This investigation, conducted at 24 full‐scale activated sludge wastewater treatment plants, quantified the extent of floc breakup resulting from the manner in which mixed liquors in aeration basins and conveyance systems are handled. Results showed that the concentration of dispersed solids increases with increasing aeration basin mixing intensity in the case of diffused air aeration systems. Also, the beneficial effect of the tapered aeration mode of operation on the extent of flocculation was shown. In mechanically aerated basins, the location of the aerator nearest the basin discharge point was found to be critical with respect to floc integrity since the degree of solids dispersion was shown to vary inversely with distance from a mechanical aerator. The presence of elbows and free falls of less than 0.5 m in mixed liquor transport systems was found to slightly increase solids dispersion. Free falls greater than 1.2 m however, were observed to cause significant floc breakup. Shear rates normally present in conveyance pipelines resulted in net floc aggregation.

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We show that a flat two dimensional network of connected vertices, when stretched, may deform plastically by producing "pleats"; system spanning linear structures with width comparable to the lattice spacing, where the network overlaps on itself. To understand the pleating process, we introduce an external field that couples to local non-affine displacements, i.e. those displacements of neighbouring vertices that cannot be represented as a local affine strain. We obtain both zero and finite temperature phase diagrams in the strain -field plane. Pleats occur here as a result of an equilibrium first-order transition from the homogeneous network to a heterogeneous phase where stress is localised within pleats and eliminated elsewhere. We show that in the thermodynamic limit the un-pleated state is always metastable at vanishing field for infinitesimal strain. Plastic deformation of the initially homogeneous network is akin to the decay of a metastable phase via a dynamical transition. We make predictions concerning local stress distributions and thermal effects associated with pleats which may be observable in suitable experimental systems. arXiv:1803.05241v2 [cond-mat.soft]

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We derive exact results for correlations in the displacement fields {δ r} ≡ {δr µ=x,y } in near-crystalline athermal systems in two dimensions. We analyze the displacement correlations produced by different types of microscopic disorder, and show that disorder at the microscopic scale gives rise to longrange correlations with a dependence on the system size L given by δr µ δr ν ∼ c µν (r/L, θ). In addition, we show that polydispersity in the constituent particle sizes and random bond disorder give rise to a logarithmic system size scaling, with c µν (ρ, θ) ∼ const µν − a µν (θ) log ρ + b µν (θ)ρ 2 for ρ (= r/L) → 0. This scaling is different for the case of displacement correlations produced by random external forces at each vertex of the network, given byAdditionally, we find that correlations produced by polydispersity and the correlations produced by disorder in bond stiffness differ in their symmetry properties. Finally, we also predict the displacement correlations for a model of polydispersed soft disks subject to external pinning forces, that involve two different types of microscopic disorder. We verify our theoretical predictions using numerical simulations of polydispersed soft disks with random spring contacts in two dimensions.