相关论文: Decorated vertices with 3-edged cells in 2D foams:…

Vertex models have been extensively used for simulating the evolution of multicellular systems, and have given rise to important global properties concerning their macroscopic rheology or jamming transitions. These models are based on the…

In order to describe two-dimensionally packed cells in epithelial tissues both mathematically and physically, there have been developed several sorts of geometrical models, such as the vertex model, the finite element model, the…

The elegant properties of conformal mappings, when applied to two dimensional (2D) lattices, find interesting applications in 2D foams and other cellular or close packed structures. In particular the 2D honeycomb (whose dual is the…

The mechanics of a foam typically depends on the bubble geometry, topology, and the material at hand, be it metallic or polymeric, for example. While the foam energy functional for each bubble is typically minimization of surface area for a…

After a brief introduction to several variational problems in the study of shapes of thin thickness structures, we deal with variational problems on 2-dimensional surface in 3-dimensional Euclidian space by using exterior differential…

The use of floating bipolar electrodes in copper electro-winning cells represents an emerging technology that promises economic and operational impacts. This article presents a computational tool designed for the simulation and analysis of…

In this paper we characterize foams and tetrahedral structures in a unified way, by a simplified representation of both that conserves the system topology. The paper presents a workflow for an automated characterization of the topology of…

A liquid foam in contact with a solid surface forms a two-dimensional foam on the surface. We derive the equilibrium equations for this 2D foam when the solid surface is curved and smooth, generalising the standard case of flat Hele Shaw…

In a recent series of papers [1--3], a statistical model that accounts for correlations between topological and geometrical properties of a two-dimensional shuffled foam has been proposed and compared with experimental and numerical data.…

The Vertex Model for epithelia models the apical surface of the tissue by a tiling, with polygons representing cells and edges representing cell-cell junctions. The mechanics are described by an energy governed by deviations from a target…

The equilibrium conditions impose nontrivial geometrical constraints on the configurations that a two-dimensional foam can attain. In the first place, the three centers of the films that converge to a vertex have to be on a line, i.e. all…

Considering the popularity of two-dimensional particle-in-cell simulations, a 2D model of plasma wakefield in the strongly nonlinear (bubble) regime in transversely non-uniform plasma is developed. A differential equation for the boundary…

A 2D foam can be characterised by its distribution of bubble areas, and of number of sides. Both distributions have an average and a width (standard deviation). There are therefore at least two very different ways to characterise the…

We explore the stability of floating objects through mathematical modeling and experimentation. Our models are based on standard ideas of center of gravity, center of buoyancy, and Archimedes' Principle. We investigate a variety of floating…

We investigate connections between the continuum and atomistic descriptions of deformable crystals, using certain interesting results from number theory. The energy of a deformed crystal is calculated in the context of a lattice model with…

Vertex Models, as used to describe cellular tissue, have an energy controlled by deviations of each cell area and perimeter from target values. The constrained nonlinear relation between area and perimeter leads to new mechanical response.…

This review introduces the elasticity theory of two-dimensional crystals and nematic liquid crystals on curved surfaces, the energetics of topological defects (disclinations, dislocations and pleats) in these ordered phases, and the…

We investigate the influence of self-energy diagrams beyond the two-particle vertex level within dual fermion theory. Specifically, we calculate the local three-particle vertex and construct from it selected dual fermion self-energy…

Open-cell graphitic foams were fabricated by chemical vapor deposition using nickel templates and their compressive responses were measured over a range of relative densities. The mechanical response required an interpretation in terms of a…

We propose a continuum model to describe the molecular alignment in thin nematic shells. By contrast with previous accounts, the two-dimensional free energy, aimed at describing the physics of thin films of nematics deposited on curved…