scholarly journals Dynamical arrest of topological defects in 2D hyperuniform disk packings

2021 ◽  
Vol 249 ◽  
pp. 15002
Author(s):  
Sungyeon Hong ◽  
Michael A. Klatt ◽  
Gerd Schröder-Turk ◽  
Nicolas François ◽  
Mohammad Saadatfar
Keyword(s):  
Topological Defects ◽  
2D Systems ◽  
Voronoi Cells ◽  
Geometric Frustration ◽  
Energy Minimisation ◽  
Hexatic Phase ◽  
Collective Motions ◽  
Disk Packings

We investigate collective motions of points in 2D systems, orchestrated by Lloyd algorithm. The algorithm iteratively updates a system by minimising the total quantizer energy of the Voronoi landscape of the system. As a result of a tradeoff between energy minimisation and geometric frustration, we find that optimised systems exhibit a defective landscape along the process, where strands of 5- and 7-coordinated dislocations are embedded in the hexatic phase. In particular, dipole defects, each of which is the simplest possible pair of a pentagon and a heptagon, come into the picture of dynamical arrest, as the system freezes down to a disordered hyperuniform state. Moreover, we explore the packing fractions of 2D disk packings associated to the obtained hyperuniform systems by considering the maximum inscribed disks in their Voronoi cells.

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 Unified analysis of Topological Defects in 2D systems of Active and Passive disks

Soft Matter ◽  
2021 ◽  
Author(s):  
Pasquale Digregorio ◽  
Demian Levis ◽  
Leticia Cugliandolo ◽  
Giuseppe Gonnella ◽  
Ignacio Pagonabarraga
Keyword(s):  
Steady State ◽  
Quantitative Analysis ◽  
Topological Defects ◽  
2D Systems

We provide a comprehensive quantitative analysis of localized and extended topological defects in the steady state of 2D passive and active repulsive Brownian disk systems. We show that, both in...

scholarly journals How geometric frustration shapes twisted fibres, inside and out: competing morphologies of chiral filament assembly

2017 ◽  
Vol 7 (4) ◽  
pp. 20160140 ◽  
Author(s):  
Douglas M. Hall ◽  
Gregory M. Grason
Keyword(s):  
Continuum Theory ◽  
Topological Defects ◽  
Equilibrium Structure ◽  
Generic Model ◽  
Finite Width ◽  
Mechanical Stiffness ◽  
Geometric Frustration ◽  
Filament Assembly ◽  
Morphological Responses ◽  
Filament Bundle

Chirality frustrates and shapes the assembly of flexible filaments in rope-like, twisted bundles and fibres by introducing gradients of both filament shape (i.e. curvature) and packing throughout the structure. Previous models of chiral filament bundle formation have shown that this frustration gives rise to several distinct morphological responses, including self-limiting bundle widths, anisotropic domain (tape-like) formation and topological defects in the lateral inter-filament order. In this paper, we employ a combination of continuum elasticity theory and discrete filament bundle simulations to explore how these distinct morphological responses compete in the broader phase diagram of chiral filament assembly. We show that the most generic model of bundle formation exhibits at least four classes of equilibrium structure—finite-width, twisted bundles with isotropic and anisotropic shapes, with and without topological defects, as well as bulk phases of untwisted, columnar assembly (i.e. ‘frustration escape’). These competing equilibrium morphologies are selected by only a relatively small number of parameters describing filament assembly: bundle surface energy, preferred chiral twist and stiffness of chiral filament interactions, and mechanical stiffness of filaments and their lateral interactions. Discrete filament bundle simulations test and verify continuum theory predictions for dependence of bundle structure (shape, size and packing defects of two-dimensional cross section) on these key parameters.

Understanding of social behaviour in human collective motions with non-trivial rule of control

Impact ◽  
2019 ◽  
Vol 2019 (10) ◽  
pp. 84-86
Author(s):  
Keisuke Fujii
Keyword(s):  
Machine Learning ◽  
Team Sports ◽  
Machine Learning Techniques ◽  
Theoretical Modelling ◽  
Video Footage ◽  
Learning Techniques ◽  
Collective Motions ◽  
Tracking Movements ◽  
Or Team ◽  
Computational Ability

The coordination and movement of people in large crowds, during sports games or when socialising, seems readily explicable. Sometimes this occurs according to specific rules or instructions such as in a sport or game, at other times the motivations for movement may be more focused around an individual's needs or fears. Over the last decade, the computational ability to identify and track a given individual in video footage has increased. The conventional methods of how data is gathered and interpreted in biology rely on fitting statistical results to particular models or hypotheses. However, data from tracking movements in social groups or team sports are so complex as they cannot easily analyse the vast amounts of information and highly varied patterns. The author is an expert in human behaviour and machine learning who is based at the Graduate School of Informatics at Nagoya University. His challenge is to bridge the gap between rule-based theoretical modelling and data-driven modelling. He is employing machine learning techniques to attempt to solve this problem, as a visiting scientist in RIKEN Center for Advanced Intelligence Project.

Observing the hexatic phase in 2-D melting

2021 ◽  
Vol 99 (4) ◽  
pp. 7-7
Author(s):  
Sam Lemonick
Keyword(s):  
Hexatic Phase

On farthest Bregman Voronoi cells

Optimization ◽  
2021 ◽  
pp. 1-11
Author(s):  
Juan Enrique Martínez-Legaz ◽  
Maryam Tamadoni Jahromi ◽  
Eskandar Naraghirad
Keyword(s):  
Voronoi Cells
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