相关论文: Extensions of Hitomezashi Patterns

We classify one-element extensions of a hyperplane arrangement by the induced adjoint arrangement. Based on the classification, several kinds of combinatorial invariants including Whitney polynomials, characteristic polynomials, Whitney…

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…

Origami has shown the potential to approximate three-dimensional curved surfaces by folding through designed crease patterns on flat materials. The Miura-ori tessellation is a widely used pattern in engineering and tiles the plane when…

Shell mechanisms are patterned surface-like structures with compliant deformation modes that allow them to change shape drastically. Examples include many origami and kirigami tessellations as well as other periodic truss mechanisms. The…

We investigate the response of two-dimensional pattern forming systems with a broken up-down symmetry, such as chemical reactions, to spatially resonant forcing and propose related experiments. The nonlinear behavior immediately above…

Applying circle inversion on a square grid filled with circles, we obtain a configuration that we call a fabric of kissing circles. The configuration and its components, which are two orthogonal frames and two orthogonal families of chains,…

We consider natural exponential families of Levy processes with randomized parameter. Such processes are Markov, and under suitable assumptions, pairs of such processes with shared randomization can be stitched together into a single…

A twisted quiver bundle is a set of holomorphic vector bundles over a complex manifold, labelled by the vertices of a quiver, linked by a set of morphisms twisted by a fixed collection of holomorphic vector bundles, labelled by the arrows.…

Simple closed curves in the plane can be mapped to nontrivial knots under the action of origami foldings that allow the paper to self-intersect. We show all tame knot types may be produced in this manner, motivating the development of a new…

We describe a method of defining a Hermitian metric on Kobayashi hyperbolic manifolds. The metric is distance decreasing under holomorphic mappings, up to a multiplicative constant. This method is distinct from the classical construction of…

We study, on a square lattice, an extension to fully coordinated percolation which we call iterated fully coordinated percolation. In fully coordinated percolation, sites become occupied if all four of its nearest neighbors are also…

This series explores a new notion of T-homotopy equivalence of flows. The new definition involves embeddings of finite bounded posets preserving the bottom and the top elements and the associated cofibrations of flows. In this third part,…

A grid poset -- or grid for short -- is a product of chains. We ask, what does a random linear extension of a grid look like? In particular, we show that the average "jump number," i.e., the number of times that two consecutive elements in…

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…

Based on recent advances in fibration symmetry theory, we investigate how structural symmetries influence synchronization in systems with higher-order interactions (HOI). Using bipartite graph representations, we identify a node partition…

Shape-morphing capabilities are crucial for enabling multifunctionality in both biological and artificial systems. Various strategies for shape morphing have been proposed for applications in metamaterials and robotics. However, few of…

Kirigami, the creative art of paper cutting, is a promising paradigm for mechanical metamaterials. However, to make kirigami-inspired structures a reality requires controlling the topology of kirigami to achieve connectivity and rigidity.…

Icosoku is a challenging and interesting puzzle that exhibits highly symmetrical and combinatorial nature. In this paper, we pose the questions derived from the puzzle, but with more difficulty and generality. In addition, we also present a…

We introduce a generic scheme to perform non-perturbative linked cluster expansions in long-range ordered quantum phases. Clusters are considered to be surrounded by an ordered reference state leading to effective edge-fields in the exact…

We enumerate and characterize some classes of alternating and reverse alternating involutions avoiding a single pattern of length three or four. If on one hand the case of patterns of length three is trivial, on the other hand, the length…