Related papers: Engineering Topological Materials
Topological defects are an essential part of the structure and dynamics of all liquid crystals, and they are particularly important in experiments and simulations on active liquid crystals. In a recent paper, Vromans and Giomi [Soft Matter,…
Topology is being widely adopted to understand and to categorize quantum matter in modern physics. The nexus of topology orders, which engenders distinct quantum phases with benefits to both fundamental research and practical applications…
Systems as diverse as mechanical structures assembled from elastic components, and photonic metamaterials enjoy a common geometrical feature: a sublattice symmetry. This property realizes a chiral symmetry first introduced to characterize a…
Time has entered the domain of topological phases in the field of non-Hermitian physics. Previous studies have relied on periodic modulation in time to make an intuitive connection to established spatial topological invariants, albeit with…
We develop a transitional geometry, that is, a family of geometries of constant curvatures which makes a continuous connec-tion between the hyperbolic, Euclidean and spherical geometries. In this transitional setting, several geometric…
We consider the slow and athermal deformations of amorphous solids and show how the ensuing sequence of discrete plastic rearrangements can be mapped onto a directed network. The network topology reveals a set of highly connected regions…
Topology transcends boundaries that conventionally delineate physical, biological and engineering sciences. Our ability to mathematically describe topology, combined with our access to precision tracking and manipulation approaches, has…
We introduce structural heterogeneity, a new topological characteristic for semi-ordered materials that captures their degree of organisation at a mesoscopic level and tracks their time-evolution, ultimately detecting the order-disorder…
We present theoretical and experimental results probing the rich topological structure of arbitrarily disordered finite tight binding Hamiltonians with chiral symmetry. We extend the known classification by considering the topological…
Topological defects are singularities in material fields that play a vital role across a range of systems: from cosmic microwave background polarization to superconductors, and biological materials. Although topological defects and their…
To provide a phenomenological theory for the various interesting transitions in restructuring networks we employ a statistical mechanical approach with detailed balance satisfied for the transitions between topological states. This enables…
Various topological techniques and tools have been applied to neural networks in terms of network complexity, explainability, and performance. One fundamental assumption of this line of research is the existence of a global (Euclidean)…
Modulated symmetries are internal symmetries which do not commute with spatial symmetries; dipolar symmetries are a prime example. We give a general recipe for constructing topological phases protected by modulated symmetries via a defect…
While quasi-two-dimensional (layered) materials can be highly anisotropic, their asymptotic long-distance behavior generally reflects the properties of a fully three dimensional phase of matter. However, certain topologically ordered…
The search for materials with topological properties is an ongoing effort. In this article we propose a systematic statistical method supported by machine learning techniques that is capable of constructing topological models for a generic…
In this paper we present a novel two-scale framework to optimize the structure and the material distribution of an object given its functional specifications. Our approach utilizes multi-material microstructures as low-level building blocks…
How can one fully harness the power of physics encoded in relativistic $N$-body phase space? Topologically, phase space is isomorphic to the product space of a simplex and a hypersphere and can be equipped with explicit coordinates and a…
The order parameter of the smectic liquid crystal phase is the same as that of a superfluid or superconductor, namely a complex scalar field. We show that the essential difference in boundary conditions between these systems leads to a…
Micro-structured materials consisting of an array of microstructures are engineered to provide the specific material properties. This present work investigates the design of cellular materials under the framework of level set, so as to…
This work concerns a structural topology optimisation problem for 4D printing based on the phase field approach. The concept of 4D printing as a targeted evolution of 3D printed structures can be realised in a two-step process. One first…