibrium values are commented on. Finally, a suitable continuous trading limit is considered, leading to a simpler system of Fokker-Planck-type kinetic equations, with specific contributions accounting for transfers.This article is part of the theme issue 'Kinetic exchange models of societies and economies'
Damping forces exerted by rarefied gas mixtures in micro-electro-mechanical system devices vibrating at high frequencies
No full textMultidimensional Scaling in Cluster Analysis: examples in Science and Mathematics Education
No full textSeveral researches in STEM education research highlight the advantages of an inte- grated approach to these disciplines that relates knowledge and know-how, design and implementation, theoretical and practical problems [5, 4, 6]. In some researches, the effectiveness of these approaches on students conceptual understanding and motivation and has been studied through the use of quantitative analysis tools such as cluster analysis
(CLA) [1, 7]. Through CLA it is possible to characterize students analyzing the strategies they deploy to tackle, for example, questionnaires built so as to investigate the lines of reasoning implemented by them when they are proposed with problematic situations. In particular, it is possible to characterize the students in terms of a limited number, m, of typical ways of answering the questionnaire questions [2]. Each student is therefore identified by a binary vector (each component can be 1 or 0) with m dimensions. Cluster Analysis techniques allow students to be grouped into homogeneous groups based on com- mon characteristics and the representation of these groups is ideally referred to an m-sized space. However, for reasons of simplicity and clarity, it is often preferred to perform the representation of groups in three or two dimensional spaces. One of the techniques used for this purpose is Multidimensional Scaling [3] (MDS). It allows the researcher to move from the m-sized space to a space with a smaller number of dimensions that is a function of the initial m-dimensional representation, preserving the global distances between the group elements. However, the application of the MDS methodologies depends strongly on the typology of the initial data and a non-thorough knowledge of the mathematical details at their base can lead to obtaining results that are not reliable and / or of little significance. In this paper we will study a MDS methodology based on Principal Component Analysis, with particular reference to a set of binary data, highlighting how the results obtained through this methodology can be reliable and significant for the researcher in education
Erratum: "Fluid-dynamic equations for granular particles in a host medium" [J. Math. Phys. 46, 113301 (2005)]
No full textMathematical models for the large spread of a contact-based infection: a statistical mechanics approach
No full textIn this work, we derive a system of Boltzmann-type equations to describe the spread of contact-based infections, such as SARS-CoV-2 virus, at the microscopic scale, that is, by modeling the human-to-human mechanisms of transmission. To this end, we consider two populations, characterized by specific distribution functions, made up of individuals without symptoms (population 1) and infected people with symptoms (population 2). The Boltzmann operators model the interactions between individuals within the same population and among different populations with a probability of transition from one to the other due to contagion or, vice versa, to recovery. In addition, the influence of innate and adaptive immune systems is taken into account. Then, starting from the Boltzmann microscopic description we derive a set of evolution equations for the size and mean state of each population considered. Mathematical properties of such macroscopic equations, as equilibria and their stability, are investigated, and some numerical simulations are performed in order to analyze the ability of our model to reproduce the characteristic features of Covid-19 type pandemics
Kinetic models for systems of interacting agents with multiple microscopic states
No full textWe propose and investigate general kinetic models with transition probabilities that can describe the simultaneous change of multiple microscopic states of the interacting agents. These models can be applied to many problems in socio-economic sciences, where individuals may change both their compartment and their characteristic microscopic variable, as for instance kinetic models for epidemic diffusion or for international trade with possible transfers of agents. Mathematical properties of the kinetic model are proved, as existence and uniqueness of a solution for the Cauchy problem in suitable Wasserstein spaces. The quasi-invariant asymptotic regime, leading to simpler kinetic Fokker-Planck-type equations, is investigated and commented on in comparison with other existing models. Some numerical tests are performed in order to show the time evolution of distribution functions and of meaningful macroscopic fields, even in case of non-constant interaction rates and transfer probabilities
Reaction-diffusion equations derived from kinetic models and their Turing instability
No full textWe consider a binary mixture composed by a polyatomic (diatomic) and a monatomic gas, diffusing in a gaseous background (typically, the atmosphere), and undergoing reversible and irreversible chemical reactions. We show the derivation of proper reaction–diffusion equations for the number densities of the constituents, starting from suitably rescaled kinetic Boltzmann equations. The dominant process is assumed to be the elastic scattering with the host medium, while we present two different scalings for the various chemical reactions: the first option leads to a system of three reaction– diffusion equations, while the second regime leads to two reaction–diffusion equations similar to the classical Brusselator system. Then, we study the Turing instability properties of such macroscopic systems, showing their dependence on particle masses, on collision frequencies of the Boltzmann operators, and, above all, on particle internal energie
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