Towards a Mathematical Theory of Behavioral Human Crowds

Nicola Bellomo acknowledges the support of the University of Granada, Project Modeling in Nature MNat from micro to macro, https://www.modelingnature.org.This paper has been partially supported by the MINECO-Feder (Spain) research Grant Number RTI2018-098850-B-I00, the Junta de Andalucia (Spain) Project PY18-RT-2422, A-FQM-311-UGR18, and B-FQM-580-UGR20. Livio Gibelli, gratefully acknowledges the financial support of the Engineering and Physical Sciences Research Council (EPSRC) Under Grants EP/N016602/1, EP/R007438/1. Annalisa Quaini acknowledges support from the Radcliffe Institute for Advanced Study at Harvard University where she has been a 2021-2022 William and Flora Hewlett Foundation Fellow. Alessandro Reali acknowledges the partial support of the MIUR-PRIN Project XFAST-SIMS (No. 20173C478N).The first part of our paper presents a general survey on the modeling, analytic problems, and applications of the dynamics of human crowds, where the specific features of living systems are taken into account in the modeling approach. This critical analysis leads to the second part which is devoted to research perspectives on modeling, analytic problems, multiscale topics which are followed by hints towards possible achievements. Perspectives include the modeling of social dynamics, multiscale problems and a detailed study of the link between crowds and swarms modeling.University of Granada, Project Modeling in Nature MNat from micro to macroSpanish Government RTI2018-098850-B-I00Junta de AndaluciaEuropean Commission PY18-RT-2422 A-FQM-311-UGR18 B-FQM-580-UGR20UK Research & Innovation (UKRI)Engineering & Physical Sciences Research Council (EPSRC) EP/N016602/1 EP/R007438/1Radcliffe Institute for Advanced Study at Harvard UniversityMinistry of Education, Universities and Research (MIUR) 20173C478

A multiscale model of virus pandemic: Heterogeneous interactive entities in a globally connected world

This paper is devoted to the multidisciplinary modelling of a pandemic initiated by an aggressive virus, specifically the so-called SARS–CoV–2 Severe Acute Respiratory Syndrome, corona virus n.2. The study is developed within a multiscale framework accounting for the interaction of different spatial scales, from the small scale of the virus itself and cells, to the large scale of individuals and further up to the collective behaviour of populations. An interdisciplinary vision is developed thanks to the contributions of epidemiologists, immunologists and economists as well as those of mathematical modellers. The first part of the contents is devoted to understanding the complex features of the system and to the design of a modelling rationale. The modelling approach is treated in the second part of the paper by showing both how the virus propagates into infected individuals, successfully and not successfully recovered, and also the spatial patterns, which are subsequently studied by kinetic and lattice models. The third part reports the contribution of research in the fields of virology, epidemiology, immune competition, and economy focussed also on social behaviours. Finally, a critical analysis is proposed looking ahead to research perspectives.publishedVersionFil: Bellomo, Nicola. Universidad de Granada. Departamento de Matemática Aplicada; España.Fil: Bingham, Richard. University of York. Departments of Mathematics and Biology. Cross-disciplinary Centre for Systems Analysis; United Kingdom.Fil: Chaplain, Mark A. J. University of St Andrews. School of Mathematics and Statistics; Scotland.Fil: Dosi, Giovanni. Scuola Superiore Sant’Anna. Institute of Economics and EMbeDS; Italia.Fil: Forni, Guido. Accademia Nazionale dei Lincei; Italia.Fil: Knopoff, Damian A. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina.Fil: Knopoff, Damian A. Consejo Nacional de Investigaciones Científicas y Técnicas de Argentina. Centro de Investigacion y Estudios de Matematica; Argentina.Fil: Lowengrub, John. University California Irvine. Department of Mathematics; United States.Fil: Twarock, Reidun. University of York. Departments of Mathematics and Biology. Cross-disciplinary Centre for Systems Analysis; United Kingdom.Fil: Virgillito, Maria Enrica.Scuola Superiore Sant’Anna. Institute of Economics and EMbeDS; Italia

Confronting Grand Challenges in environmental fluid mechanics

Environmental fluid mechanics underlies a wealth of natural, industrial and, by extension, societal challenges. In the coming decades, as we strive towards a more sustainable planet, there are a wide range of grand challenge problems that need to be tackled, ranging from fundamental advances in understanding and modeling of stratified turbulence and consequent mixing, to applied studies of pollution transport in the ocean, atmosphere and urban environments. A workshop was organized in the Les Houches School of Physics in France in January 2019 with the objective of gathering leading figures in the field to produce a road map for the scientific community. Five subject areas were addressed: multiphase flow, stratified flow, ocean transport, atmospheric and urban transport, and weather and climate prediction. This article summarizes the discussions and outcomes of the meeting, with the intent of providing a resource for the community going forward

Visual modeling and simulation of multiscale phenomena

Many large-scale systems seen in real life, such as human crowds, fluids, and granular materials, exhibit complicated motion at many different scales, from a characteristic global behavior to important small-scale detail. Such multiscale systems are computationally expensive for traditional simulation techniques to capture over the full range of scales. In this dissertation, I present novel techniques for scalable and efficient simulation of these large, complex phenomena for visual computing applications. These techniques are based on a new approach of representing a complex system by coupling together separate models for its large-scale and fine-scale dynamics. In fluid simulation, it remains a challenge to efficiently simulate fine local detail such as foam, ripples, and turbulence without compromising the accuracy of the large-scale flow. I present two techniques for this problem that combine physically-based numerical simulation for the global flow with efficient local models for detail. For surface features, I propose the use of texture synthesis, guided by the physical characteristics of the macroscopic flow. For turbulence in the fluid motion itself, I present a technique that tracks the transfer of energy from the mean flow to the turbulent fluctuations and synthesizes these fluctuations procedurally, allowing extremely efficient visual simulation of turbulent fluids. Another large class of problems which are not easily handled by traditional approaches is the simulation of very large aggregates of discrete entities, such as dense pedestrian crowds and granular materials. I present a technique for crowd simulation that couples a discrete per-agent model of individual navigation with a novel continuum formulation for the collective motion of pedestrians. This approach allows simulation of dense crowds of a hundred thousand agents at near-real-time rates on desktop computers. I also present a technique for simulating granular materials, which generalizes this model and introduces a novel computational scheme for friction. This method efficiently reproduces a wide range of granular behavior and allows two-way interaction with simulated solid bodies. In all of these cases, the proposed techniques are typically an order of magnitude faster than comparable existing methods. Through these applications to a diverse set of challenging simulation problems, I demonstrate the benefits of the proposed approach, showing that it is a powerful and versatile technique for the simulation of a broad range of large and complex systems