Related papers: Variable offsets and processing of implicit forms …
Covering-based rough set theory is a useful tool to deal with inexact, uncertain or vague knowledge in information systems. Geometric lattice has widely used in diverse fields, especially search algorithm design which plays important role…
A novel Transformer variation architecture is proposed in the implicit sparse style. Unlike "traditional" Transformers, instead of attention to sequential or batch entities in their entirety of whole dimensionality, in the proposed Batch…
We consider a simply supported plate with constant thickness, defined on an unknown multiply connected domain. We optimize its shape according to some given performance functional. Our method is of fixed domain type, easy to be implemented,…
The algorithmic self-assembly of shapes has been considered in several models of self-assembly. For the problem of \emph{shape construction}, we consider an extended version of the Two-Handed Tile Assembly Model (2HAM), which contains…
Inorganic/inorganic composites are found in multiple applications crucial for the energy transition, from nuclear reactor to energy storage devices. Their microstructures dictate a number of properties, such as mass transport or fracture…
Modulated symmetries are internal symmetries that are not invariant under spacetime symmetry actions. We propose a general way to describe the lattice translation modulated symmetries in 1+1D, including the non-invertible ones, via the…
For their excellent stiffness-to-weight characteristics, triply periodic minimal surfaces (TPMS) are widely adopted in architected materials. However, their geometric regularity often leads to elastic anisotropy, limiting their…
This paper explores the embedding of lattice structures $L \subseteq \mathbb{R}^n$ into smooth manifolds $M \subseteq \mathbb{R}^n$ through a rigorous mathematical framework. Building upon the foundational results established in "Embedding…
Amorphous solids form an enormous and underutilized class of materials. In order to drive the discovery of new useful amorphous materials further we need to achieve a closer convergence between computational and experimental methods. In…
Traditionally, shape transformation using implicit functions is performed in two distinct steps: 1) creating two implicit functions, and 2) interpolating between these two functions. We present a new shape transformation method that…
Acoustic transparency is the capability of a medium to transmit mechanical waves to adjacent media, without scattering. This characteristic can be achieved by carefully engineering the acoustic impedance of the medium -- a combination of…
Real-world 3D data may contain intricate details defined by salient surface gaps. Automated reconstruction of these open surfaces (e.g., non-watertight meshes) is a challenging problem for environment synthesis in mixed reality…
Recently, a method to compute the implicit equation of a parametrized hypersurface has been developed by the authors. We address here some questions related to this method. First, we prove that the degree estimate for the stabilization of…
The work explores a specific scenario for structural computational optimization based on the following elements: (a) a relaxed optimization setting considering the ersatz (bi-material) approximation, (b) a treatment based on a nonsmoothed…
Porous materials are relevant for a broad range of technologies from catalysis and filtration, to tissue engineering and lightweight structures. Controlling the porosity of these materials over multiple length scales often leads to enticing…
Using numerical simulations we investigate the transverse depinning of moving vortex lattices interacting with random disorder. We observe a finite transverse depinning barrier for vortex lattices that are driven with high longitudinal…
We introduce DMTet, a deep 3D conditional generative model that can synthesize high-resolution 3D shapes using simple user guides such as coarse voxels. It marries the merits of implicit and explicit 3D representations by leveraging a novel…
Implicit surface representations, such as signed-distance functions, combined with deep learning have led to impressive models which can represent detailed shapes of objects with arbitrary topology. Since a continuous function is learned,…
We present in this paper a new family of implicit function for synthesizing a wide variety of 3D surfaces. The basis of this family consists of the usual functions that are: the function rectangular pulses, the function saw-tooth pulses,…
Topological states of matter, first discovered in quantum systems, have opened new avenues for wave manipulation beyond the quantum realm. In elastic media, realizing these topological effects requires identifying lattices that support the…