Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top

2022 | Book

Variability and Heterogeneity in Natural Swarms: Experiments and Modeling Read chapter Read first chapter

Active Particles, Volume 3

Advances in Theory, Models, and Applications

Editors: Nicola Bellomo, José Antonio Carrillo, Eitan Tadmor

Publisher: Springer International Publishing

Book Series : Modeling and Simulation in Science, Engineering and Technology

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

Login to get access
insite
SEARCH

About this book

This edited volume collects six surveys that present state-of-the-art results on modeling, qualitative analysis, and simulation of active matter, focusing on specific applications in the natural sciences. Following the previously published Active Particles volumes, these chapters are written by leading experts in the field and reflect the diversity of subject matter in theory and applications within an interdisciplinary framework. Topics covered include:Variability and heterogeneity in natural swarmsMultiscale aspects of the dynamics of human crowdsMathematical modeling of cell collective motion triggered by self-generated gradientsClustering dynamics on graphsRandom Batch Methods for classical and quantum interacting particle systemsThe consensus-based global optimization algorithm and its recent variantsMathematicians and other members of the scientific community interested in active matter and its many applications will find this volume to be a timely, authoritative, and valuable resource.

Table of Contents

Frontmatter
Variability and Heterogeneity in Natural Swarms: Experiments and Modeling
Abstract
Collective motion of large-scale natural swarms, such as moving animal groups or expanding bacterial colonies, has been described as self-organized phenomena. Thus, it is clear that the observed macroscopic, coarse-grained swarm dynamics depend on the properties of the individuals of which it is composed. In nature, individuals are never identical and may differ in practically every parameter. Hence, intragroup variability and its effect on the ability to form coordinated motion is of interest, both from theoretical and biological points of view. This review examines some of the fundamental properties of heterogeneous collectives in nature, with an emphasis on two widely used model organisms: swarming bacteria and locusts. Theoretical attempts to explain the observed phenomena are discussed in view of laboratory experiments, highlighting their successes and failures. In particular we show that, surprisingly, while heterogeneity typically discourages collectivity, there are several natural examples where it has the opposite effect.
G. Ariel, A. Ayali, A. Be’er, D. Knebel
Active Crowds
Abstract
This chapter focuses on the mathematical modelling of active particles (or agents) in crowded environments. We discuss several microscopic models found in the literature and the derivation of the respective macroscopic partial differential equations for the particle density. The macroscopic models share common features, such as cross-diffusion or degenerate mobilities. We then take the diversity of macroscopic models to a uniform structure and work out potential similarities and differences. Moreover, we discuss boundary effects and possible applications in life and social sciences. This is complemented by numerical simulations that highlight the effects of different boundary conditions.
Maria Bruna, Martin Burger, Jan-Frederik Pietschmann, Marie-Therese Wolfram
Mathematical Modeling of Cell Collective Motion Triggered by Self-Generated Gradients
Abstract
Self-generated gradients have attracted a lot of attention in the recent biological literature. It is considered as a robust strategy for a group of cells to find its way during a long journey. This note is intended to discuss various scenarios for modeling traveling waves of cells that constantly deplete a chemical cue and so create their own signaling gradient all along the way. We begin with one famous model by Keller and Segel for bacterial chemotaxis. We present the model and the construction of the traveling wave solutions. We also discuss the limitation of this approach and review some subsequent work addressing stability issues. Next, we review two relevant extensions, which are supported by biological experiments. They both admit traveling wave solutions with an explicit value for the wave speed. We conclude by discussing some open problems and perspectives, and particularly a striking mechanism of speed determinacy occurring at the back of the wave. All the results presented in this note are illustrated by numerical simulations.
Vincent Calvez, Mete Demircigil, Roxana Sublet
Clustering Dynamics on Graphs: From Spectral Clustering to Mean Shift Through Fokker–Planck Interpolation
Abstract
In this work, we build a unifying framework to interpolate between density-driven and geometry-based algorithms for data clustering and, specifically, to connect the mean shift algorithm with spectral clustering at discrete and continuum levels. We seek this connection through the introduction of Fokker–Planck equations on data graphs. Besides introducing new forms of mean shift algorithms on graphs, we provide new theoretical insights on the behavior of the family of diffusion maps in the large sample limit as well as provide new connections between diffusion maps and mean shift dynamics on a fixed graph. Several numerical examples illustrate our theoretical findings and highlight the benefits of interpolating density-driven and geometry-based clustering algorithms.
Katy Craig, Nicolas GarciaTrillos, Dejan Slepčev
Random Batch Methods for Classical and Quantum Interacting Particle Systems and Statistical Samplings
Abstract
We review the Random Batch Methods (RBM) for interacting particle systems consisting of N-particles, with N being large. The computational cost of such systems is of \(\mathcal {O}(N^2)\), which is prohibitively expensive. The RBM methods use small but random batches so the computational cost is reduced, per time step, to \(\mathcal {O}(N)\). In this article we discuss these methods for both classical and quantum systems, the corresponding theory, and applications from molecular dynamics, statistical samplings, to agent-based models for collective behavior, and quantum Monte Carlo methods.
Shi Jin, Lei Li
Trends in Consensus-Based Optimization
Abstract
In this chapter we give an overview of the consensus-based global optimization algorithm and its recent variants. We recall the formulation and analytical results of the original model, and then we discuss variants using component-wise independent or common noise. In combination with mini-batch approaches those variants were tailored for machine learning applications. Moreover, it turns out that the analytical estimates are dimension independent, which is useful for high-dimensional problems. We discuss the relationship of consensus-based optimization with particle swarm optimization, a method widely used in the engineering community. Then we survey a variant of consensus-based optimization that is proposed for global optimization problems constrained to hyper-surfaces. We conclude the chapter with remarks on applications, preprints and open problems.
Claudia Totzeck
Metadata
Title
Active Particles, Volume 3
Editors
Nicola Bellomo
José Antonio Carrillo
Eitan Tadmor
Copyright Year
2022
Electronic ISBN
978-3-030-93302-9
Print ISBN
978-3-030-93301-2
DOI
https://doi.org/10.1007/978-3-030-93302-9

Premium Partners

    Image Credits