Striated populations in disordered environments with advection

Chotibut, Thiparat; Nelson, David R.; Succi, Sauro

doi:10.1016/j.physa.2016.08.059

Cited by 10 publications

(11 citation statements)

References 54 publications

(81 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In some models, an advective term is added to the FKPP equation, such that reactions, advection and diffusion occur simultaneously. This can give rise to rich phenomenology -for instance, when disorder is involved [3,8], or when reactions release heat [9], causing the coupling between the concentration of reacting species and the advective flow field. In other instances, however, advection takes place in a separate competing transport channel, often associated with a flow over a substrate on which reaction-diffusion processes take place.…”

Section: Introductionmentioning

confidence: 99%

Fragility of reaction-diffusion models with respect to competing advective processes

2017

View full text Add to dashboard Cite

We study the coupling of a Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) equation to a separate, advection-only transport process. We find that an infinitesimal coupling can cause a finite change in the speed and shape of the reaction front, indicating the fragility of the FKPP model with respect to such a perturbation. The front dynamics can be mapped to an effective FKPP equation only at sufficiently fast diffusion or large coupling strength. We also discover conditions when the front width diverges, and when its speed is insensitive to the coupling. At zero diffusion in our mean-field description, the downwind front speed goes to a finite value as the coupling goes to zero.

show abstract

Section: Introductionmentioning

confidence: 99%

Fragility of reaction-diffusion models with respect to competing advective processes

2017

View full text Add to dashboard Cite

show abstract

“…(5) is validated. On the other hand, Succi and his coworkers analyzed the FKPP equation with nonzero flow-flux, namely, δu = 0 using the lattice Boltzmann method (LBM) [25,26]. The application of the LBM to the FKPP equation, which demonstrates the epidemic spread, is interesting issue in our future study, definitely.…”

Section: Analogy To Fkpp Equationmentioning

confidence: 95%

Kinetic Modeling of Local Epidemic Spread and Its Simulation

Yano

2017

J Sci Comput

View full text Add to dashboard Cite

The local epidemic spread in physical space is modeled using the kinetic equation. In particular, the infection occurs via the binary interaction between the uninfected and infected individuals. Then, the local epidemic spread can be modeled on the basis of the stochastic Boltzmann type equation. In this paper, the normalized virus titer inside the infected human body is defined as the function of the elapsed time, which is measured from the infection time. Consequently, the probability of the infection at the binary human interaction increases, as the normalized virus titer inside the human body increases, whereas the normalized virus titer inside the infected human body decreases, after the normalized virus titer reaches to its maximum value, namely, unity, in the characteristic time. Numerical results indicate that the propagation speed of the boundary between the infected and uninfected domains depends on such a characteristic time, strongly, when the Knudsen number and temperature are fixed. Such a dependency of the propagation speed of the boundary between the infected and uninfected domains on the characteristic time can be described by the Fisher-Kolmogorov-Petrovsky-Piscounov equation which is introduced from the stochastic Boltzmann type equation. Finally, we consider three types of the human behavior as plausible actions to the local epidemic spread.

show abstract

“…For sufficiently strong flows such that α > µ, there is a "thinning catastrophe", see Figure 10d), such that the colony population collapses at long times. In this limit, of course, the discrete nature of the cells making up the colony, neglected in Eqs (15) and (19), becomes important. Finally, we check the qualitative agreement between this simplified model and the experiments by determining the colony expansion rate during the superlinear growth regime (t < t * ) as a function of substrate viscosity.…”

Section: Model Coupling Growth With Dilational Flowmentioning

confidence: 99%

“…Microorganism growing on agar plates cannot be advected as the underlying substrate is a solid, mimicking expansions on land. Although investigated theoretically [16][17][18][19], few laboratory systems exist to systematically study the interplay between the transport by fluid flow and spatial population dynamics. In this paper, we introduce a novel experimental system to grow microbial range expansions on the surface of a nutrient-rich fluid 10 4 to 10 5 times more viscous than water.…”

Section: Introductionmentioning

confidence: 99%

Microbial Range Expansions on Liquid Substrates

et al. 2019

Self Cite

View full text Add to dashboard Cite

Despite the importance that fluid flow plays in transporting and organizing populations, few laboratory systems exist to systematically investigate the impact of advection on their spatial evolutionary dynamics. To address this problem, we study the morphology and genetic spatial structure of microbial colonies growing on the surface of a nutrient-laden fluid 10 4 to 10 5 times more viscous than water in Petri dishes; the extreme but finite viscosity inhibits undesired thermal convection and allows populations to effectively live at the air-liquid interface due to capillary forces. We discover that S. cerevisiae (baker's yeast) growing on a viscous liquid behave like "active matter": they metabolically generate fluid flows many times larger than their unperturbed colony expansion speed, and that flow, in return, can dramatically impact their colony morphology and spatial population genetics. We show that yeast cells generate fluid flows by consuming surrounding nutrients and decreasing the local substrate density, leading to misaligned fluid pressure and density contours, which ultimately generates vorticity via a thresholdless baroclinic instability. Numerical simulations with experimentally measured parameters demonstrate that an intense vortex ring is produced below the colony's edge and quantitatively predict the observed flow. As the viscosity of the substrate is lowered and the self-induced flow intensifies, we observe three distinct morphologies: at the highest viscosity, cell proliferation and movement produces compact circular colonies similar to those grown on hard agar plates except with a stretched regime of exponential expansion, intermediate viscosities give rise to compact colonies with "fingers" that are usually monoclonal and are ripped away to break into smaller cell clusters, and at the lowest viscosity, the expanding colony breaks up into many genetically-diverse, mutually repelling, island-like fragments of yeast colonies that can colonize an entire 94 mm-diameter Petri dish within 36 hours. We propose a simple phenomenological model in the spirit of the lubrication approximation that predicts the early colony dynamics. Our results provide rich opportunities for future investigations and suggest that microbial range expansions on viscous fluids can provide a useful framework to examine the interplay between fluid flow and spatial population genetics. arXiv:1812.09797v1 [cond-mat.soft]

show abstract

Striated populations in disordered environments with advection

Cited by 10 publications

References 54 publications

Fragility of reaction-diffusion models with respect to competing advective processes

Fragility of reaction-diffusion models with respect to competing advective processes

Kinetic Modeling of Local Epidemic Spread and Its Simulation

Microbial Range Expansions on Liquid Substrates

Contact Info

Product

Resources

About