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We introduce a new property of tile self-assembly systems that we call size-separability. A system is size-separable if every terminal assembly is a constant factor larger than any intermediate assembly. Size-separability is motivated by…
Symmetry in mathematical programming may lead to a multiplicity of solutions. In nonconvex optimisation, it can negatively affect the performance of the branch-and-bound algorithm. Symmetry may induce large search trees with multiple…
We investigate the universality of multi-spin systems in architectures of various symmetries of coupling type and topology. Explicit reachability sets under symmetry constraints are provided. Thus for a given (possibly symmetric)…
Reachability analysis plays a central role in low-thrust spacecraft trajectory optimization by identifying which target states can be achieved under constraints on time, thrust, and propellant. Classical approaches construct reachable sets…
We propose a model-based, automated, bottom-up approach for design, which is applicable to various physical domains, but in this work we focus on the electrical domain. This bottom-up approach is based on a meta-topology in which each link…
The complicated mesoscopic configurations of composite plate and shell structures requires a huge amount of computational overhead for directly simulating their mechanical problems. In this paper, a unified high-order multi-scale method,…
Complex nanophotonic structures hold the potential to deliver exquisitely tailored optical responses for a range of applications. Metal-insulator-metal (MIM) metasurfaces arranged in supercells, for instance, can be tailored by geometry and…
Penalty methods have proven to be particularly effective for achieving the required $C^1$-continuity in the context of multi-patch isogeometric Kirchhoff-Love shells. Due to their conceptual simplicity, these algorithms are readily…
Ordered nanoarrays, i.e. regular patterns of quantum structures at the nanometre scale, have recently been synthesized in a wide range of systems. Here I explore a possible route to technological exploitation: assuming a simple form of…
Halbach spheres provide a theoretically elegant means of generating highly homogeneous magnetic fields, but practical implementation is hindered by challenging fabrication and restricted interior access. This study examines discrete…
Imagine we want to split a group of agents into teams in the most \emph{efficient} way, considering that each agent has their own preferences about their teammates. This scenario is modeled by the extensively studied \textsc{Coalition…
We propose a simple and efficient scheme based on adaptive finite elements over conforming quadtree meshes for collapse plastic analysis of structures. Our main interest in kinematic limit analysis is concerned with both purely…
Designing complex engineered systems requires managing tightly coupled trade-offs between subsystem capabilities and resource requirements. Monotone co-design provides a compositional language for such problems, but its generality does not…
Realizing metasurfaces for anomalous scattering is fundamental to designing reflector arrays, reconfigurable intelligent surfaces, and metasurface antennas. However, the basic cost of steering scattering into non-specular directions is not…
Physical symmetries provide a strong inductive bias for constructing functions to analyze data. In particular, this bias may improve robustness, data efficiency, and interpretability of machine learning models. However, building machine…
Directed assembly of block polymers is rapidly becoming a viable strategy for lithographic patterning of nanoscopic features. One of the key attributes of directed assembly is that an underlying chemical or topographic substrate pattern…
Solution and analysis of mathematical programming problems may be simplified when these problems are symmetric under appropriate linear transformations. In particular, a knowledge of the symmetries may help reduce the problem dimension, cut…
The matrix formation associated to high-order discretizations is known to be numerically demanding. Based on the existing procedure of interpolation and lookup, we design a multiscale assembly procedure to reduce the exorbitant assembly…
Microplastic particle ingestion or inhalation by humans is a problem of growing concern. Unfortunately, current research methods that use machine learning to understand their potential harms are obstructed by a lack of available data. Deep…
We consider the shape and topology optimization problem to design a structure that minimizes a weighted sum of material consumption and (linearly) elastic compliance under a fixed given boundary load. As is well-known, this problem is in…