Related papers: First-order patterning transitions on a sphere as …
Complex distribution networks are pervasive in biology. Examples include nutrient transport in the slime mold \emph{Physarum polycephalum} as well as mammalian and plant venation. Adaptive rules are believed to guide development of these…
We introduce a general, efficient method to completely describe the topology of individual grains, bubbles, and cells in three-dimensional polycrystals, foams, and other multicellular microstructures. This approach is applied to a pair of…
We explore a simplified class of models we call swarms, which are inspired by the collective behavior of social insects. We perform a mean-field stability analysis and perform numerical simulations of the model. Several interesting types of…
The advances in understanding complex networks have generated increasing interest in dynamical processes occurring on them. Pattern formation in activator-inhibitor systems has been studied in networks, revealing differences from the…
During development, highly ordered structures emerge as cells collectively coordinate with each other. While recent advances have clarified how individual cells process and respond to external signals, understanding collective cellular…
The co-evolution of structure and dynamics, known as adaptivity, is a fundamental property in various systems and drives diverse emergent behaviors. However, the adaptivity in previous works is primarily stemmed from pairwise situations,…
A collection of thin structures buckle, bend, and bump into each-other when confined. This contact can lead to the formation of patterns: hair will self-organize in curls; DNA strands will layer into cell nuclei; paper, when crumpled, will…
Flocks of birds and schools of fish are familiar examples of spatial patterns formed by living organisms. In contrast to the patterns on the skins of, say, zebra and giraffe, the patterns of our interest are {\it transient} although…
A big challenge in current biology is to understand the exact self-organization mechanism underlying complex multi-physics coupling developmental processes. With multiscale computations of from subcellular gene expressions to cell…
We show that the tethered surface model of Helfrich and Polyakov-Kleinert undergoes a first-order phase transition separating the smooth phase from the crumpled one. The model is investigated by the canonical Monte Carlo simulations on…
One-dimensional model of a system where first-order phase transition occurs is examined in the present paper. It is shown that basic properties of the phenomenon, such as a well defined temperature of transition, are caused both by…
Pattern forming systems allow for a wealth of states, where wavelengths and orientation of patterns varies and defects disrupt patches of monocrystalline regions. Growth of patterns has long been recognized as a strong selection mechanism.…
Reaction-diffusion systems may lead to the formation of steady state heterogeneous spatial patterns, known as Turing patterns. Their mathematical formulation is important for the study of pattern formation in general and play central roles…
Contrary to canonical expectations we show that lattice translational symmetry breaking often accompanies uniformly ordered flux phases. We demonstrate this phenomena by studying a spinless-fermion model on a square latttice with…
Cylindrical interfaces occur in sheared or deformed emulsions and as biological or technological lipid monolayer or bilayer tubules. Like the corresponding spherical droplets and vesicles, these cylinder-like surfaces may host orientaional…
General topological principles how to transfer the planar orders onto a sphere are considered. Formation of extended topological defects (ETDs), which have a reconstructed inner structure surrounded by perfect initial order, is discussed.…
A key process in the life of any multicellular organism is its development from a single egg into a full grown adult. The first step in this process often consists of forming a tissue layer out of randomly placed cells on the surface of the…
Recent experiments have exploited elastic instabilities in membranes to create complex patterns. However, the rational design of such structures poses many challenges, as they are products of nonlinear elastic behavior. We pose a simple…
Charged pattern formation on the surfaces of self--assembled cylindrical micelles formed from oppositely charged heterogeneous molecules such as cationic and anionic peptide amphiphiles is investigated. The net incompatibility $\chi$ among…
The next step in the understanding of the genome organization, after the determination of complete sequences, involves proteomics. The proteome includes the whole set of protein-protein interactions, and two recent independent studies have…