Critical percolation in the ordering kinetics of twisted nematic phases
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866916089786531840 |
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| author | Almeida, Renan A. L. |
| author_facet | Almeida, Renan A. L. |
| contents | I report on the experimental confirmation that critical percolation statistics underlie the ordering kinetics of twisted nematic phases in the Allen-Cahn universality class. Soon after the ordering starts from a homogeneous disordered phase and proceeds towards a broken $\mathbb{Z}_2$-symmetry phase, the system seems to be attracted to the random percolation fixed point at a special timescale $t_{\textrm{p}}$. At this time, exact formulae for crossing probabilities in percolation theory agree with the corresponding probabilities in the experimental data. The ensuing evolution for the number density of hull-enclosed areas is described by an exact expression derived from a percolation model endowed with curvature-driven interface motion. Scaling relation for hull-enclosed areas versus perimeters reveals that the fractal percolation geometry is progressively morphed into a regular geometry up to the order of the classical coarsening length. In view of its universality and experimental possibilities, the study opens a path for exploring percolation keystones in the realm of nonequilibrium, phase-ordering systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2306_11672 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Critical percolation in the ordering kinetics of twisted nematic phases Almeida, Renan A. L. Statistical Mechanics Soft Condensed Matter I report on the experimental confirmation that critical percolation statistics underlie the ordering kinetics of twisted nematic phases in the Allen-Cahn universality class. Soon after the ordering starts from a homogeneous disordered phase and proceeds towards a broken $\mathbb{Z}_2$-symmetry phase, the system seems to be attracted to the random percolation fixed point at a special timescale $t_{\textrm{p}}$. At this time, exact formulae for crossing probabilities in percolation theory agree with the corresponding probabilities in the experimental data. The ensuing evolution for the number density of hull-enclosed areas is described by an exact expression derived from a percolation model endowed with curvature-driven interface motion. Scaling relation for hull-enclosed areas versus perimeters reveals that the fractal percolation geometry is progressively morphed into a regular geometry up to the order of the classical coarsening length. In view of its universality and experimental possibilities, the study opens a path for exploring percolation keystones in the realm of nonequilibrium, phase-ordering systems. |
| title | Critical percolation in the ordering kinetics of twisted nematic phases |
| topic | Statistical Mechanics Soft Condensed Matter |
| url | https://arxiv.org/abs/2306.11672 |