相关论文: Stratifications of cellular patterns

A phase-separation front will leave in its wake a phase-separated morphology that differs markedly from homogeneous phase-separation morphologies. For a purely diffusive system such a front, moving with constant velocity, will generate very…

In this paper we discuss reconstruction problems for graphs. We develop some new ideas like isomorphic extension of isomorphic graphs, partitioning of vertex sets into sets of equivalent points, subdeck property, etc. and develop an…

Regularity of the deformation of the Fermi surface under short-range interactions is established to all orders in perturbation theory. The proofs are based on a new classification of all graphs that are not doubly overlapping. They turn out…

Counter-streaming systems are a canonical model for beam-plasma instabilities, such as the filamentation instability, which is critical in high energy density physics. However, scenarios involving intersecting fast electron beams break the…

Quantifying the outcomes of cells collisions is a crucial step in building the foundations of a kinetic theory of living matter. Here, we develop a mechanical theory of such collisions by first representing individual cells as extended…

We develop the fundamentals of a new theory of convex geometry -- which we call "broken line convex geometry". This is a theory of convexity where the ambient space is the rational tropicalization of a cluster variety, as opposed to an…

Inter-layer synchronization is a dynamical state occurring in multi-layer networks composed of identical nodes. The state corresponds to have all layers synchronized, with nodes in each layer which do not necessarily evolve in unison. So…

We show that a flat two dimensional network of connected vertices, when stretched, may deform plastically by producing `pleats'; system spanning linear structures with width comparable to the lattice spacing, where the network overlaps on…

When following the growth of structure in the Universe, we propose replacing merger trees with merger graphs, in which haloes can both merge and split into separate pieces. We show that this leads to smoother mass growth and eliminates…

A theory for surface transitions in the presence of a disordered pinning potential is presented. Arbitrary disorder correlations are treated in the framework of a dynamical functional renormalization group. The roughening transition, where…

Comprehensive and quantitative investigations of social theories and phenomena increasingly benefit from the vast breadth of data describing human social relations, which is now available within the realm of computational social science.…

Much information about a graph can be obtained by studying its spanning trees. On the other hand, a graph can be regarded as a 1-dimensional cell complex, raising the question of developing a theory of trees in higher dimension. As observed…

Multi-layer graphs consist of several graphs (layers) over the same vertex set. They are motivated by real-world problems where entities (vertices) are associated via multiple types of relationships (edges in different layers). We chart the…

The lattice gas model of condensation in a heterogeneous pore system, represented by a random graph of cells, is studied using an exact analytical solution. A binary mixture of pore cells with different coordination numbers is shown to…

Plane wave density functional theory codes generally assume periodicity in all three dimensions. This causes difficulties when studying charged systems, for instance energies per unit cell become infinite, and, even after being renormalised…

As a confined thin sheet crumples, it spontaneously segments into flat facets delimited by a network of ridges. Despite the apparent disorder of this process, statistical properties of crumpled sheets exhibit striking reproducibility.…

We characterize the order-disorder transition in a model lipid bilayer using molecular dynamics simulations. We find that the ordered phase is hexatic. In particular, in-plane structures possess a finite concentration of 5-7 disclination…

We study theoretically the shapes of a dividing epithelial monolayer of cells lying on top of an elastic stroma. The negative tension created by cell division provokes a buckling instability at a finite wave vector leading to the formation…

When a block made of an elastomer is subjected to large shear, its surface remains flat. When a block of biological soft tissue is subjected to large shear, it is likely that its surface in the plane of shear will buckle (apparition of…

Twisted and rope-like assemblies of filamentous molecules are common and vital structural elements in cells and tissue of living organisms. We study the intrinsic frustration occurring in these materials between the two-dimensional…