Related papers: Leaf growth is conformal
An evolutionary tree is a rooted tree where each internal vertex has at least two children and where the leaves are labeled with distinct symbols representing species. Evolutionary trees are useful for modeling the evolutionary history of…
We derive a course grained, continuum model of the 2D vertex model, applicable for different underlying geometries, and allowing for analytical analysis of an otherwise numerical model. Using a geometric approach and out--of--equilibrium…
The main result is the identification of the orthogonal complement of the subalgebra of conformal vector field inside the algebra of all vector fields of a compact flat 2-manifold. As a fundamental tool, the complete Hodge decomposition for…
Estimation of a single leaf area can be a measure of crop growth and a phenotypic trait to breed new varieties. It has also been used to measure leaf area index and total leaf area. Some studies have used hand-held cameras, image processing…
Plant phenotyping (Guo et al. 2021; Pieruschka et al. 2019) focuses on studying the diverse traits of plants related to the plants' growth. To be more specific, by accurately measuring the plant's anatomical, ontogenetical, physiological…
We propose and test a model that describes the morphology of cities, the scaling of the urban perimeter of individual cities, and the area distribution of systems of cities. The model is also consistent with observable urban growth…
We present a model for mechanically-induced pattern formation in growing biological tissues and discuss its application to the development of leaf venation networks. Drawing an analogy with phase transitions in solids, we use a phase field…
An important question in biology is how the relative size of different organs is kept nearly constant during growth of an animal. This property, called proportionate growth, has received increased attention in recent years. We discuss our…
Understanding how growth induces form is a longstanding biological question. Many studies concentrated on the shapes of plant cells, fungi or bacteria. Some others have shown the importance of the mechanical properties of bacterial walls…
This paper proposes a novel framework for fluorescence plant video processing. The plant research community is interested in the leaf-level photosynthetic analysis within a plant. A prerequisite for such analysis is to segment all leaves,…
We investigate the evolution of matter density perturbations within a fractional cosmological framework inspired by fractal space-time constructions in field theory, where a deformation of the integration measure induces non-locality and…
Desorption of deposited species plays a role in determining the evolution of surface morphology during crystal growth when the desorption time constant is short compared to the time to diffuse to a defect site, step edge or kink. However,…
The growth of several biological tissues is known to be controlled in part by local geometrical features, such as the curvature of the tissue interface. This control leads to changes in tissue shape that in turn can affect the tissue's…
We study a model of growing planar tree graphs where in each time step we separate the tree into two components by splitting a vertex and then connect the two pieces by inserting a new link between the daughter vertices. This model…
Vegetation patterns, a natural phenomenon observed worldwide, are typically driven by spatially distributed feedback. However, the spatial colonization mechanisms of clonal plants, driven by the growth of a rhizome, are usually not…
Plant organ outgrowth superficially appears like the continuous mechanical deformation of a sheet of cells. Yet, how precisely cells as individual mechanical entities can act to morph a tissue reliably and efficiently into three dimensions…
Plants are a paradigm for active shape control in response to stimuli. For instance, it is well-known that a tilted plant will eventually straighten vertically, demonstrating the influence of both an external stimulus, gravity, and an…
The main intention of the paper is to investigate an osculating curve under the conformal map. We obtain a sufficient condition for the conformal invariance of an osculating curve. We also find an equivalent system of a geodesic curve under…
The intentional growth of metastable surface structures of organic molecules adsorbed on inorganic substrates is a challenging task. It is usually unclear which kinetic mechanism leads to the metastable surface polymorph after a deposition…
Flexible broad leaves are thought to reconfigure in the wind and water to reduce the drag forces that act upon them. Simple mathematical models of a flexible beam immersed in a two-dimensional flow will also exhibit this behavior. What is…