Related papers: Phyllotaxis: a framework for foam topological evol…
The structure of cloud complexes appears to be well described by a "tree structure" representation when the image is partitioned into "clouds". In this representation, the parent-child relationships are assigned according to containment.…
Certain foams and relations on them are introduced to interpret functors and natural transformations in categories of representations of iterated wreath products of cyclic groups of order two. We also explain how patched surfaces with…
Spacetime is represented by ordered sequences of topologically closed Poincare sections of the primary space constructed of primary empty cells. These mappings are constrained to provide homeomorphic structures serving as frames of…
Given a collection $\tau$ of subsets of a finite set $X$, we say that $\tau$ is {\em phylogenetically flexible} if, for any collection $R$ of rooted phylogenetic trees whose leaf sets comprise the collection $\tau$, $R$ is compatible (i.e.…
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…
Tendrils coil their shape to anchor the plant to supporting structures, allowing vertical growth toward light. Although climbing plants have been studied for a long time, extracting information regarding the relationship between the…
Epithelial cell clusters often move collectively on a substrate. Mechanical signals play a major role in organizing this behavior. There are a number of experimental observations in these systems which await a comprehensive explanation.…
Foliated fracton order is a qualitatively new kind of phase of matter. It is similar to topological order, but with the fundamental difference that a layered structure, referred to as a foliation, plays an essential role and determines the…
Fiberboids are active filaments trapped at the interface of two phases, able of harnessing energy (and matter) fluxes across the interface in order to produce a rolling-like self-propulsion. We discuss several table-top examples and develop…
This article presents formalistic tool for description of structural and biochemical relations between cells in the course of development of the body of plants. This is flexible formalistic space, based on the Category theory and the Petri…
Phylogenetic tree shapes capture fundamental signatures of evolution. We consider ``ranked'' tree shapes, which are equipped with a total order on the internal nodes compatible with the tree graph. Recent work has established an elegant…
Biological cells can actively tune their intracellular architecture according to their overall shape. Here we explore the rheological implication of such coupling in a minimal model of a dense cellular material where each cell exerts an…
The phase spiral is a perturbation to the vertical phase-space distribution of stars in the Milky Way disk. We study the phase spiral's properties and how they vary with spatial position, in order to constrain its origin and evolution, as…
Navigating topological transitions in cellular mechanical systems is a significant challenge for existing simulation methods. While abstract models lack predictive capabilities at the cellular level, explicit network representations…
Deformations of cell sheets during morphogenesis are driven by developmental processes such as cell division and cell shape changes. In morphoelastic shell theories of development, these processes appear as variations of the intrinsic…
The global scales of solar convection are studied through three-dimensional simulations of compressible convection carried out in spherical shells of rotating fluid which extend from the base of the convection zone to within 15 Mm of the…
Adiabatic invariants foliate phase space, and impart a macro-scale hierarchy by separating microscopic variables. On a macroscopic leaf, long-scale ordered structures are created while maximizing entropy. A plasma confined in a…
Stylolites are ubiquitous geo-patterns observed in rocks in the upper crust, from geological reservoirs in sedimentary rocks to deformation zones, in folds, faults, and shear zones. These rough surfaces play a major role in the dissolution…
During neurodevelopment, neuronal axons navigate through the extracellular environment, guided by various cues to establish connections with distant target cells. Among other factors, axon trajectories are influenced by heterogeneities in…
The dynamical processes that control star formation in molecular clouds are not well understood, and in particular, it is unclear if rotation plays a major role in cloud evolution. We investigate the importance of rotation in cloud…