Related papers: Leaf growth is conformal
Roots provide basic functions to plants such as water/nutrient uptake and anchoring in soil. The growth and development of root systems contribute to colonizing the surrounding soil and optimizing the access to resources. It is usually…
Superficial (two dimensional) crack patterns appear when a thin layer of material elastically attached to a substrate contracts. We study numerically the maturation process undergone by these crack patterns when they are allowed to adapt in…
Convergent extension of epithelial tissue is a key motif of animal morphogenesis. On a coarse scale, cell motion resembles laminar fluid flow; yet in contrast to a fluid, epithelial cells adhere to each other and maintain the tissue layer…
Plants are fundamentally important to life. Key research areas in plant science include plant species identification, weed classification using hyper spectral images, monitoring plant health and tracing leaf growth, and the semantic…
The general equations of motion for two dimensional Laplacian growth are derived using the conformal mapping method. In the singular case, all singularities of the conformal map are on the unit circle, and the map is a degenerate…
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…
We propose a variational framework for accretive surface growth driven by an optimality principle. Rather than prescribing a kinetic law, the configuration at each time step is obtained, within a time-discrete setting, as the solution of a…
Although the corresponding carbon-metal interactions can be very different, a similar nonlinear growth behavior of graphene has been observed for different metal substrates. To understand this interesting experimental observation, a…
Mollusk shells are an ideal model system for understanding the morpho-elastic basis of morphological evolution of invertebrates' exoskeletons. During the formation of the shell, the mantle tissue secretes proteins and minerals that calcify…
We discuss shape profiles emerging in inhomogeneous growth of squeezed tissues. Two approaches are used simultaneously: i) conformal embedding of two-dimensional domain with hyperbolic metrics into the plane, and ii) a pure energetic…
Deformation of morphisms along leaves of foliations define the tangential foliation on the corresponding space of morphisms. We prove that codimension one fo-liations having a tangential foliation with at least one non-algebraic leaf are…
We study the degree growth of iterates of meromorphic selfmaps of compact Kahler surfaces. Using cohomology classes on the Riemann-Zariski space we show that the degrees grow similarly to those of mappings that are algebraically stable on…
We study conformal structure and topology of leaves of singular foliations by Riemann surfaces.
Although understanding the collective migration of cells, such as that seen in epithelial sheets, is essential for understanding diseases such as metastatic cancer, this motion is not yet as well characterized as individual cell migration.…
During embryonic development tissue morphogenesis and signaling are tightly coupled. It is therefore important to simulate both tissue morphogenesis and signaling simultaneously in in silico models of developmental processes. The resolution…
We introduce a new equation describing epitaxial growth processes. This equation is derived from a simple variational geometric principle and it has a straightforward interpretation in terms of continuum and microscopic physics. It is also…
Plants are dynamic organisms and understanding temporal variations in vegetation is an essential problem for robots in the wild. However, associating repeated 3D scans of plants across time is challenging. A key step in this process is…
Two dimensional magnetic films with perpendicular magnetization spontaneously form magnetic domain patterns that evolve or undergo symmetry transformations as a function of temperature. When the system is driven from equilibrium by a rapid…
I show that the evolution of a two dimensional surface in a Laplacian field can be described by Hamiltonian dynamics. First the growing region is mapped conformally to the interior of the unit circle, creating in the process a set of…
We study the evolution of the universe which contains a multiple number of non-relativistic scalar fields decaying into both radiation and pressureless matter. We present a powerful analytic formalism to calculate the matter and radiation…