An age-structured continuum model for myxobacteria

DOI10.1142/S0218202518400043zbMath1414.35234arXiv1702.06939OpenAlexW2590967790MaRDI QIDQ4630558

Hui Yu, Angelika Manhart, Pierre Degond

Publication date: 27 March 2019

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.06939

zbMATH Keywords

hydrodynamic limitrefractory periodmyxobacteriadiffusion correctionself-propelled particlesgeneralized collision invariantnematic alignmentwave formation

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Interacting particle systems in time-dependent statistical mechanics (82C22) PDEs in connection with biology, chemistry and other natural sciences (35Q92) First-order nonlinear hyperbolic equations (35L60) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Developmental biology, pattern formation (92C15) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Transport processes in time-dependent statistical mechanics (82C70) Classical dynamic and nonequilibrium statistical mechanics (general) (82C05) Computational methods for problems pertaining to biology (92-08) Animal behavior (92D50) Fokker-Planck equations (35Q84)

Related Items (11)

Emergent behaviors of the Justh-Krishnaprasad model with uncertain communications ⋮ Cauchy Theory for General Kinetic Vicsek Models in Collective Dynamics and Mean-Field Limit Approximations ⋮ Large-scale dynamics of self-propelled particles moving through obstacles: model derivation and pattern formation ⋮ On the stochastic robustness of complete clustering predictability for a first‐order consensus model ⋮ Reversal collision dynamics ⋮ Stochastic persistency of nematic alignment state for the Justh–Krishnaprasad model with additive white noises ⋮ Challenges in active particles methods: Theory and applications ⋮ Counter-propagating wave patterns in a swarm model with memory ⋮ Kinetic modelling of colonies of myxobacteria ⋮ A continuum model for nematic alignment of self-propelled particles ⋮ Nematic alignment of self-propelled particles: From particle to macroscopic dynamics

Cites Work

• Topological interactions in a Boltzmann-type framework
• Mean-field limit for the stochastic Vicsek model
• Hyperbolic and kinetic models for self-organized biological aggregations and movement: a brief review
• A continuum model for nematic alignment of self-propelled particles
• Double milling in self-propelled swarms from kinetic theory
• A nonlinear structured population model of tumor growth with quiescence
• A non-local model for a swarm
• Emerging patterns in a hyperbolic model for locally interacting cell systems
• Wavenumber selection in coupled transport equations
• State transitions and the continuum limit for a 2D interacting, self-propelled particle system
• Continuum model for linked fibers with alignment interactions
• HYDRODYNAMICS OF SELF-ALIGNMENT INTERACTIONS WITH PRECESSION AND DERIVATION OF THE LANDAU–LIFSCHITZ–GILBERT EQUATION
• ON THE MATHEMATICAL THEORY OF THE DYNAMICS OF SWARMS VIEWED AS COMPLEX SYSTEMS
• A CONTINUUM MODEL FOR ALIGNMENT OF SELF-PROPELLED PARTICLES WITH ANISOTROPY AND DENSITY-DEPENDENT PARAMETERS
• Numerical Simulations of a Nonconservative Hyperbolic System with Geometric Constraints Describing Swarming Behavior
• Evolution of wealth in a non-conservative economy driven by local Nash equilibria
• DIFFUSION IN A CONTINUUM MODEL OF SELF-PROPELLED PARTICLES WITH ALIGNMENT INTERACTION
• Nonequilibrium statistical mechanics of self-propelled hard rods
• A multi-layer model for self-propelled disks interacting through alignment and volume exclusion
• CONTINUUM LIMIT OF SELF-DRIVEN PARTICLES WITH ORIENTATION INTERACTION
• Hydrodynamic equations for self-propelled particles: microscopic derivation and stability analysis
• A Boltzmann model for rod alignment and schooling fish
• A new flocking model through body attitude coordination
• Dynamics of a structured neuron population

This page was built for publication: An age-structured continuum model for myxobacteria