Related papers: First-order patterning transitions on a sphere as …
Two types of surface models have been investigated by Monte Carlo simulations on triangulated spheres with compartmentalized domains. Both models are found to undergo a first-order collapsing transition and a first-order surface fluctuation…
Many systems where interactions compete with each other or with constraints are well described by a model first introduced by Brazovskii. Such systems include block copolymers, alloys with modulated phases, Rayleigh-Benard Cells and type-I…
Pollen grains are known for their impressive variety of species-specific, microscale surface patterning. Despite having similar biological developmental steps, pollen grain surface features are remarkably geometrically varied. Previous work…
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…
A first-order transition is numerically found in a spherical surface model with skeletons, which are linked to each other at junctions. The shape of the triangulated surfaces is maintained by skeletons, which have a one-dimensional bending…
We consider diffusion limited aggregation of particles of two different kinds. It is assumed that a particle of one kind may adhere only to another particle of the same kind. The particles aggregate on a linear substrate which consists of…
We found that three types of tethered surface model undergo a first-order phase transition between the smooth and the crumpled phase. The first and the third are discrete models of Helfrich, Polyakov, and Kleinert, and the second is that of…
Statistical physics can describe the behavior of microbial populations consisting of many heterogeneous individuals. A direct consequence is the existence of phase transitions, where the behavior of a population changes discontinuously upon…
The order-disorder transition of a sphere-forming block copolymer thin film was numerically studied through a Cahn-Hilliard model. Simulations show that the fundamental mechanisms of pattern formation are spinodal decomposition and…
Dynamically triangulated surface model is found to undergo a first-order crumpling transition between the smooth phase and a crumpled phase. Triangulated spheres are divided into compartmentalized domains, whose boundary bonds remain…
It is well known that life on Earth alters its environment over evolutionary and geological timescales. An important open question is whether this is a result of evolutionary optimization or a universal feature of life. In the latter case,…
Self-organization, the ability of a system of microscopically interacting entities to shape macroscopically ordered structures, is ubiquitous in Nature. Spatio-temporal patterns are abundantly observed in a large plethora of applications,…
Turing theory of pattern formation is among the most popular theoretical means to account for the variety of spatio-temporal structures observed in Nature and, for this reason, finds applications in many different fields. While Turing…
A phase separation in a spatially heterogeneous environment is closely related to intracellular science and material science. For the phase separation, initial heterogeneous perturbations play an important role in pattern formations. In…
Biological systems excel at building spatial structures on scales ranging from nanometers to kilometers and exhibit temporal patterning from milliseconds to years. One approach that nature has taken to accomplish this relies on the…
A model of pattern formation in living systems is presented. The pattern is achieved by the sequential interaction of two signaling pathways. The coupling of the pattern to the (thick) epithelial sheet changes is given, when the Gauss…
Search for possible relationships between phylogeny and ontogeny is one of the most important issues in the field of evolutionary developmental biology. By representing developmental dynamics of spatially located cells with gene expression…
Topology and geometry of a sphere create constraints for particles that lie on its surface which they otherwise do not experience in Euclidean space. Notably, the number of particles and the size of the system can be varied separately,…
We examine a spatially discrete reaction diffusion model based on the interactions that create a periodic pattern in the Drosophila eye imaginal disc. This model is capable of generating a regular hexagonal pattern of gene expression behind…
Percolation plays an important role in fields and phenomena as diverse as the study of social networks, the dynamics of epidemics, the robustness of electricity grids, conduction in disordered media, and geometric properties in statistical…