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The models introduced in this paper describe a uniform distribution of plant stems competing for sunlight. The shape of each stem, and the density of leaves, are designed in order to maximize the captured sunlight, subject to a cost for…
Non-equilibrium self-organized patterns formed by particles interacting through competing range interaction are driven over a substrate by an external force. We show that, with increasing driving force, the pre-existed static patterns…
Neuronal networks constitute a special class of dynamical systems, as they are formed by individual geometrical components, namely the neurons. In the existing literature, relatively little attention has been given to the influence of…
The innumerable shapes of plant leaves present a challenge to the explanatory power of biophysical theory. A model is needed that can produce these shapes with a small set of parameters. This paper presents a simple model of leaf shape…
The structural properties of packed soft-core particles provide a platform to understand the cross-pollinated physical concepts in solid-state- and soft-matter physics. Confined on spherical surface, the traditional differential geometry…
The shape of a cell influences and it is influenced by interactions with its neighbouring partners. Here, we introduce a coarse-grained model of non-reciprocal interactions between single-cell organisms to study emergent morphologies during…
Growth pattern dynamics lie at the heart of morphogenesis. Here, we investigate the growth of plant leaves. We compute the conformal transformation that maps the contour of a leaf at a given stage onto the contour of the same leaf at a…
A growing or shrinking disc will adopt a conical shape, its intrinsic geometry characterized by a surplus angle $se$ at the apex. If growth is slow, the cone will find its equilibrium. Whereas this is trivial if $se <= 0$, the disc can fold…
Collective dynamics in proliferating anisotropic particle systems arise from an interplay between growth, division, and mechanical interactions, often mediated by particle shape. In classical models of prolate, rod-like growth, flow-induced…
A lattice $\Lambda$ is said to be an extension of a sublattice $L$ of smaller rank if $L$ is equal to the intersection of $\Lambda$ with the subspace spanned by $L$. The goal of this paper is to initiate a systematic study of the geometry…
Each self-similar dendrite K with a finite self-similar boundary defines a finite acyclic edge-labeled bipartite graph G, called the sprout of K. The paper shows that the sprout G determines the combinatorial properties of the dendrite K…
The optimal shapes attained by contractile cells on adhesive substrates are determined by the interplay between intracellular forces and adhesion with the extracellular matrix. We model the cell as a contractile film bounded by an elastic…
Networks having the geometry and the connectivity of trees are considered as the spatial support of spatiotemporal dynamical processes. A tree is characterized by two parameters: its ramification and its depth. The local dynamics at the…
Eutectic dendrites forming in a model ternary system have been studied using the phase-field theory. The eutectic and one-phase dendrites have similar forms, and the tip radius scales with the interface free energy as for one-phase…
We investigate dendritic sidebranching during crystal growth in an undercooled melt by simulation of a phase-field model which incorporates thermal noise of microscopic origin. As a non-trivial quantitative test of this model, we first show…
In this paper we develop a generalization of foliated manifolds in the context of metric spaces. In particular we study dendritations of surfaces that are defined as maximal atlases of compatible upper semicontinuous local decompositions…
We study how a two-dimensional square sheet of droplets evolves to the preferred triangular lattice. The rearrangement can be induced either by an impurity seed for flat sheets or by curving the sheet. We analyze the propagation of…
We introduce a general theoretical framework to study the shape dynamics of actively growing and remodeling surfaces. Using this framework we develop a physical model for growing bacterial cell walls and study the interplay of cell shape…
Symmetries -- whether explicit, latent, or hidden -- are fundamental to understanding topological materials. This work introduces a prototypical spring-mass model that extends beyond established canonical models, revealing topological edge…
Tip-driven growth processes underlie the development of many plants. To date, tip-driven growth processes have been modelled as an elongating path or series of segments without taking into account lateral expansion during elongation.…