Related papers: Developed Smectics: When Exact Solutions Agree

This article gives the construction and complete classification of all three-dimensional spherical manifolds, and orders them by decreasing volume, in the context of multiconnected universe models with positive spatial curvature. It…

We construct a well-behaved compactification of finite covers of a stacky curve using admissible cover degenerations. Using our construction, we compactify the space of tetragonal curves on Hirzebruch surfaces. As an application, we…

An intuitive design method is proposed for generating developable ruled B-spline surfaces from a sequence of straight line segments indicating the surface shape. The first and last line segments are enforced to be the head and tail ruling…

Generative models have enabled intuitive image creation and manipulation using natural language. In particular, diffusion models have recently shown remarkable results for natural image editing. In this work, we propose to apply diffusion…

We consider the problem of approximating a two-dimensional shape contour (or curve segment) using discrete assembly systems, which allow to build geometric structures based on limited sets of node and edge types subject to edge length and…

Mechanically quenching a thin film of smectic-C liquid crystal results in the formation of a dense array of thousands of topological defects in the director field. The subsequent rapid coarsening of the film texture by the mutual…

We show that an entire branched cover of finite distortion cannot have a compact branch set if its distortion satisfies a certain asymptotic growth condition. We furthermore show that this bound is strict by constructing an entire,…

A novel mathematical model for fiber-reinforced materials is proposed. It is based on a 1-dimensional beam model for the thin fiber structures, a flexible and general 3-dimensional elasticity model for the matrix and an overlapping domain…

This paper presents an experimental investigation on pattern formation and evolution in bilayered tubular organs using swelling deformation of polydimethylsiloxane (PDMS) and aims at supplying a thorough comparison with theoretical and…

Recent years have seen the development of mature solutions for reconstructing deformable surfaces from a single image, provided that they are relatively well-textured. By contrast, recovering the 3D shape of texture-less surfaces remains an…

This paper is the first part in a 2 part study of an elementary functorial construction from the category of finite non-abelian groups to a category of singular compact, oriented 2-manifolds. After a desingularization process this…

In this paper we develop some combinatorial models for continuous spaces. In this spirit we study the approximations of continuous spaces by graphs, molecular spaces and coordinate matrices. We define the dimension on a discrete space by…

We present a generic and systematic approach for constructing D-dimensional lattice models with exactly solvable d-dimensional boundary states localized to corners, edges, hinges and surfaces. These solvable models represent a class of…

Computer simulations and scaling theory are used to investigate the damping of oscillations during epitaxial growth on high-symmetry surfaces. The crossover from smooth to rough growth takes place after the deposition of (D/F)^\delta…

Expanding the use of physical degrees of freedom to employ spatial multiplexing of data in optical communication is considered the most disruptive and effective solution to meet the capacity demand of the growing information traffic.…

3D terrain models are essential in fields such as video game development and film production. Since surface color often correlates with terrain geometry, capturing this relationship is crucial to achieving realism. However, most existing…

We consider a singularly perturbed semilinear boundary value problem of a general form that allows various types of turning points. A solution decomposition is derived that separates the potential exponential boundary layer terms. The…

We introduce pseudo-spherical non-null framed curves in the three-dimensional anti-de Sitter spacetime and establish the existence and uniqueness of these curves. We then give moving frames along pseudo-spherical framed curves, which are…

Liquid-liquid phase separation, whereby two liquids spontaneously demix, is ubiquitous in industrial, environmental, and biological processes. While isotropic fluids are known to condense into spherical droplets in the binodal region, these…

Hierarchical structures exhibit critical features across multiple scales. However, designing multiscale structures demands significant computational resources, and ensuring connectivity between microstructures remains a key challenge. To…