scholarly journals Topological invariants of Floquet systems: General formulation, special properties, and Floquet topological defects

2017 ◽  
Vol 96 (19) ◽  
Author(s):  
Shunyu Yao ◽  
Zhongbo Yan ◽  
Zhong Wang
Keyword(s):  
Topological Defects ◽  
Topological Invariants

scholarly journals Tackling tangledness of cosmic strings by knot polynomial topological invariants

2017 ◽  
Vol 32 (27) ◽  
pp. 1750164 ◽  
Author(s):  
Xinfei Li ◽  
Xin Liu ◽  
Yong-Chang Huang
Keyword(s):  
Cosmic Strings ◽  
Topological Defects ◽  
Topological Invariant ◽  
Topological Invariants ◽  
String Topology ◽  
Promising Candidate ◽  
Linking Numbers ◽  
Quintessence Field ◽  
Chern Simons ◽  
Knot Polynomial

Cosmic strings in the early universe have received revived interest in recent years. In this paper, we derive these structures as topological defects from singular distributions of the quintessence field of dark energy. Our emphasis is placed on the topological charge of tangled cosmic strings, which originates from the Hopf mapping and is a Chern–Simons action possessing strong inherent tie to knot topology. It is shown that the Kauffman bracket knot polynomial can be constructed in terms of this charge for unoriented knotted strings, serving as a topological invariant much stronger than the traditional Gauss linking numbers in characterizing string topology. Especially, we introduce a mathematical approach of breaking-reconnection which provides a promising candidate for studying physical reconnection processes within the complexity-reducing cascades of tangled cosmic strings.

A Pseudo Five-Fold Symmetrical Ligand Drives Geometric Frustration in Porous Metal-Organic and Hydrogen Bonded Frameworks

2020 ◽  
Author(s):  
Frederik Haase ◽  
Gavin Craig ◽  
Mickaele Bonneau ◽  
kunihisa sugimoto ◽  
Shuhei Furukawa
Keyword(s):  
Topological Defects ◽  
Porous Metal ◽  
Building Blocks ◽  
Structural Features ◽  
Equilibrium Structure ◽  
Sorption Behavior ◽  
Building Unit ◽  
Geometric Frustration ◽  
Secondary Building Units ◽  
Hydrogen Bonded

Reticular framework materials thrive on designability, but unexpected reaction outcomes are crucial in exploring new structures and functionalities. By combining “incompatible” building blocks, we employed geometric frustration in reticular materials leading to emergent structural features. The combination of a pseudo C<sub>5</sub> symmetrical organic building unit based on a pyrrole core, with a C<sub>4</sub> symmetrical copper paddlewheel synthon led to three distinct frameworks by tuning the synthetic conditions. The frameworks show structural features typical for geometric frustration: self-limiting assembly, internally stressed equilibrium structures and topological defects in the equilibrium structure, which manifested in the formation of a hydrogen bonded framework, distorted and broken secondary building units and dangling functional groups, respectively. The influence of geometric frustration on the CO<sub>2</sub> sorption behavior and the discovery of a new secondary building unit shows geometric frustration can serve as a strategy to obtain highly complex porous frameworks.

A Pseudo Five-Fold Symmetrical Ligand Drives Geometric Frustration in Porous Metal-Organic and Hydrogen Bonded Frameworks

2020 ◽  
Author(s):  
Frederik Haase ◽  
Gavin Craig ◽  
Mickaele Bonneau ◽  
kunihisa sugimoto ◽  
Shuhei Furukawa
Keyword(s):  
Topological Defects ◽  
Porous Metal ◽  
Building Blocks ◽  
Structural Features ◽  
Equilibrium Structure ◽  
Sorption Behavior ◽  
Building Unit ◽  
Geometric Frustration ◽  
Secondary Building Units ◽  
Hydrogen Bonded

Reticular framework materials thrive on designability, but unexpected reaction outcomes are crucial in exploring new structures and functionalities. By combining “incompatible” building blocks, we employed geometric frustration in reticular materials leading to emergent structural features. The combination of a pseudo C<sub>5</sub> symmetrical organic building unit based on a pyrrole core, with a C<sub>4</sub> symmetrical copper paddlewheel synthon led to three distinct frameworks by tuning the synthetic conditions. The frameworks show structural features typical for geometric frustration: self-limiting assembly, internally stressed equilibrium structures and topological defects in the equilibrium structure, which manifested in the formation of a hydrogen bonded framework, distorted and broken secondary building units and dangling functional groups, respectively. The influence of geometric frustration on the CO<sub>2</sub> sorption behavior and the discovery of a new secondary building unit shows geometric frustration can serve as a strategy to obtain highly complex porous frameworks.

scholarly journals Defects and perturbation

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Enrico M. Brehm
Keyword(s):  
Entanglement Entropy ◽  
Topological Defects ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Conformal Field

Abstract We investigate perturbatively tractable deformations of topological defects in two-dimensional conformal field theories. We perturbatively compute the change in the g-factor, the reflectivity, and the entanglement entropy of the conformal defect at the end of these short RG flows. We also give instances of such flows in the diagonal Virasoro and Super-Virasoro Minimal Models.

Base polynomials for degree and distance based topological invariants of n-bilinear straight pentachain

2021 ◽  
pp. 1-17
Author(s):  
Abdul Rauf Nizami ◽  
Khurram Shabbir ◽  
Muhammad Shoaib Sardar ◽  
Muhammad Qasim ◽  
Murat Cancan ◽  
...  
Keyword(s):  
Topological Invariants

scholarly journals Properties of twisted topological defects in 2D nematic liquid crystals

Soft Matter ◽  
2021 ◽  
Author(s):  
Daniel Pearce ◽  
Karsten Kruse
Keyword(s):  
Liquid Crystals ◽  
Nematic Liquid Crystals ◽  
Topological Defects ◽  
Two Dimensional

Topological defects are one of the most conspicuous features of liquid crystals. In two dimensional nematics, they have been shown to behave effectively as particles with both, charge and orientation,...

Topological defects involving Fe/N co-doped mesoporous carbon nanosheets as novel electrocatalysts for the oxygen reduction reaction and Zn–air batteries

Nanoscale ◽  
2021 ◽  
Author(s):  
Junjie Ding ◽  
Dongchuang Wu ◽  
Senhe Huang ◽  
Chenbao Lu ◽  
Yu Chen ◽  
...  
Keyword(s):  
Oxygen Reduction Reaction ◽  
Oxygen Reduction ◽  
Topological Defects ◽  
Reduction Reaction ◽  
Defect Engineering ◽  
Carbon Nanosheets ◽  
Renewable Energy Technologies ◽  
Central Focus ◽  
Energy Technologies ◽  
Co Doped

Developing effective electrocatalysts for oxygen reduction reaction is of great significance for clean and renewable energy technologies, such as metal–air batteries and fuel cells. Defect engineering is the central focus...

scholarly journals Unification of topological invariants in Dirac models

2021 ◽  
Vol 103 (24) ◽  
Author(s):  
Gero von Gersdorff ◽  
Shahram Panahiyan ◽  
Wei Chen
Keyword(s):  
Topological Invariants
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