Biological advection and cross-diffusion with parameter regimes

Chung, Jaywan; Kim, Yong Jung; Kwon, Oh‐Min; Yoon, Changwook

doi:10.3934/math.2019.6.1721

Cited by 8 publications

(8 citation statements)

References 16 publications

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“…We return to the turning operator (9). As expected, due to assumption A2, we observe that the total cell density during turning will be conserved:…”

supporting

confidence: 62%

“…An example of adaptability in a biological context is provided in [9,8], addressing starvationdriven diffusion. Here, starvation induces the organism to increase motility and find a better environment, even if it is not known where that may be, i .e.…”

Section: Comparison To Diffusion Of Passive Particlesmentioning

confidence: 99%

“…the migration is unbiased. We further note that the three forms of diffusion equation ( 55),(57),(58) can be derived from space-jump processes, where variation in jumping depends on environment assessment of the current location, between locations or the destination [31,9,29], with spatially homogeneous jumping times. When both the jumping time and length are spatially heterogeneous, a mixed structure similar to (27) arises.…”

Section: Comparison To Diffusion Of Passive Particlesmentioning

confidence: 99%

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Direction-Dependent Turning Leads to Anisotropic Diffusion and Persistence

Loy¹,

Hillen²,

Painter³

2021

Preprint

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Cells and organisms follow aligned structures in their environment, a process that can generate persistent migration paths. Kinetic transport equations are a popular modelling tool for describing biological movements at the mesoscopic level, yet their formulations usually assume a constant turning rate. Here we relax this simplification, extending to include a turning rate that varies according to the anisotropy of a heterogeneous environment. We extend known methods of parabolic and hyperbolic scaling and apply the results to cell movement on micro-patterned domains. We show that inclusion of orientation dependence in the turning rate can lead to persistence of motion in an otherwise fully symmetric environment, and generate enhanced diffusion in structured domains.

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“…We return to the turning operator (9). As expected, due to assumption A2, we observe that the total cell density during turning will be conserved:…”

supporting

confidence: 62%

Section: Comparison To Diffusion Of Passive Particlesmentioning

confidence: 99%

Section: Comparison To Diffusion Of Passive Particlesmentioning

confidence: 99%

See 1 more Smart Citation

Direction-Dependent Turning Leads to Anisotropic Diffusion and Persistence

Loy¹,

Hillen²,

Painter³

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…An example of adaptability in a biological context is provided in [11,10], addressing starvation-driven diffusion. Here, starvation induces the organism to increase motility and find a better environment, even if it is not known where that may be, that is, the migration is unbiased.…”

Section: Comparison To Diffusion Of Passive Particlesmentioning

confidence: 99%

“…Here, starvation induces the organism to increase motility and find a better environment, even if it is not known where that may be, that is, the migration is unbiased. We further note that the three forms of diffusion equation (4.3),(4.5) and (4.6) can be derived from space-jump processes, where variation in jumping depends on environment assessment of the current location, between locations or the destination [33,11,31], with spatially homogeneous jumping times. When both the jumping time and length are spatially heterogeneous, a mixed structure similar to (3.11) arises.…”

Section: Comparison To Diffusion Of Passive Particlesmentioning

confidence: 99%

Direction-dependent turning leads to anisotropic diffusion and persistence

Loy¹,

Hillen

Painter

2021

Eur. J. Appl. Math

View full text Add to dashboard Cite

Cells and organisms follow aligned structures in their environment, a process that can generate persistent migration paths. Kinetic transport equations are a popular modelling tool for describing biological movements at the mesoscopic level, yet their formulations usually assume a constant turning rate. Here we relax this simplification, extending to include a turning rate that varies according to the anisotropy of a heterogeneous environment. We extend known methods of parabolic and hyperbolic scaling and apply the results to cell movement on micropatterned domains. We show that inclusion of orientation dependence in the turning rate can lead to persistence of motion in an otherwise fully symmetric environment and generate enhanced diffusion in structured domains.

show abstract