Related papers: Active particles methods towards modeling in scien…
This essay provides a critical overview of the mathematical kinetic theory of active particles, which is used to model and study collective systems consisting of interacting living entities, such as those involved in behavior and evolution.…
This chapter focuses on the mathematical modelling of active particles (or agents) in crowded environments. We discuss several microscopic models found in literature and the derivation of the respective macroscopic partial differential…
Active particles contain internal degrees of freedom with the ability to take in and dissipate energy and, in the process, execute systematic movement. Examples include all living organisms and their motile constituents such as molecular…
The term active matter describes diverse systems, spanning macroscopic (e.g. shoals of fish and flocks of birds) to microscopic scales (e.g. migrating cells, motile bacteria and gels formed through the interaction of nanoscale molecular…
The study of systems with sustained energy uptake and dissipation at the scale of the constituent particles is an area of central interest in nonequilibrium statistical physics. Identifying such systems as a distinct category -- Active…
We present the first steps of interaction spaces theory, a universal mathematical theory of complex systems which is able to embed cellular automata, agent based models, master equation based models, stochastic or deterministic, continuous…
This article is based on lecture notes for the Marie Curie Training school "Initial Training on Numerical Methods for Active Matter". It provides an introductory overview of modeling approaches for active matter and is primarily targeted at…
These lecture notes are designed to provide a brief introduction into the phenomenology of active matter and to present some of the analytical tools used to rationalize the emergent behavior of active systems. Such systems are made of…
In this perspective article, we discuss bacterial populations as a model system of active matter. It allows for the exploration and characterization of various phases of active matter and brings rich implications for both physics and…
A variety of computational models have been developed to describe active matter at different length and time scales. The diversity of the methods and the challenges in modeling active matter---ranging from molecular motors and cytoskeletal…
Basic principles of mathematical modeling are reviewed in this book, with the focus on physics and its practical applications, and examples of selected mathematical methods are presented. Most of the models have been imported from physics…
This paper develops a conceptual extension of the Kinetic Theory of Active Particles, building upon the framework introduced in [2]. Living systems cannot be adequately described within classical single-scale paradigms, even when refined.…
Studying systems where many individual bodies in motion interact with one another is a complex and interesting area. Simple mechanisms that may be determined for biological, chemical, or physical reasons can lead to astonishingly complex…
We introduce and study a class of active matter models in which we keep track of fuel (stored energy) consumption. They are by construction, thermodynamically consistent. Using these models it is possible for us to observe and follow how…
This paper provides an overview and critical analysis on the modeling and applications of the dynamics of human crowds, where social interactions can have an important influence on the behavioral dynamics of the crowd viewed as a living,…
Scientists investigate the dynamics of complex systems with quantitative models, employing them to synthesize knowledge, to explain observations, and to forecast future system behavior. Complete specification of systems is impossible, so…
This paper proposes a systems approach to social sciences based on mathematical framework derived from a generalization of the mathematical kinetic theory and on theoretical tools of game theory. Social systems are modeled as a living…
In this Chapter, I will explore the use of modeling in order to understand how Science works. I will discuss the modeling of scientific communities, providing a general, non-comprehensive overview of existing models, with a focus on the use…
Mathematical models are increasingly a part of microbiological research. Here, we share our perspective on how modeling advances the discipline by: (i) enforcing logical consistency, (ii) enabling quantitative prediction, (iii) extracting…
Biology is data-rich, and it is equally rich in concepts and hypotheses. Part of trying to understand biological processes and systems is therefore to confront our ideas and hypotheses with data using statistical methods to determine the…