Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · physics/9706008

Mean-field analysis of a dynamical phase transition in a cellular automaton model for collective motion

H. J. Bussemaker·A. Deutsch·E. Geigant
View original source ↗Read source document ↗Export metadata ↓

Abstract

A cellular automaton model is presented for random walkers with biologically motivated interactions favoring local alignment and leading to collective motion or swarming behavior. The degree of alignment is controlled by a sensitivity parameter, and a dynamical phase transition exhibiting spontaneous breaking of rotational symmetry occurs at a critical parameter value. The model is analyzed using nonequilibrium mean field theory: Dispersion relations for the critical modes are derived, and a phase diagram is constructed. Mean field predictions for the two critical exponents describing the phase transition as a function of sensitivity and density are obtained analytically.

Explore related subjects

physics.bio-phcond-mat.stat-mech

Keep this discovery

BibTeXRIS

H. J. Bussemaker, A. Deutsch, E. Geigant. 1997-09-05. Mean-field analysis of a dynamical phase transition in a cellular automaton model for collective motion. https://doi.org/10.1103/physrevlett.78.5018

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Multiscale retinal flow on a spherical cap of varying aperture

Modelling retinal haemodynamics is crucial for understanding retinal microcirculation but is computationally demanding because it involves coupling between the vasculature and surrounding tissue across multiple scales. This computational burden has been substantially alleviated by a recent analytic solution on the planar disc that enables lumping the capillary bed and surrounding tissue into an effective resistor. However, that formulation treats the retina as a flat surface, whereas the retina is a curved surface with a finite anterior aperture. In this work, we develop a nontrivial and physiologically necessary extension to spherical-cap tissue domains with varying apertures, where surface curvature and finite-aperture boundaries complicate solving coupled Darcy equations on a curved manifold. Using a stereographic projection and a decoupling transformation, we derive an analytic solution for the capillary-tissue system on the spherical cap that represents flow in both the capillary bed and interstitial tissue more realistically while retaining the efficient resistor formulation, a key advantage of the planar-disc formulation. This solution is coupled to one-dimensional (1D) arteriolar and venular flows to obtain a multiscale description of retinal haemodynamics. Using a vasculature model designed to capture retinal vascular features, we show that the multiscale model's predictions are consistent with experimental data. We further explore aperture effects using both a fixed hemispherical vasculature and aperture-dependent vasculature. The aperture affects retinal haemodynamics mainly through changes in the constructed vasculature itself, whereas the surface-averaged pressures and relative terminal flow distributions remain nearly unchanged. This framework provides a foundation for studying retinal pathophysiology on more anatomically realistic domains.

physics.bio-ph↗
arXiv2026

Double-well potentials and crucial estimations in nonlinear dynamics of microtubules

In the present work, we study the two-component model of microtubules, the basic components of the eukaryotic cytoskeleton. We introduce a couple of estimations, which tremendously simplified the model. The paper is devoted to tangential oscillations of dimers, but we explain that the model can explain the radial oscillations as well. Finally, we study the stability of all solutions of differential equations, describing the dynamics of the microtubules.

physics.bio-ph↗
arXiv2026

A thermodynamically consistent framework for finite growth of multi-constituent mixtures with application to tumor growth

Biological tissues grow by continuously producing, transporting, and reorganizing multiple interacting constituents. These processes are intrinsically coupled to finite deformation and residual stress. Existing models typically capture either finite growth kinematics or multi-constituent transport, but rarely both within a thermodynamically consistent setting. In particular, existing approaches do not consistently link the volume created by finite growth to the mass produced for each individual constituent. In this work, we develop a general continuum framework that unifies finite growth kinematics and multiphase mixture theory for fully saturated multi-constituent mixtures containing an arbitrary number of dilute dissolved solutes. Formulated in a solid-skeleton-based description, the framework rests on constituent-wise balance laws and a free-energy dissipation principle, from which thermodynamically admissible constitutive closures are derived for all mass-exchange, transport, reaction, and growth processes. The central novelty of the framework is a coupling between growth-induced volume creation and constituent mass production, expressed through volume accumulation fractions that distribute the newly created volume among the constituents while preserving saturation. We cast the resulting model in a total Lagrangian mixed weak form and specialize the general theory to a four-constituent, two-solute model of avascular tumor growth that couples nutrient transport, waste production, phenotype transitions between proliferative, hypoxic, and necrotic cells, volume growth, elastic deformation, and growth-induced residual stress. The model is implemented within a finite element setting and its capabilities are demonstrated on representative benchmark problems.

physics.bio-ph↗