Algorithm Achieves Targeted Disorder in Networks with Coordination Numbers up to Four

Disordered spatial networks represent fundamental models for understanding structures and interactions across diverse scales, exhibiting complex behaviours like structural phase transitions and wave localization. Florin Hemmann, Vincent Glauser, and Ullrich Steiner, alongside Matthias Saba, all from the Adolphe Merkle Institute and University of Fribourg, have developed a novel computational method to generate these networks with specifically targeted structural properties. Their research extends the established Wooten-Weaire-Winer algorithm by incorporating bond repulsion, allowing for the creation of networks with arbitrary coordination numbers. This advancement is significant because it overcomes limitations in existing methods and enables the precise tuning of disorder within these networks. By training a neural network to predict structural characteristics, the team successfully reproduced the complex structures of four biophotonic networks, paving the way for new discoveries regarding structure-property relationships and phenomena such as band gaps in disordered materials.

Efficient numerical methods are required to computer-generate disordered networks with targeted structural properties. The established Wooten-Weaire-Winer algorithm introduces disorder into an initial network through bond switch moves. This research extends the algorithm to accommodate arbitrary coordination number statistics by introducing a general formulation of the strain energy, overcoming limitations in existing methods and enabling precise tuning of disorder.

The approach involves a rigorous mathematical derivation of the strain energy, ensuring thermodynamic consistency and accurate reflection of the network’s underlying physics. Implementation was achieved through computational simulations, validating functionality and efficiency. The resulting networks were characterised using structural metrics including coordination number and bond length distributions. Specific contributions include a generalised strain energy formulation, a validated implementation of the extended Wooten-Weaire-Winer algorithm, and comprehensive network characterisation, providing a powerful tool for investigating structure-property relationships in disordered networks and opening new avenues for materials design. This methodology is applicable to diverse scientific disciplines, including materials science, physics, and engineering.

Disordered Network Generation via Bond Manipulation

The research details a method for generating disordered networks with specific structural properties, utilising a modified Monte Carlo algorithm. The technique tunes disorder within initially crystalline networks by manipulating the bond-bending force constant within a Keating strain energy model and adjusting the temperature profile during simulation, allowing for controlled introduction of imperfections and subsequent analysis. Researchers employed the Wooten-Weaire-Winer algorithm as the foundation for their approach, introducing disorder through bond switching, vertex translation, and acceptance of new states based on the Metropolis acceptance probability. To quantify the effects of varying parameters, a suite of order metrics were used, capturing characteristics in both direct and reciprocal space.

A feedforward neural network was trained on the generated data, allowing for prediction of structural characteristics and facilitating targeted network generation. This predictive capability was demonstrated through the statistical reproduction of four disordered biophotonic networks exhibiting structural colour, highlighting the versatility of the method for generating networks with tailored properties. Potential applications include gaining insights into phenomena such as photonic band gaps and furthering understanding of complex systems across diverse scientific fields.

Tailoring Disordered Networks with Bond Repulsion

Scientists achieved a breakthrough in generating disordered networks with tailored structural properties, extending the Wooten-Weaire-Winer algorithm to accommodate networks with arbitrary coordination numbers. The research team modified the Keating strain energy by introducing bond repulsion, enabling the creation of complex 3D structures previously inaccessible. Experiments revealed the ability to generate networks containing up to 20,000 vertices, a substantial increase in scale for disordered network modelling. The study meticulously tuned disorder through variations in bond-bending force constant and temperature profiles, carefully analysing the effects using a suite of order metrics.

Measurements confirm that the modified Keating energy, incorporating a repulsive force between bonds, facilitates the creation of networks with uniformly distributed bond angles regardless of coordination number. Results demonstrate the successful statistical reproduction of four disordered biophotonic networks exhibiting structural colour, validating the algorithm’s capacity to generate networks with specific characteristics. The team established that for networks with valency greater than five, multiple minimum energy configurations exist, allowing for greater morphological diversity. Furthermore, a feedforward neural network was trained to predict structural characteristics from algorithm inputs, enabling targeted network generation and accelerating the design process. This versatile method promises new insights into structure-property relationships, particularly concerning band gaps in disordered networks and the design of advanced materials.

Disordered Network Generation via Keating Strain Energy

Computer-generated disordered spatial networks are crucial across diverse scientific disciplines. This research modified the Wooten-Weaire-Winer algorithm, traditionally limited to specific network types, to accommodate networks with arbitrary coordination numbers through a generalized Keating strain energy. By tuning parameters within this energy and the Monte Carlo evolution, the authors successfully generated disordered networks and quantified their structural characteristics using a comprehensive suite of order metrics. The study demonstrated precise control over short-range order metrics, specifically bond lengths and angles, while acknowledging a higher degree of variance in longer-range metrics related to pore size and hyperuniformity.

As validation, the algorithm statistically reproduced four disordered biophotonic networks responsible for structural colouration in beetles. Future work will focus on optical simulations to correlate structural features with optical properties, including photonic band gaps and the potential for random lasing. Additionally, the authors suggest training neural networks to predict optical properties directly from structural data, offering a computationally efficient alternative to direct simulation and extending the algorithm’s applicability beyond photonic materials. Their research extends the established Wooten-Weaire-Winer algorithm by incorporating bond repulsion, allowing for the creation of networks with arbitrary coordination numbers. By training a neural network to predict structural characteristics, the team successfully reproduced the complex structures of four biophotonic networks, paving the way for new discoveries regarding structure-property relationships and phenomena such as band gaps in disordered materials.