Reaction processes among self-propelled particles

Abstract

We study a system of self-propelled disks that perform run-and-tumble motion, where particles can adopt more than one internal state. One of those internal states can be transmitted to another particle if the particle carrying this state maintains physical contact with another particle for a finite period of time. We refer to this process as a reaction process and to the different internal states as particle species making an analogy to chemical reactions. The studied system may fall into an absorbing phase, where due to the disappearance of one of the particle species no further reaction can occur or remain in an active phase where particles constantly react. Combining individualbased simulations and mean-field arguments, we study the dependence of the equilibrium densities of particle species with motility parameters, specifically the active speed v 0 and tumbling frequency λ. We find that the equilibrium densities of particle species exhibit two very distinct, non-trivial scaling regimes with v 0 and λ depending on whether the system is in the so-called ballistic or diffusive regime. Our mean-field estimates lead to an effective renormalization of reaction rates that allow building the phase-diagram v 0 -λ that separates the absorbing and active phase. We find an excellent agreement between numerical simulations and estimates. This study is a necessary step to an understanding of phase transitions into an absorbing state in active systems and sheds light on the spreading of information/signaling among moving elements.

Contagion dynamics in self-organized systems of self-propelled agents

“…We show that different collective states characterized by different time-dependent, self-organized spatial structures result in dramatically different contagion dynamics, both in terms of the overall magnitude of the outbreaks and of the detailed spatial characteristics of the spreading process. Our results also confirm that the importance of the contagion time-scale in agent-based contagion process, as discussed [13], in a more general and complex setting.…”

“…Therefore, core parameters of a SIR-contagion process: contact rate and contact duration are in fact emergent properties of the self-organized, spatial dynamics. This has been investigated for example in gas-like systems of self-propelled agents [12,13,14], where among other it was shown that contact rate and contact duration may be affected in different ways by the speed of individual agents, leading to nontrivial dependence of the contagion dynamics on this single movement parameter [13].…”

Understanding contagion dynamics through microscopic processes in active Brownian particles

“…Second, if the WCA potential does not drastically change the speed v 0 , we approximately obtain that �|� v ij rel | 2 � ≈ 2v 2 0 since �v 2 i � ≈ v 2 0 . By considering the total area swept for N particles in a time interval τ c as A sw = N(2R + πR 2 ) , we define the maximum contagion probability p c = A sw /A = 1 , and using the relation = √ 2v 0 τ c , we recover the analytical expression of the contagion rate given in (2).…”

“…Nevertheless, a more realistic model must consider the mobility of infectious particles and particle density within its environment. In this direction, self-propelled particles 2 , 3 , the random motion of non-interacting particles 4 , 5 , cellular automaton 6 , 7 , dynamical density functional theory approach 8 , and reaction–diffusion models 9 , 10 have been proposed to introduce the spatial motion of infectious particles. As a matter of universality, active matter models are intuitive and are extensively used to describe a wide range of biological processes ranging from bacteria motion to animal movement 11 .…”

“…Here, we explore infection propagation through active vectors that carry an internal state using an AM based model with underlying microscopic processes. The infection occurs through horizontal transmission when a susceptible agent comes into contact with an infected agent such as viruses propagating in salmon hatcheries, honeycombs 33 , 34 , or in mesoscale organisms such as cats with influenza or humans carrying flu 2 , 3 , 35 .

Figure 1 Schematic representation of the AM model based on ABP.

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