Mathematical Models and Methods in Applied Sciences, May 28, 2015
This paper proposes a survey and critical analysis focused on a variety of chemotaxis models in b... more This paper proposes a survey and critical analysis focused on a variety of chemotaxis models in biology, namely the classical Keller–Segel model and its subsequent modifications, which, in several cases, have been developed to obtain models that prevent the non-physical blow up of solutions. The presentation is organized in three parts. The first part focuses on a survey of some sample models, namely the original model and some of its developments, such as flux limited models, or models derived according to similar concepts. The second part is devoted to the qualitative analysis of analytic problems, such as the existence of solutions, blow-up and asymptotic behavior. The third part deals with the derivation of macroscopic models from the underlying description, delivered by means of kinetic theory methods. This approach leads to the derivation of classical models as well as that of new models, which might deserve attention as far as the related analytic problems are concerned. Finally, an overview of the entire contents leads to suggestions for future research activities.
This chapter is devoted to the investigation, through targeted numerical experiments, of various ... more This chapter is devoted to the investigation, through targeted numerical experiments, of various social scenarios predicted by the model presented in Chap. 3 in consequence of different simulated welfare policies. Qualitative simulations are developed with a mainly exploratory purpose, especially in order to test the ability of the model to account for the emergence of nontrivial collective average trends out of the probabilistic description of microscopic individual interactions. To this aim, a parameter sensitivity analysis is performed, which guides the organization of the simulations and the critical assessment of their results.
This paper deals with the derivation of macroscopic equations for a class of equations modelling ... more This paper deals with the derivation of macroscopic equations for a class of equations modelling complex multicellular systems delivered by the kinetic theory for active particles. The analysis is focused on growing cancer tissues. A critical analysis is proposed to enlighten the technical difficulties generated by dealing with living tissues and to focus the strategy to overcome them by new mathematical approaches.
Mathematical Models and Methods in Applied Sciences, Jun 15, 2021
This editorial paper presents the articles published in a special issue devoted to active particl... more This editorial paper presents the articles published in a special issue devoted to active particle methods applied to modeling, qualitative analysis, and simulation of the collective dynamics of large systems of interacting living entities in science and society. The modeling approach refers to the mathematical tools of behavioral swarms theory and to the kinetic theory of active particles. Applications focus on classical problems of swarms theory, on crowd dynamics related to virus contagion problems, and to multiscale problems related to the derivation of models at a large scale from the mathematical description at the microscopic scale. A critical analysis of the overall contents of the issue is proposed, with the aim to provide a forward look to research perspectives.
Mathematical Models and Methods in Applied Sciences, Aug 19, 2020
This editorial paper is devoted to present the papers published in a special issue focused on mod... more This editorial paper is devoted to present the papers published in a special issue focused on modeling, qualitative analysis and simulation of the collective dynamics of living, self-propelled particles. A critical analysis of the overall contents of the issue is proposed, thus leading to a forward look to research perspectives.
Mathematical Models and Methods in Applied Sciences, May 28, 2015
This paper proposes a survey and critical analysis focused on a variety of chemotaxis models in b... more This paper proposes a survey and critical analysis focused on a variety of chemotaxis models in biology, namely the classical Keller–Segel model and its subsequent modifications, which, in several cases, have been developed to obtain models that prevent the non-physical blow up of solutions. The presentation is organized in three parts. The first part focuses on a survey of some sample models, namely the original model and some of its developments, such as flux limited models, or models derived according to similar concepts. The second part is devoted to the qualitative analysis of analytic problems, such as the existence of solutions, blow-up and asymptotic behavior. The third part deals with the derivation of macroscopic models from the underlying description, delivered by means of kinetic theory methods. This approach leads to the derivation of classical models as well as that of new models, which might deserve attention as far as the related analytic problems are concerned. Finally, an overview of the entire contents leads to suggestions for future research activities.
This chapter is devoted to the investigation, through targeted numerical experiments, of various ... more This chapter is devoted to the investigation, through targeted numerical experiments, of various social scenarios predicted by the model presented in Chap. 3 in consequence of different simulated welfare policies. Qualitative simulations are developed with a mainly exploratory purpose, especially in order to test the ability of the model to account for the emergence of nontrivial collective average trends out of the probabilistic description of microscopic individual interactions. To this aim, a parameter sensitivity analysis is performed, which guides the organization of the simulations and the critical assessment of their results.
This paper deals with the derivation of macroscopic equations for a class of equations modelling ... more This paper deals with the derivation of macroscopic equations for a class of equations modelling complex multicellular systems delivered by the kinetic theory for active particles. The analysis is focused on growing cancer tissues. A critical analysis is proposed to enlighten the technical difficulties generated by dealing with living tissues and to focus the strategy to overcome them by new mathematical approaches.
Mathematical Models and Methods in Applied Sciences, Jun 15, 2021
This editorial paper presents the articles published in a special issue devoted to active particl... more This editorial paper presents the articles published in a special issue devoted to active particle methods applied to modeling, qualitative analysis, and simulation of the collective dynamics of large systems of interacting living entities in science and society. The modeling approach refers to the mathematical tools of behavioral swarms theory and to the kinetic theory of active particles. Applications focus on classical problems of swarms theory, on crowd dynamics related to virus contagion problems, and to multiscale problems related to the derivation of models at a large scale from the mathematical description at the microscopic scale. A critical analysis of the overall contents of the issue is proposed, with the aim to provide a forward look to research perspectives.
Mathematical Models and Methods in Applied Sciences, Aug 19, 2020
This editorial paper is devoted to present the papers published in a special issue focused on mod... more This editorial paper is devoted to present the papers published in a special issue focused on modeling, qualitative analysis and simulation of the collective dynamics of living, self-propelled particles. A critical analysis of the overall contents of the issue is proposed, thus leading to a forward look to research perspectives.
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