Beyond the Ising Spin Glass I m-Vector, Potts, p-Spin, Spherical, Induced Moment, Random Graphs
Chapter in Spin Glass Theory and Far Beyond, World Scientific Publishing (2023) 21-35
Viscoelastic confinement induces periodic flow reversals in active nematics
arXiv preprint arXiv:2307.14919
Abstract:
We use linear stability analysis and hybrid lattice Boltzmann simulations to study the dynamical behaviour of an active nematic confined in a channel made of viscoelastic material. We find that the quiescent, ordered active nematic is unstable above a critical activity. The transition is to a steady flow state for high elasticity of the channel surroundings. However, below a threshold elastic modulus, the system produces spontaneous oscillations with periodic flow reversals. We provide a phase diagram that highlights the region where time-periodic oscillations are observed and explain how they are produced by the interplay of activity and viscoelasticity. Our results suggest new experiments to study the role of viscoelastic confinement in the spatio-temporal organization and control of active matter.
Maximum mutational robustness in genotype-phenotype maps follows a self-similar blancmange-like curve
Journal of the Royal Society Interface Royal Society 20:204 (2023) 20230169
Abstract:
Phenotype robustness, defined as the average mutational robustness of all the genotypes that map to a given phenotype, plays a key role in facilitating neutral exploration of novel phenotypic variation by an evolving population. By applying results from coding theory, we prove that the maximum phenotype robustness occurs when genotypes are organized as bricklayer's graphs, so-called because they resemble the way in which a bricklayer would fill in a Hamming graph. The value of the maximal robustness is given by a fractal continuous everywhere but differentiable nowhere sums-of-digits function from number theory. Interestingly, genotype-phenotype maps for RNA secondary structure and the hydrophobic-polar (HP) model for protein folding can exhibit phenotype robustness that exactly attains this upper bound. By exploiting properties of the sums-of-digits function, we prove a lower bound on the deviation of the maximum robustness of phenotypes with multiple neutral components from the bricklayer's graph bound, and show that RNA secondary structure phenotypes obey this bound. Finally, we show how robustness changes when phenotypes are coarse-grained and derive a formula and associated bounds for the transition probabilities between such phenotypes.Supersymmetry on the honeycomb lattice: resonating charge stripes, superfrustration, and domain walls
(2023)
Statistics of matrix elements of local operators in integrable models
ArXiv 2307.1241 (2023)