Surveys and essays towards research perspectives on complex systems. (English) Zbl 07830485
From the text: This editorial is dedicated to presenting the papers published in a special issue focused on modeling, qualitative analysis and simulation of the collective dynamics of systems in engineering and life sciences. All papers have a minor or major reference to living, i.e. complex systems, and a critical analysis of the overall content of the issue is proposed, leading to a forward look at research perspectives. This paper first defines the goals of the issue. Then, a brief description of the scientific contribution of the papers published in this issue is given. Finally, a look into the future is proposed.
MSC:
| 00Bxx | Conference proceedings and collections of articles |
| 26A16 | Lipschitz (Hölder) classes |
| 28A33 | Spaces of measures, convergence of measures |
| 35B30 | Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs |
| 35F10 | Initial value problems for linear first-order PDEs |
| 35L50 | Initial-boundary value problems for first-order hyperbolic systems |
| 35R02 | PDEs on graphs and networks (ramified or polygonal spaces) |
| 46E27 | Spaces of measures |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 82D99 | Applications of statistical mechanics to specific types of physical systems |
| 91D10 | Models of societies, social and urban evolution |
| 92B05 | General biology and biomathematics |
| 92C17 | Cell movement (chemotaxis, etc.) |
| 92D40 | Ecology |
| 92C15 | Developmental biology, pattern formation |
Keywords:
complexity; active particles; nonlinear interactions; computing; multicellular systems; behavioral economicsReferences:
| [1] | Aristov, V. V., Biological systems as nonequilibrium structures described by kinetic methods, Res. Phys.13 (2019) 102232. |
| [2] | Bellomo, N., Burini, D., Dosi, G., Gibelli, L., Knopoff, D., Outada, N., Terna, P. and Virgillito, M.-E., What is life? A perspective of the mathematical kinetic theory of active particles, Math. Models Methods Appl. Sci.31 (2021) 1821-1866. · Zbl 1480.92012 |
| [3] | Bellomo, N. and Egidi, M., From Herbert A. Simon’s legacy to the evolutionary artificial world with heterogeneous collective behaviors, Math. Models Methods Appl. Sci.34(1) (2024) 145-180. · Zbl 1534.91032 |
| [4] | Bellomo, N., Liao, J., Quaini, A., Russo, L. and Siettos, C., Human behavioral crowds review, critical analysis and research perspectives, Math. Models Methods Appl. Sci.33 (2023) 1611-1650. · Zbl 1517.90024 |
| [5] | Burini, D. and Chouhad, N., Virus models in complex frameworks towards modeling space patterns of SARS-CoV-2 epidemics, Math. Models Methods Appl. Sci.33 (2023) 1611-1650. |
| [6] | Düll, C., Gwiazda, P., Marciniak-Czochra, A. and Skrzeczkowski, J., Structured population models on polish spaces: A unified approach including graphs, Riemannian Manifolds and measure spaces to describe dynamics of heterogeneous populations, Math. Models Methods Appl. Sci.34(1) (2024) 109-143. · Zbl 07830488 |
| [7] | Hartwell, H. L., Hopfield, J. J., Leibler, S. and Murray, A. W., From molecular to modular cell biology, Nature402 (1999) c47-c52. |
| [8] | Hilbert, D., Mathematical problems, Bull. Amer. Math. Soc.8 (1902) 437-479. · JFM 33.0976.07 |
| [9] | Hillen, T. and Painter, K. J., A user’s guide to PDE models for chemotaxis, J. Math. Biol.58 (2009) 183-217. · Zbl 1161.92003 |
| [10] | Painter, K. J., Hillen, T. and Potts, J. R., Biological modelling with nonlocal advection diffusion equations, Math. Models Methods Appl. Sci.34(1) (2024) 57-107. · Zbl 1536.92018 |
| [11] | Pareschi, L. and Toscani, G., Interacting Multiagent Systems: Kinetic Equations and Monte Carlo Methods (Oxford University Press, Oxford, 2013). |
| [12] | Schrödinger, E., What is Life? The Physical Aspect of the Living Cell (Cambridge University Press, Cambridge, 1944). |
| [13] | Simon, H. A., The Science of the Artificial, 1st edn. (MIT Press, Cambridge Massachussets, 1981). |
| [14] | Takizawa, K., Bazilevs, Y. and Tezduyar, T. E., Isogeometric discretization methods in computational fluid mechanics, Math. Models Methods Appl. Sci.32 (2022) 2359-2370. · Zbl 1512.76058 |
| [15] | Tezduyar, T. E., Takizawa, K. and Bazilevs, Y., Isogeometric analysis in computation of complex-geometry flow problems with moving boundaries and interfaces, Math. Models Methods Appl. Sci.34(1) (2024) 7-55. · Zbl 1534.76054 |
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