A bifurcation analysis is developed for the initial value problem for a nonlinear system of integ... more A bifurcation analysis is developed for the initial value problem for a nonlinear system of integro-differential equations modelling the competition between tumor cells and immune system. It is shown that there exists a critical value of a bifurcation parameter separating situations where the immune system controls the neoplastic growth from those where tumor growth is not contrasted. This result refers to conjecture that the action of cytokine signals can modify the outputs of the competition. (~
Mathematical Models and Methods in Applied Sciences, Jan 12, 2022
Re-use and distribution is strictly not permitted, except for Open Access articles. 322 N. Bellom... more Re-use and distribution is strictly not permitted, except for Open Access articles. 322 N. Bellomo et al. include the modeling of social dynamics, multiscale problems and a detailed study of the link between crowds and swarms modeling.
Partially supported by Marie Curie Network MRTN-CT-2004-503661-Modelling, Mathematical Methods an... more Partially supported by Marie Curie Network MRTN-CT-2004-503661-Modelling, Mathematical Methods and Computer Simulations of Tumor Growth and Therapy. biological phenomena with special focus on the immune competition. Then, some specific applications are proposed referring to the competition between neoplastic and immune cells. Finally, the last part is devoted to research perspectives towards the objective of developing a mathematical-biological theory. A critique is presented of what has already been achieved towards the above target and what is still missing with special focus on multiscale systems.
These Lectures Notes attempt to provide an introduction to the above issues and will exploit the ... more These Lectures Notes attempt to provide an introduction to the above issues and will exploit the use of electronic diffusion to update periodically the contents also on the basis of interactions with students, taking advantage of suggestions generally useful from those who are involved pursuing the objective of a master graduation in mathematics for engineering sciences.
Synthesis Lectures on Mathematics and Statistics, Oct 22, 2020
The contents of this brief Lecture Note are devoted to modeling, simulations, and applications wi... more The contents of this brief Lecture Note are devoted to modeling, simulations, and applications with the aim of proposing a unified multiscale approach accounting for the physics and the psychology of people in crowds. The modeling approach is based on the mathematical theory of active particles, with the goal of contributing to safety problems of interest for the well-being of our society, for instance, by supporting crisis management in critical situations such as sudden evacuation dynamics induced through complex venues by incidents.
This article deals with a review and critical analysis of first order hydrodynamic models of vehi... more This article deals with a review and critical analysis of first order hydrodynamic models of vehicular traffic flow obtained by the closure of the mass conservation equation. The closure is obtained by phenomenological models suitable to relate the local mean velocity to local density profiles. Various models are described and critically analyzed in the deterministic and stochastic case. The analysis is developed in view of applications of the models to traffic flow simulations for networks of roads. Some research perspectives are derived from the above analysis and proposed in the last part of the paper. To cite this article:
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.
Modeling and simulation in science, engineering & technology, 2008
, except for brief excerpts in connection with reviews or scholarly analysis. Use in connection w... more , except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights.
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.
A bifurcation analysis is developed for the initial value problem for a nonlinear system of integ... more A bifurcation analysis is developed for the initial value problem for a nonlinear system of integro-differential equations modelling the competition between tumor cells and immune system. It is shown that there exists a critical value of a bifurcation parameter separating situations where the immune system controls the neoplastic growth from those where tumor growth is not contrasted. This result refers to conjecture that the action of cytokine signals can modify the outputs of the competition. (~
Mathematical Models and Methods in Applied Sciences, Jan 12, 2022
Re-use and distribution is strictly not permitted, except for Open Access articles. 322 N. Bellom... more Re-use and distribution is strictly not permitted, except for Open Access articles. 322 N. Bellomo et al. include the modeling of social dynamics, multiscale problems and a detailed study of the link between crowds and swarms modeling.
Partially supported by Marie Curie Network MRTN-CT-2004-503661-Modelling, Mathematical Methods an... more Partially supported by Marie Curie Network MRTN-CT-2004-503661-Modelling, Mathematical Methods and Computer Simulations of Tumor Growth and Therapy. biological phenomena with special focus on the immune competition. Then, some specific applications are proposed referring to the competition between neoplastic and immune cells. Finally, the last part is devoted to research perspectives towards the objective of developing a mathematical-biological theory. A critique is presented of what has already been achieved towards the above target and what is still missing with special focus on multiscale systems.
These Lectures Notes attempt to provide an introduction to the above issues and will exploit the ... more These Lectures Notes attempt to provide an introduction to the above issues and will exploit the use of electronic diffusion to update periodically the contents also on the basis of interactions with students, taking advantage of suggestions generally useful from those who are involved pursuing the objective of a master graduation in mathematics for engineering sciences.
Synthesis Lectures on Mathematics and Statistics, Oct 22, 2020
The contents of this brief Lecture Note are devoted to modeling, simulations, and applications wi... more The contents of this brief Lecture Note are devoted to modeling, simulations, and applications with the aim of proposing a unified multiscale approach accounting for the physics and the psychology of people in crowds. The modeling approach is based on the mathematical theory of active particles, with the goal of contributing to safety problems of interest for the well-being of our society, for instance, by supporting crisis management in critical situations such as sudden evacuation dynamics induced through complex venues by incidents.
This article deals with a review and critical analysis of first order hydrodynamic models of vehi... more This article deals with a review and critical analysis of first order hydrodynamic models of vehicular traffic flow obtained by the closure of the mass conservation equation. The closure is obtained by phenomenological models suitable to relate the local mean velocity to local density profiles. Various models are described and critically analyzed in the deterministic and stochastic case. The analysis is developed in view of applications of the models to traffic flow simulations for networks of roads. Some research perspectives are derived from the above analysis and proposed in the last part of the paper. To cite this article:
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.
Modeling and simulation in science, engineering & technology, 2008
, except for brief excerpts in connection with reviews or scholarly analysis. Use in connection w... more , except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights.
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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Papers by Nicola Bellomo