Related papers: Dynamical Riemannian Geometry and Plant Growth
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…
Riemannian metric on real 2n-dimensional space associated with the equation governing complex diffusion of pure states of an open quantum system is introduced and studied. Examples of a qubit under the influence of dephasing and thermal…
Tumor growth has a number of features in common with a physical process known as molecular beam epitaxy. Both growth processes are characterized by the constraint of growth development to the body border, and surface diffusion of…
Growth patterns of complex systems predict how they change in sizes, numbers, masses, etc. Understanding growth is important, especially for many biological, ecological, urban, and socioeconomic systems. One noteworthy growth behavior is…
We consider a generalization of the classical logistic growth model introducing more than one inflection point. The growth, called multi-sigmoidal, is firstly analyzed from a deterministic point of view in order to obtain the main…
In the past 50 years, the formalism of L-systems has been successfully used and developed to model the growth of filamentous and branching biological forms. These simulations take place in classical 2-D or 3-D Euclidean spaces. However,…
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…
Learning 3D parametric shape models of objects has gained popularity in vision and graphics and has showed broad utility in 3D reconstruction, generation, understanding, and simulation. While powerful models exist for humans and animals,…
In this paper, we analyse a model for the growth of three-dimensional walled cells. In this model the biomechanical expansion of the cell is coupled with the geometry of its wall. We consider that the density of building material depends on…
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…
Complex systems have motivated continuing interest from the scientific community, leading to new concepts and methods. Growing systems represent a case of particular interest, as their topological, geometrical, and also dynamical properties…
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…
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…
The Riemannian geometry is one of the main theoretical pieces in Modern Mathematics and Physics. The study of Riemann Geometry in the relevant literature is performed by using a well defined analytical path. Usually it starts from the…
The Riemannian geometry of elastica in one and two dimensions is considered. An example is given of the deflexion or Frenet curvature of the elastic filament rod where the Riemannian curvature vanishes, since the curve is one dimensional.…
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…
Shape analysis and compuational anatomy both make use of sophisticated tools from infinite-dimensional differential manifolds and Riemannian geometry on spaces of functions. While comprehensive references for the mathematical foundations…
The Dynamic Template model of biological cell membranes and the cytoplasm as spatially organised fluid layers is extended to plant cells, and is shown to offer a feasible shear driven mechanism for the co-alignment of internal and external…
The Hamiltonian dynamics of classical planar Heisenberg model is numerically investigated in two and three dimensions. By considering the dynamics as a geodesic flow on a suitable Riemannian manifold, it is possible to analytically estimate…
The three-dimensional shapes of thin lamina such as leaves, flowers, feathers, wings etc, are driven by the differential strain induced by the relative growth. The growth takes place through variations in the Riemannian metric, given on the…