Related papers: Engineering Topological Materials
Topological materials are quantum materials with nontrivial ground-state entanglement that are irremovable so long as certain rules, like invariance under symmetries and the existence of an energy gap, are respected. They showcase…
As a method for controlling active materials, researchers have suggested designing patterns of activity on a substrate, which should guide the motion of topological defects. To investigate this concept, we model the behavior of a single…
We are dealing with the problem of space layout planning here. We present an architectural conceptual CAD approach. Starting with design specifications in terms of constraints over spaces, a specific enumeration heuristics leads to a…
Molecules have seemed like a natural fit to deep learning's tendency to handle a complex structure through representation learning, given enough data. However, this often continuous representation is not natural for understanding chemical…
The standard approach to characterizing topological matter, computing topological invariants, fails when the symmetry protecting the topological phase is preserved only on average in a disordered system. Because topological invariants rely…
Topology optimization is a valuable tool in engineering, facilitating the design of optimized structures. However, topological changes often require a remeshing step, which can become challenging. In this work, we propose an isogeometric…
Although topological materials have recently seen tremendous development, their applications have remained elusive. Simultaneously, there exists considerable interest in pushing the limits of topological materials, including the exploration…
Mathematical descriptions of dynamical systems are deeply rooted in topological spaces defined by non-Euclidean geometry. This paper proposes leveraging structure-rich geometric spaces for machine learning to achieve structural…
Defects are a ubiquitous feature of ordered media. They have certain universal features, independent of the underlying physical system, reflecting their topological origins. While the topological properties of defects are robust, they…
A stirring device consisting of a periodic motion of rods induces a mapping of the fluid domain to itself, which can be regarded as a homeomorphism of a punctured surface. Having the rods undergo a topologically-complex motion guarantees at…
The thesis presents the subject of synthetic topology, especially with relation to metric spaces. A model of synthetic topology is a categorical model in which objects possess an intrinsic topology in a suitable sense, and all morphisms are…
Robustness against small perturbations is a crucial feature of topological properties. This robustness is both a source of theoretical interest and a drive for technological applications, but presents a challenge when looking for new…
General topological principles how to transfer the planar orders onto a sphere are considered. Formation of extended topological defects (ETDs), which have a reconstructed inner structure surrounded by perfect initial order, is discussed.…
This paper proposes a novel paradigm for machine learning that moves beyond traditional parameter optimization. Unlike conventional approaches that search for optimal parameters within a fixed geometric space, our core idea is to treat the…
In this paper, we present a topology optimization (TO) framework to enable automated design of mechanical components while ensuring the result can be manufactured using multi-axis machining. Although TO improves the part's performance, the…
Progresses in additive manufacturing technologies allow the realization of finely graded microstructured materials with tunable mechanical properties. This paves the way to a wealth of innovative applications, calling for the combined…
The homotopy theory of topological defects is a powerful tool for organizing and unifying many ideas across a broad range of physical systems. Recently, experimental progress has been made in controlling and measuring colloidal inclusions…
Topological phases are characterised by a topological invariant that remains unchanged by deformations in the Hamiltonian. Materials exhibiting topological phases include topological insulators, superconductors exhibiting strong spin-orbit…
Liquid crystals generally support orientational singularities of the director field known as topological defects. These latter modifiy transport properties in their vicinity as if the geometry was non-Euclidean. We present a state of the…
Topological mechanics can realize soft modes in mechanical metamaterials in which the number of degrees of freedom for particle motion is finely balanced by the constraints provided by interparticle interactions. However, solid objects are…