Related papers: Sidebranch Structures of Dendritic Patterns in a C…
Morphological trends in growing colonies of living cells are at the core of physiological and evolutionary processes. Using active gel equations, which include cell division, we show that shape changes during the growth can be regulated by…
It was studied the growth of Temperley-Lieb type algebras with orthogonal and commutative relations associated with 2-colored edges graphs. Depending on the structure of the graphs they can be finite-dimensional or to have linear or…
The dynamic response of dendritic solidification to spatially homogeneous time-periodic forcing has been studied. Phase-field calculations performed in two dimensions (2D) and experiments on thin (quasi 2D) liquid crystal layers show that…
We study the structure of the asymptotic expansion of the probability that a combinatorial object is connected. We show that the coefficients appearing in those asymptotics are integers and can be interpreted as the counting sequences of…
We investigate the wave packet dynamics for a one-dimensional incommensurate optical lattice with a special on-site potential which exhibits the mobility edge in a compactly analytic form. We calculate the density propagation, long-time…
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…
We consider a class of simple one parameter families of interval maps, and we study how metric (resp. topological) entropy changes as the parameter varies. We show that in many cases the entropy displays a semi-regular behaviour, i.e. it is…
We develop the theory of linear evolution equations associated with the adjacency matrix of a graph, focusing in particular on infinite graphs of two kinds: uniformly locally finite graphs as well as locally finite line graphs. We discuss…
We propose a new method for quantitative characterization of spatial network-like patterns with loops, such as surface fracture patterns, leaf vein networks and patterns of urban streets. Such patterns are not well characterized by purely…
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…
We study a system of dipolar molecules confined in a two-dimensional trap and subject to an optical square lattice. The repulsive long-range dipolar interaction $D/r^3$ favors an equilateral triangular arrangement of the molecules, which…
Intuitively, an envelope of a family of curves is a curve that is tangent to a member of the family at each point. Here we use envelopes of families of circles to study objects from matrix theory and hyperbolic geometry. First we explore…
The propagation of sidewall steps during the growth of nanowires is calculated in the frame of the Burton-Cabrera-Frank model. The stable shape of the nanowire comprises a cylinder section on top of a cone section: their characteristics are…
We propose a modeling framework for growing multiplexes where a node can belong to different networks. We define new measures for multiplexes and we identify a number of relevant ingredients for modeling their evolution such as the coupling…
A contemporary procedure to grow artificial tissue is to seed cells onto a porous biomaterial scaffold and culture it within a perfusion bioreactor to facilitate the transport of nutrients to growing cells. Typical models of cell growth for…
When two molecular species with mutual affinity are mixed together, various self-assembled phases can arise at low temperature, depending on the shape of like and unlike interactions. Among them, stripes -- where layers of one type are…
Pattern-forming processes, such as electrodeposition, dielectric breakdown or viscous fingering are often driven by instabilities. Accordingly, the resulting growth patterns are usually highly branched, fractal structures. However, in some…
The evolution of a probe D-brane in the p-brane background has been considered. The anisotropic evolution of the world-volume of the D-brane with a given topology of a world-volume in a form of a direct product of a n-dimensional flat space…
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…
A model for economic behavior, under heterogeneous spatial economic conditions is developed. The role of selection pressure in a Bak-Sneppen-like dynamics with entity diffusion on a lattice is studied by Monte-Carlo simulation taking into…