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Beyond unicellular and multicellular organisms, there is a third type of structural complexity in living animals: that of the mechanical self-assembly of groups of distinct multicellular organisms into dynamical, functional structures. One…
Recently self-affine sponges have been shown to be interesting counter-examples to several previously open problems. One class of recently studied sponges are Bedford-McMullen sponges with a weak coordinate ordering condition, that is,…
Edge states protected by bulk topology of photonic crystals show robustness against short-range disorder, making robust information transfer possible. Here, topological photonic crystals under long-range deformations are investigated.…
Architected materials derive their properties from the geometric arrangement of their internal structural elements. Their designs rely on continuous networks of members to control the global mechanical behavior of the bulk. Here, we…
Origami and kirigami have emerged as potential tools for the design of mechanical metamaterials whose properties such as curvature, Poisson ratio, and existence of metastable states can be tuned using purely geometric criteria. A major…
Networked structures arise in a wide array of different contexts such as technological and transportation infrastructures, social phenomena, and biological systems. These highly interconnected systems have recently been the focus of a great…
We investigate a set of design principles that link specific features of interparticle interactions to predictable structural and dynamic outcomes in two-dimensional self-assembly, a framework relevant to soft matter and biological…
The ordered configuration space of $n$ open unit squares in the $w$ by $h$ rectangle exhibits homological stability in the space direction. That is, for fixed $n$ and fixed homological degree $k$, once the underlying rectangle is large…
We propose second-order topological insulators (SOTIs) whose lattice structure has the hexagonal symmetry $C_{6}$ in three and two dimensions. We start with a three-dimensional weak topological insulator constructed on the stacked…
We study fermions in a lattice, with on-site and nearest neighbor attractive interactions between two spin species. We consider two geometries: both spins in a triangular lattice, and a mixed geometry with up-spins in honeycomb and…
Correlation and frustration play essential roles in physics, giving rise to novel quantum phases [1-6]. A typical frustrated system is correlated bosons on moat bands, which could host topological orders with long-range quantum entanglement…
We present a systematic study of the influence of cell geometry on the orientational distribution of microtubules (MTs) nucleated from a single microtubule organizing center (MTOC). For simplicity we consider an elliptical cell geometry, a…
We study the organization of topological defects in a system of nematogens confined to the two-dimensional sphere (S^2). We first perform Monte Carlo simulations of a fluid system of hard rods (spherocylinders) living in the tangent plane…
A small-world topology characterizes many complex systems including the structural and functional organization of brain networks. The topology allows simultaneously for local and global efficiency in the interaction of the system…
Extensive recent research on Lieb and kagome lattices highlights their unique physics characterized by the coexistence of Dirac points, van Hove singularities, and flat bands. In these models, flat bands are typically pinned at the center…
Higher-order topological insulators (HOTIs) are unique topological materials supporting edge states with the dimensionality at least by two lower than the dimensionality of the underlying structure. HOTIs were observed on lattices with…
The Cellular Potts model, also known as the Glazier-Graner-Hogeweg model, is a lattice-based approach by which biological tissues at the level of individual cells can be numerically studied. Traditionally, a square or hexagonal underlying…
We investigate the local structural fluctuations of a model equilibrium fluid with an aim of better understanding the structural basis of locally heterogeneous dynamics identified in recent simulations and experimental studies of…
Networks have in recent years emerged as an invaluable tool for describing and quantifying complex systems in many branches of science. Recent studies suggest that networks often exhibit hierarchical organization, where vertices divide into…
We study the topological structure and the topological dynamics of groups of homeomorphisms of scattered spaces. For a large class of them (including the homeomorphism group of any ordinal space or of any locally compact scattered space),…