Related papers: Leaf growth is conformal
This paper investigates the motion of falling leaves through modeling using papers and the corresponding data collected from more than four thousands experiments. Two series of experiments were designed in order to study the relationship…
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,…
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.…
We model evolution of plants in a world, made up of different locations, with multiple environments (mutually exclusive and collectively exhaustive subsets of locations). Each environment (landmass) has temperature, rainfall, and other…
Coordinated cellular movements are key processes in tissue morphogenesis. Using a cell-based modeling approach we study the dynamics of epithelial layers lining surfaces with constant and varying curvature. We demonstrate that extrinsic…
The self-organization of cells into complex tissues relies on a tight coordination of cell behavior. Identifying the cellular processes driving tissue growth is key to understanding the emergence of tissue forms and devising targeted…
We present a classical conformal field theory on an arbitrary two-dimensional spacetime background. The dynamical object is a space-filling string, and the evolution may be thought as occurring on the manifold of the conformal group. The…
In this paper we study planar morphs between straight-line planar grid drawings of trees. A morph consists of a sequence of morphing steps, where in a morphing step vertices move along straight-line trajectories at constant speed. We show…
In this article, we propose a general framework to study the dynamics and topology of cellular networks that capture the geometry of cell packings in two-dimensional tissues. Such epithelia undergo large-scale deformation during…
Understanding the rules underlying organismal development is a major unsolved problem in biology. Each cell in a developing organism responds to signals in its local environment by dividing, excreting, consuming, or reorganizing, yet how…
Plant reflectance spectra - the profile of light reflected by leaves across different wavelengths - supply the spectral signature for a species at a spatial location to enable estimation of functional and taxonomic diversity for plants. We…
We produce examples of codimension one foliations of the Euclidean and hyperbolic planes with bounded geometry which are topologically products, but for which leaves are non-recursively distorted. That is, the function which compares…
Collective cell motions underlie structure formation during embryonic development. Tissues exhibit emergent multicellular characteristics such as jamming, rigidity transitions, and glassy dynamics, but there remain questions about how those…
We present a framework for shape matching in computational anatomy allowing users control of the degree to which the matching is diffeomorphic. This control is given as a function defined over the image and parameterises the template…
We consider the set of all 2-step recurrences (difference equations) that are given by linear fractional maps. These give birational maps of the plane. We determine the degree growth of these birational maps. We find the all the maps in…
We present a detailed systematical theoretical analysis of the post-growth processes occurring in nanofractals grown on surface. For this study we developed a method which accounts for the internal dynamics of particles in a fractal. We…
In this work, a new model for macroscopic plant tissue growth based on dynamical Riemannian geometry is presented. We treat 1D and 2D tissues as continuous, deformable, growing geometries for sizes larger than 1mm. The dynamics of the…
The process of morphogenesis, which can be defined as an evolution of the form of an organism, is one of the most intriguing mysteries in the life sciences. It is clear, that gene expression patterns cannot explain the development of the…
Nutation is an oscillatory movement that plants display during their development. Despite its ubiquity among plants movements, the relation between the observed movement and the underlying biological mechanisms remains unclear. Here we show…
The article provides a pedagogical review aimed at graduate students in materials science, physics, and applied mathematics, focusing on recent developments in the subject. Following a brief summary of concepts from complex analysis, the…