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Optical metasurfaces are planar arrangements of subwavelength meta-atoms that implement a wide range of transformations on incident light. The design of efficient metasurfaces requires that the responses of and interactions among meta-atoms…
A spherical $t$-design is a finite subset $X$ of the unit sphere such that every polynomial of degree at most $t$ has the same average over $X$ as it does over the entire sphere. Determining the minimum possible size of spherical designs,…
Topology optimization offers great opportunities to design permanent magnetic systems that have specific external field characteristics. Additive manufacturing of polymer bonded magnets with an end-user 3D printer can be used to manufacture…
Shells, i.e., objects made of a thin layer of material following a surface, are among the most common structures in use. They are highly efficient, in terms of material required to maintain strength, but also prone to deformation and…
Self-assembly is the autonomous organization of components into patterns or structures: an essential ingredient of biology and a desired route to complex organization. At equilibrium, the structure is encoded through specific interactions,…
We present a new theoretical framework for modelling the cluster growing process. Starting from the initial tetrahedral cluster configuration, adding new atoms to the system and absorbing its energy at each step, we find cluster growing…
Discrete-time stochastic systems with continuous spaces are hard to verify and control, even with MDP abstractions due to the curse of dimensionality. We propose an abstraction-based framework with robust dynamic programming mappings that…
This paper introduces a methodology designed to augment the inverse design optimization process in scenarios constrained by limited compute, through the strategic synergy of multi-fidelity evaluations, machine learning models, and…
Algorithmic self-assembly, a generalization of crystal growth processes, has been proposed as a mechanism for autonomous DNA computation and for bottom-up fabrication of complex nanostructures. A `program' for growing a desired structure…
This paper presents a density-based topology optimization method for designing 3D thin-walled structures with adaptive meshing. Uniform wall thickness is achieved by simultaneously constraining the minimum and maximum feature sizes using…
The construction of optimal line packings in real or complex Euclidean spaces has shown to be a tantalizingly difficult task, because it includes the problem of finding maximal sets of equiangular lines. In the regime where equiangular…
Finite element methods usually construct basis functions and quadrature rules for multidimensional domains via tensor products of one-dimensional counterparts. While straightforward, this approach results in integration spaces larger than…
We apply a simple model system of patchy particles to study monodisperse self-assembly, using the Platonic solids as target structures. We find marked differences between the assembly behaviours of the different systems. Tetrahedra,…
We construct maximally recoverable codes (corresponding to partial MDS codes) which are based on linearized Reed-Solomon codes. The new codes have a smaller field size requirement compared with known constructions. For certain asymptotic…
Despite the rapidly evolving field of computational electromagnetics, few open-source tools have managed to tackle the problem of automatic mesh generation for properly discretizing the problem of interest into a finite set of elements…
Given a function f defined on a bidimensional bounded domain and a positive integer N, we study the properties of the triangulation that minimizes the distance between f and its interpolation on the associated finite element space, over all…
Curved structures in soft matter and biological systems commonly emerge as a result of self-assembly processes where building blocks aggregate in a controlled manner, giving rise to specific system structure and properties. Learning how to…
Solving large-scale optimization on-the-fly is often a difficult task for real-time computer graphics applications. To tackle this challenge, model reduction is a well-adopted technique. Despite its usefulness, model reduction often…
We propose an optimisation method for the inverse structural design of self-assembly of anisotropic patchy particles. The anisotropic interaction can be expressed by the spherical harmonics of the surface pattern on a patchy particle, and…
A major goal in nanoscience and nanotechnology is the self-assembly of any desired complex structure with a system of particles interacting through simple potentials. To achieve this objective, intense experimental and theoretical efforts…