arXiv subjects

James A. Glazier

Publications and source records attributed to James A. Glazier.

24 records · Page 2Linked to original sources

arXiv2006

Viscous instabilities in flowing foams: A Cellular Potts Model approach

The Cellular Potts Model (CPM) succesfully simulates drainage and shear in foams. Here we use the CPM to investigate instabilities due to the flow of a single large bubble in a dry, monodisperse two-dimensional flowing foam. As in experiments in a Hele-Shaw cell, above a threshold velocity the large bubble moves faster than the mean flow. Our simulations reproduce analytical and experimental predictions for the velocity threshold and the relative velocity of the large bubble, demonstrating the utility of the CPM in foam rheology studies.

cond-mat.soft↗

arXiv2005

Solving the Advection-Diffusion Equations in Biological Contexts using the Cellular Potts Model

The Cellular Potts Model (CPM) is a robust, cell-level methodology for simulation of biological tissues and morphogenesis. Both tissue physiology and morphogenesis depend on diffusion of chemical morphogens in the extra-cellular fluid or matrix (ECM). Standard diffusion solvers applied to the cellular potts model use finite difference methods on the underlying CPM lattice. However, these methods produce a diffusing field tied to the underlying lattice, which is inaccurate in many biological situations in which cell or ECM movement causes advection rapid compared to diffusion. Finite difference schemes suffer numerical instabilities solving the resulting advection-diffusion equations. To circumvent these problems we simulate advection-diffusion within the framework of the CPM using off-lattice finite-difference methods. We define a set of generalized fluid particles which detach advection and diffusion from the lattice. Diffusion occurs between neighboring fluid particles by local averaging rules which approximate the Laplacian. Directed spin flips in the CPM handle the advective movement of the fluid particles. A constraint on relative velocities in the fluid explicitly accounts for fluid viscosity. We use the CPM to solve various diffusion examples including multiple instantaneous sources, continuous sources, moving sources and different boundary geometries and conditions to validate our approximation against analytical and established numerical solutions. We also verify the CPM results for Poiseuille flow and Taylor-Aris dispersion.

physics.bio-ph↗

arXiv2003

Dynamics and Topological Aspects of a Reconstructed Two-Dimensional Foam Time Series Using Potts Model on a Pinned Lattice

We discuss a method to reconstruct an approximate two-dimensional foam structure from an incomplete image using the extended Potts mode with a pinned lattice we introduced in a previous paper. The initial information consists of the positions of the vertices only. We locate the centers of the bubbles using the Euclidean distance-map construction and assign at each vertex position a continuous pinning field with a potential falling off as $1/r$. We nucleate a bubble at each center using the extended Potts model and let the structure evolve under the constraint of scaled target areas until the bubbles contact each other. The target area constraint and pinning centers prevent further coarsening. We then turn the area constraint off and let the edges relax to a minimum energy configuration. The result is a reconstructed structure very close to the simulation. We repeated this procedure for various stages of the coarsening of the same simulated foam and investigated the simulation and reconstruction dynamics, topology and area distribution, finding that they agree to good accuracy.

physics.comp-ph↗

arXiv2003

A texture tensor to quantify deformations: the example of two-dimensional flowing foams

In a continuum description of materials, the stress tensor field $\bar{% \barσ}$ quantifies the internal forces the neighbouring regions exert on a region of the material. The classical theory of elastic solids assumes that $\bar{\barσ}$ determines the strain, while hydrodynamics assumes that $\bar{\barσ}$ determines the strain rate. To extend both successful theories to more general materials, which display both elastic and fluid properties, we recently introduced a descriptor generalizing the classical strain to include plastic deformations: the ``statistical strain'', based on averages on microscopic details (``A texture tensor to quantify deformations'' M.Au., Y.J., J.A.G., F.G, companion paper, {\em Granular Matter}, same issue). Here, we apply such a statistical analysis to a two-dimensional foam steadily flowing through a constriction, a problem beyond reach of both theories, and prove that the foam has the elastic properties of a (linear and isotropic) continuous medium.

cond-mat.soft↗

arXiv2003

A texture tensor to quantify deformations

Under mechanical deformation, most materials exhibit both elastic and fluid (or plastic) responses. No existing formalism derived from microscopic principles encompasses both their fluid-like and solid-like aspects. We define the {\it statistical texture tensor} to quantify the intuitive notion of stored deformation. This tensor links microscopic and macroscopic descriptions of the material, and extends the definition of elastic strain.

cond-mat.soft↗

arXiv2000

A Model of Convergent Extension in Animal Morphogenesis

In this paper we argue that the pattern of cell movements in the morphogenetic process known as convergent extension can be understood as a energy minimization process, provided the cell-cell adhesive energy has a certain kind of anisotropy. This single simple property is sufficient cause for the type of cell elongation, alignment, and intercalation of a cellular array that is the characteristic of convergent extension. We describe the type of anisotropy required. We show that the final aspect ratio of the array of cells is independent of the initial configuration and of the degree of cell elongation. We find how it depends on the anisotropy.

physics.bio-ph↗