Related papers: Developed Smectics: When Exact Solutions Agree
The tenfold classification provides a powerful framework for organizing topological phases of matter based on symmetry and spatial dimension. However, it does not offer a systematic method for transitioning between classes or engineering…
We introduce a method for modeling a configuration of objects in 2D or 3D images using a mathematical "skeletal linking structure" which will simultaneously capture the individual shape features of the objects and their positional…
We propose a dual-domain generative model to estimate a texture map from a single image for colorizing a 3D human model. When estimating a texture map, a single image is insufficient as it reveals only one facet of a 3D object. To provide…
Dislocation based modeling of plasticity is one of the central challenges at the crossover of materials science and continuum mechanics. Developing a continuum theory of dislocations requires the solution of two long standing problems: (i)…
We investigate the interaction between two cracks propagating in a thin sheet. Two different experimental geometries allow us to tear sheets by imposing an out-of-plane shear loading. We find that two tears converge along self-similar paths…
As several industries are moving towards modeling massive 3D virtual worlds, the need for content creation tools that can scale in terms of the quantity, quality, and diversity of 3D content is becoming evident. In our work, we aim to train…
Transformation optics offers an unconventional approach to the control of electromagnetic fields. A transformation optical structure is designed by first applying a form-invariant coordinate transform to Maxwell's equations, in which part…
Introducing flexibility in the time-discretisation mesh can improve convergence and computational time when solving differential equations numerically, particularly when the solutions are discontinuous, as commonly found in control problems…
The boundaries of central place models proved to be fractal lines, which compose fractal texture of central place networks. A textural fractal can be employed to explain the scale-free property of regional boundaries such as border lines,…
Flexible mechanical metamaterials possess repeating structural motifs that imbue them with novel, exciting properties including programmability, anomalous elastic moduli and nonlinear and robust response. We address such structures via…
Structural disorder can improve the optical properties of metasurfaces, whether it is emerging from some large-scale fabrication methods, or explicitly designed and built lithographically. Correlated disorder, induced by a minimum…
We develop a theory of holomorphic differentials on a certain class of non-compact Riemann surfaces obtained by opening infinitely many nodes.
Simplified proxy models are commonly used to represent architectural structures, reducing storage requirements and enabling real-time rendering. However, the geometric simplifications inherent in proxies result in a loss of fine color and…
This paper is the fifth and final in a series on embedded minimal surfaces. Following our earlier papers on disks, we prove here two main structure theorems for non-simply connected embedded minimal surfaces of any given fixed genus. The…
The gluing technique is used to construct hypersurfaces in Euclidean space having approximately constant prescribed mean curvature. These surfaces are perturbations of unions of finitely many spheres of the same radius assembled end-to-end…
Defects in conformal field theories are interesting objects to study from both formal and applied points of view. In this paper, we construct conformal defects in free scalar field CFTs in diverse dimensions. After discussing the possible…
Speckle patterns are ubiquitous in optics and have multiple applications for which the control of their spatial correlations is essential. Here, we report on a method to engineer speckle correlations behind a scattering medium through the…
We use orbifold structures to deduce degeneracy statements for holomorphic maps into logarithmic surfaces. We improve former results in the smooth case and generalize them to singular pairs. In particular, we give applications on nodal…
Smooth and curved microstructural topologies found in nature - from soap films to trabecular bone - have inspired several mimetic design spaces for architected metamaterials and bio-scaffolds. However, the design approaches so far have been…
The satisfiability and optimization of finite-dimensional Boolean formulas are studied using percolation theory, rare region arguments, and boundary effects. In contrast with mean-field results, there is no satisfiability transition, though…