Condensed Matter Theory

Abstract:

Using particle-tracking techniques, the translational and rotational diffusion of paralyzed E. coli with and without flagella are studied experimentally. The position and orientation of the bacteria are tracked in the lab frame and their corresponding mean-square displacements are analyzed in the lab frame and in the body frame to extract the intrinsic anisotropic translational diffusion coefficients as well as the rotational diffusion coefficient for both strains. The deflagellated strain is found to show an anisotropic translational diffusion, with diffusion coefficients that are compatible with theoretical estimates based on its measured geometrical features. The corresponding translational diffusion coefficients of the flagellated strain have been found to be reduced as compared to those of the deflagellated counterpart. Similar results have also been found for the rotational diffusion coefficients of the two strains. Our results suggest that the presence of flagella --even as a passive component-- has a significant role in the dynamics of E. coli, and should be taken into account in theoretical studies of its motion.

Abstract:

Synchronization of coupled oscillators on a d-dimensional lattice with the power-law coupling G(r) = g0/rα and randomly distributed intrinsic frequency is analyzed. A systematic perturbation theory is developed to calculate the order parameter profile and correlation functions in powers of ϵ = α/d-1. For α ≤ d, the system exhibits a sharp synchronization transition as described by the conventional mean-field theory. For α > d, the transition is smeared by the quenched disorder, and the macroscopic order parameter ψ decays slowly with g0 as |ψ| ∝ g(0)(2).

Abstract:

Using particle-tracking techniques, the translational and rotational diffusion of paralyzed E. coli with and without flagella are studied experimentally. The position and orientation of the bacteria are tracked in the lab frame and their corresponding mean-square displacements are analyzed in the lab frame and in the body frame to extract the intrinsic anisotropic translational diffusion coefficients as well as the rotational diffusion coefficient for both strains. The deflagellated strain is found to show an anisotropic translational diffusion, with diffusion coefficients that are compatible with theoretical estimates based on its measured geometrical features. The corresponding translational diffusion coefficients of the flagellated strain have been found to be reduced as compared to those of the deflagellated counterpart. Similar results have also been found for the rotational diffusion coefficients of the two strains. Our results suggest that the presence of flagella --even as a passive component-- has a significant role in the dynamics of E. coli, and should be taken into account in theoretical studies of its motion.

Abstract:

We study the spin quantum Hall effect and transitions between Hall plateaus in quasi two-dimensional network models consisting of several coupled layers. Systems exhibiting the spin quantum Hall effect belong to class C in the symmetry classification for Anderson localisation, and for network models in this class there is an established mapping between the quantum problem and a classical one involving random walks. This mapping permits numerical studies of plateau transitions in much larger samples than for other symmetry classes, and we use it to examine localisation in systems consisting of $n$ weakly coupled layers. Standard scaling ideas lead one to expect $n$ distinct plateau transitions, but in the case of the unitary symmetry class this conclusion has been questioned. Focussing on a two-layer model, we demonstrate that there are two separate plateau transitions, with the same critical properties as in a single-layer model, even for very weak interlayer coupling.