相关论文: Phyllotaxis, Pushed Pattern-Forming Fronts and Opt…

The basic result of this note is a statement about the existence of families of partitions of the set of natural numbers with some favourable properties, the n-optimal matrices of partitions. We use this to improve a decomposition result…

A first-principles statistical theory is constructed for the evolution of two dimensional interfaces in Laplacian fields. The aim is to predict the pattern that the growth evolves into, whether it becomes fractal and if so the…

The problem of pattern selection arises when the evolution equations have many solutions, whereas observed patterns constitute a much more restricted set. An approach is advanced for treating the problem of pattern selection by defining the…

\textit{Parastichies} are spiral patterns observed in plants and numerical patterns generated using golden angle method. We generalize this method by using Markoff theory and the theory of product of linear forms, to obtain a theory for…

We give a characterization of optimal transport plans for a variant of the usual quadratic transport cost introduced in [33]. Optimal plans are composition of a deterministic transport given by the gradient of a continuously differentiable…

We study pattern selection of cracks in directionally drying fractures by analyzing the experimental systems recently devised by C. Allain and L. Limat. [Phys. Rev. Lett. {\bf 74}, 2981 (1995).] Proposing a simple picture of crack…

The entries of frieze patterns may be interpreted as coordinates of roots of a finite Weyl groupoid of rank two. We prove the existence of maximal elements in their root posets and classify those frieze patterns which can be used to build…

Optimal structure of proteins is described by linear stochastic differential equation with mean decrease of free energy and volatility. Structure determining strategy is given by a twin of stochastic variables for which empirical conditions…

First introduced by Fernholz in stochastic portfolio theory, functionally generated portfolio allows its investment performance to be attributed to directly observable and easily interpretable market quantities. In previous works we showed…

How does growth encode form in developing organisms? Many different spatiotemporal growth profiles may sculpt tissues into the same target 3D shapes, but only specific growth patterns are observed in animal and plant development. In…

In eukaryotic cell chemotaxis, cells extend and retract transient actin-driven protrusions at their membrane that facilitate both the detection of external chemical gradients and directional movement via the formation of focal adhesions…

Orientation mapping is a widely used technique for revealing the microstructure of a polycrystalline sample. The crystalline orientation at each point in the sample is determined by analysis of the diffraction pattern, a process known as…

Actin cytoskeletal protrusions in crawling cells, or lamellipodia, exhibit various morphological properties such as two characteristic peaks in the distribution of filament orientation with respect to the leading edge. To understand these…

A central question in developmental biology is how size and position are determined. The genetic code carries instructions on how to control these properties in order to regulate the pattern and morphology of structures in the developing…

The hormone auxin is actively transported throughout plants via protein machineries including the dedicated transporter known as PIN. The associated transport is ordered with nearby cells driving auxin flux in similar directions. Here we…

Pattern forming systems allow for a wealth of states, where wavelengths and orientation of patterns varies and defects disrupt patches of monocrystalline regions. Growth of patterns has long been recognized as a strong selection mechanism.…

We analyze an 'up-the-gradient' model for the formation of transport channels of the phytohormone auxin, through auxin-mediated polarization of the PIN1 auxin transporter. We show that this model admits a family of travelling wave solutions…

We investigate evolution equations for anomalous diffusion employing fractional derivatives in space and time. Linkage between the space-time variables leads to a new type of fractional derivative operator. Fractional diffusion equations…

Leaves of vascular plants are arranged regularly around stems, a phenomenon known as phyllotaxis. A constant angle between two successive leaves is called divergence angle. On the one side, the divergence angle $\alpha_0$ of an initial…

The original problem of phyllotaxis was focused on the regular arrangements of leaves on mature stems represented by common fractions such as 1/2, 1/3, 2/5, 3/8, 5/13, etc. The phyllotaxis fraction is not fixed for each plant but it may…