Related papers: Growth Models for Tree Stems and Vines
The paper studies a PDE model for the growth of a tree stem or a vine, having the form of a differential inclusion with state constraints. The equations describe the elongation due to cell growth, and the response to gravity and to external…
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…
Shape is one of the important characteristics for the structures observed in living organisms. Whereas biologists have proposed models where the shape is controlled on a molecular level [1], physicists, following Turing [2] and d'Arcy…
Regardless of a system's complexity or scale, its growth can be considered to be a spontaneous thermodynamic response to a local convergence of down-gradient material flows. Here it is shown how growth can be constrained to a few distinct…
Heterogeneous growth plays an important role in the shape and pattern formation of thin elastic structures ranging from the petals of blooming lilies to the cell walls of growing bacteria. Here we address the stability and regulation of…
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…
We discuss solution algorithms for calibrating a tumor growth model using imaging data posed as a deterministic inverse problem. The forward model consists of a nonlinear and time-dependent reaction-diffusion partial differential equation…
A new model for biological growth is introduced that couples the geometry of an organism (or part of the organism) to the flow and deposition of material. The model has three dynamical variables (a) a Riemann metric tensor for the geometry,…
Using formal asymptotic methods we derive a free boundary problem representing one of the simplest mathematical descriptions of the growth and death of a tumour or other biological tissue. The mathematical model takes the form of a closed…
I consider how cell shape and environmental geometry affect the rate of nutrient capture and the consequent maximum growth rate of a cell, focusing on rod-like species like \textit{E.\ coli}. Simple modeling immediately implies that it is…
We consider a free boundary problem for a system of PDEs, modeling the growth of a biological tissue. A morphogen, controlling volume growth, is produced by specific cells and then diffused and absorbed throughout the domain. The geometric…
In this paper, the growth-induced bending deformation of a thin hyperelastic plate is studied. For a plane-strain problem, the governing PDE system is formulated, which is composed of the mechanical equilibrium equations, the constraint…
We consider a model for the dynamics of active cells interacting with their quiescent counterparts under the influence of acidity characterized by proton concentration. The active cells perform nonlinear diffusion and infer proliferation or…
In this article we consider a class of state-dependent delay differential equations which is modelling the dynamics of the number of adult trees in forests. We prove the boundedness of solutions for a single species model as well as a…
A non-local model describing the growth of a tree-like transportation network with given allocation rules is proposed. In this model we focus on tree like networks, and the network transports the very resource it needs to build itself. Some…
Cell division is a process that involves many biochemical steps and complex biophysical mechanisms. To simplify the understanding of what triggers cell division, three basic models that subsume more microscopic cellular processes associated…
Dynamic regression trees are an attractive option for automatic regression and classification with complicated response surfaces in on-line application settings. We create a sequential tree model whose state changes in time with the…
We investigate a model for the accretive growth of an elastic solid. The reference configuration of the body is accreted in its normal direction, with space- and deformation-dependent accretion rate. The time-dependent reference…
Plants have developed different tropisms: in particular, they re-orient the growth of their branches towards light (phototropism) or upwards (gravitropism). How these tropisms affect the shape of a tree crown remains unanswered. We address…
In this paper, a two-dimensional model for the growth of multi-layer tumors is presented. The model consists of a free boundary problem for the tumor cell membrane and the tumor is supposed to grow or shrink due to cell proliferation or…