相关论文: Loops and Regions in Hitomezashi Patterns
A cutting sequence is a symbolic coding of a linear trajectory on a translation surface corresponding to the sequence of sides hit in a polygonal representation of the surface. We characterize cutting sequences in a regular hexagon with…
Miura-Ori, a celebrated origami pattern that facilitates functionality in matter, has found multiple applications in the field of mechanical metamaterials. Modifications of Miura-Ori pattern can produce curved configurations during folding,…
Random-cluster measures on infinite regular trees are studied in conjunction with a general type of `boundary condition', namely an equivalence relation on the set of infinite paths of the tree. The uniqueness and non-uniqueness of…
Two coarse-grained models which capture some universal characteristics of stripe forming systems are stud- ied. At high temperatures, the structure factors of both models attain their maxima on a circle in reciprocal space, as a consequence…
We study the feasible region for consecutive patterns of pattern-avoiding permutations. More precisely, given a family $\mathcal C$ of permutations avoiding a fixed set of patterns, we consider the limit of proportions of consecutive…
Cytoskeletal networks form complex intracellular structures. Here we investigate a minimal model for filament-motor mixtures in which motors act as depolymerases and thereby regulate filament length. Combining agent-based simulations and…
Cloth detection and manipulation is a common task in domestic and industrial settings, yet such tasks remain a challenge for robots due to cloth deformability. Furthermore, in many cloth-related tasks like laundry folding and bed making, it…
Kirigami is the art of cutting paper to make it articulated and deployable, allowing for it to be shaped into complex two and three-dimensional geometries. The mechanical response of a kirigami sheet when it is pulled at its ends is enabled…
In this paper, we study how to fold a specified origami crease pattern in order to minimize the impact of paper thickness. Specifically, origami designs are often expressed by a mountain-valley pattern (plane graph of creases with relative…
Let $S_{g}$ denote the closed orientable surface of genus $g$. In joint work with Huang, the first author constructed exponentially-many (in $g$) mapping class group orbits of pairs of simple closed curves whose complement is a single…
We prove that the existence of a $1$-Lipschitz retraction (a contraction) from a space $X$ onto its subspace $A$ implies the persistence diagram of $A$ embeds into the persistence diagram of $X$. As a tool we introduce tight injections of…
An ensemble of random unistochastic (orthostochastic) matrices is defined by taking squared moduli of elements of random unitary (orthogonal) matrices distributed according to the Haar measure on U(N) (or O(N), respectively). An ensemble of…
Islamic geometric patterns are a rich and venerable ornamental tradition. Many classic designs feature periodic arrangements of rosettes: star shapes surrounded by rings of hexagonal petals. We present a new technique for generating…
Knitted fabrics are metamaterials with remarkable mechanical properties, such as extreme deformability and multiple history-dependent rest shapes. This letter shows that those properties may stem from a continuous set of metastable states…
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…
In this section, we examine the transition from statistically homogeneous turbulence to inhomogeneous turbulence with zonal flows. Statistical equations of motion can be derived from the quasilinear approximation to the Hasegawa-Mima…
An arrangement of pseudocircles is a collection of simple closed curves on the sphere or in the plane such that any two of the curves are either disjoint or intersect in exactly two crossing points. We call an arrangement intersecting if…
Heterogeneous delays with positive lower bound (gap) are taken into consideration in Kuramoto oscillators. We first establish a perturbation technique, by which universal normal forms and detailed dynamical behavior of this model can be…
In this paper we use well-known results from linear algebra as tools to explore some properties of products of Fibonacci numbers. Specifically, we explore the behavior of the eigenvalues, eigenvectors, characteristic polynomials,…
The mode-locking regions of a dynamical system are the subsets of the parameter space of the system within which there exists an attracting periodic solution. For piecewise-linear continuous maps, these regions have a curious chain…