相关论文: Stratifications of cellular patterns

In this informal expository note, we quickly introduce and survey compactifications of strata of holomorphic 1-forms on Riemann surfaces, i.e. spaces of translation surfaces. In the last decade, several of these have been constructed,…

In Chapter 1 we fully characterise pairs of finite graphs which form a gap in the full homomorphism order. This leads to a simple proof of the existence of generalised duality pairs. We also discuss how such results can be carried to…

We conclude our analysis of bubble divergences in the flat spinfoam model. In [arXiv:1008.1476] we showed that the divergence degree of an arbitrary two-complex Gamma can be evaluated exactly by means of twisted cohomology. Here, we…

In multicellular organisms, epithelial cells form layers separating compartments responsible for different physiological functions. At the early stage of epithelial layer formation, each cell of an aggregate defines an inner and an outer…

Graphs are commonly used in mathematics to represent some relationships between items. However, as simple objects, they sometimes fail to capture all relevant aspects of real-world data. To address this problem, we generalize them and model…

A novel bilayer is introduced, consisting of a stiff film adhered to a soft substrate with patterned holes beneath the film and substrate interface. To uncover the transition of surface patterns, two dimensional plane strain simulations are…

Liquid crystal layers sandwiched between a reference plate and a photosensitive substrate were investigated. We focused on the reverse geometry, where the cell was illuminated by a laser beam from the reference side. In planar cells…

The squeezing of soft solids, the constrained growth of biological tissues, and the swelling of soft elastic solids such as gels can generate large compressive stresses at their surfaces. This causes the otherwise smooth surface of such a…

The patterns arising from the differential swelling of gels are investigated experimentally and theoretically as a model for the differential growth of living tissues. Two geometries are considered: a thin strip of soft gel clamped to a…

The letter resolves several intriguing and fundamental aspects of debonding at soft interfaces, including the formation and persistence of regularly arranged nanocavities and bridges, ``adhesion-debonding hysteresis'', and vastly lower…

We generalise a fundamental graph-theoretical fact, stating that every element of the cycle space of a graph is a sum of edge-disjoint cycles, to arbitrary continua. To achieve this we replace graph cycles by topological circles, and…

The short-range attraction and long-range repulsion (SALR) between nanoparticles or macromolecules can lead to spontaneous pattern formation on solid surfaces, fluid interfaces or membranes. In order to study the self-assembly in such…

Disordered solids distort and fail as particle contacts become unstable and rearrange under sufficiently large shear strains. Such instabilities can occur at different locations and, because of their proximity, can interact with one…

We present structures comprised of identical convex polyhedra which are interlocked geometrically. These sets cannot be disassembled by removing individual polyhedra by translations and/or rotations. The shapes that permit interlocking…

We propose to study homomorphisms of connectome graphs. Homomorphisms can be studied as sequences of elementary homomorphisms - folds, which identify pairs of vertices. Several fold types are defined. Initial computation results for some…

Chemical erosion, one of the two major erosion processes along with mechanical erosion, occurs when a soluble rock like salt, gypsum or limestone is dissolved in contact with a water flow. The coupling between the geometry of the rocks, the…

Using numerical simulations, we study the dynamical evolution of particles interacting via competing long-range repulsion and short-range attraction in two dimensions. The particles are compressed using a time-dependent quasi-one…

Disordered systems like liquids, gels, glasses, or granular materials are not only ubiquitous in daily life and in industrial applications but they are also crucial for the mechanical stability of cells or the transport of chemical and…

We consider variational problems that model the bending behavior of curves that are constrained to belong to given hypersurfaces. Finite element discretizations of corresponding functionals are justified rigorously via Gamma-convergence.…

We analyze pattern formation on a network of cells where each cell inhibits its neighbors through cell-to-cell contact signaling. The network is modeled as an interconnection of identical dynamical subsystems each of which represents the…