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Cylindrical interfaces occur in sheared or deformed emulsions and as biological or technological lipid monolayer or bilayer tubules. Like the corresponding spherical droplets and vesicles, these cylinder-like surfaces may host orientaional order with $n$-fold rotational symmetry, for example in the positions of lipid molecules or of spherical nanoparticles. We examine how that order interacts with and induces shape modulations of cylindrical interfaces. While on spherical droplets $2n$ topological defects necessarily exist and can induce icosahedral droplet shapes, the cylindrical topology is compatible with a defect-free patterning. Nevertheless, once a modulation is introduced by a mechanism such as spontaneous curvature, nontrivial patterns of order, including ones with excess defects, emerge and have nonlinear effects on the shape of the tube. Examining the equilibrium energetics of the system analytically and with a lattice-based Markov chain Monte Carlo simulation, we predict low-temperature morphologies of modulated cylindrical interfaces hosting orientational order. A shape modulation induces a banded pattern of alternatingly isotropic and ordered interfacial material. Furthermore cylindrical systems can be divided into Type I, without defects, and Type II, which go through a spectrum of defect states with up to $4n$ excess defects. The character of the curvature-induced shape transition from unmodulated to modulated cylinders is continuous or discontinuous accordingly., Comment: 18 pages, 10 figures; figures changed, clarifications added

Disease control can induce both demographic and evolutionary responses in host-parasite systems. Foreseeing the outcome of control therefore requires knowledge of the eco-evolutionary feedback between control and system. Previous work has assumed that control strategies have a homogeneous effect on the parasite population. However, this is not true when control targets those traits that confer to the parasite heterogeneous levels of resistance, which can additionally be related to other key parasite traits, through evolutionary trade-offs. In this work, we develop a minimal model coupling epidemiological and evolutionary dynamics to explore possible trait-dependent effects of control strategies. Particularly, we consider a parasite expressing continuous levels of a trait determining resource exploitation, and a control treatment that can be either positively or negatively correlated with that trait. We demonstrate the potential of trait-dependent control by considering that the decision maker may want to minimise both the damage caused by the disease and the use of treatment, due to possible environmental or economic costs. We identify efficient strategies showing that the optimal type of treatment depends on the amount applied. Our results pave the way for the study of control strategies based on evolutionary constraints, such as collateral sensitivity and resistance costs, which are receiving increasing attention for both public health and agricultural purposes.

Realistic fitness landscapes generally display a redundancy-fitness trade-off: highly fit trait configurations are inevitably rare, while less fit trait configurations are expected to be more redundant. The resulting sub-optimal patterns in the fitness distribution are typically described by means of effective formulations, where redundancy provided by the presence of neutral contributions is modelled implicitly, e.g. with a bias of the mutation process. However, the extent to which effective formulations are compatible with explicitly redundant landscapes is yet to be understood, as well as the consequences of a potential miss-match. Here we investigate the effects of such trade-off on the evolution of phenotype-structured populations, characterised by continuous quantitative traits. We consider a typical replication-mutation dynamics, and we model redundancy by means of two dimensional landscapes displaying both selective and neutral traits. We show that asymmetries of the landscapes will generate neutral contributions to the marginalised fitness-level description, that cannot be described by effective formulations, nor disentangled by the full trait distribution. Rather, they appear as effective sources, whose magnitude depends on the geometry of the landscape. Our results highlight new important aspects on the nature of sub-optimality. We discuss practical implications for rapidly mutant populations such as pathogens and cancer cells, where the qualitative knowledge of their trait and fitness distributions can drive disease management and intervention policies.

Following a quench, colloidal systems with strong, short-ranged, attractive interactions can exhibit transient gelation, instead of the classical phase-ordering mechanisms of spinodal decomposition or nucleation. The particles aggregate into a tenuous, system-spanning network, which, for a time, remains robust to mechanical disturbance. Eventually, the network's ability to recover from destructive deformations becomes compromised, and the gel collapses. A detailed experimental study of gel collapse was reported in the preceding, companion article, leaving several open questions regarding the processes involved. We present a theoretical investigation into the factors affecting a gel's lifetime, concentrating in particular on the surprising influence of the size and shape of the container. We construct a model in which solvent dynamics are replaced by a dissipative coupling of the particulate network to a fixed frame and show that, in the absence of zero-frequency elasticity, such a coupling results in a novel class of matter in which stresses cannot propagate beyond a finite distance. We find our prediction of the characteristic length to be in quantitative agreement with the experimental data, and show how its ratio to the dimensions of the container controls the sedimentation. We discuss some aspects of the ageing mechanism, and suggest that a sudden collapse is ultimately due to erosion with positive feedback.

The conditions of multi-phase equilibrium are solved for generic polydisperse systems. The case of multiple polydispersity is treated, where several properties (e.g. size, charge, shape) simultaneously vary from one particle to another. By developing a perturbative expansion in the width of the distribution of constituent species, it is possible to calculate the effects of polydispersity alone, avoiding difficulties associated with the underlying many-body problem. Explicit formulae are derived in detail, for the partitioning of species at coexistence and for the shift of phase boundaries due to polydispersity. `Convective fractionation' is quantified, whereby one property (e.g. charge) is partitioned between phases due to a driving force on another. To demonstrate the ease of use and versatility of the formulae, they are applied to models of a chemically-polydisperse polymer blend, and of fluid-fluid coexistence in polydisperse colloid-polymer mixtures. In each case, the regime of coexistence is shown to be enlarged by polydispersity., 22 pages, 3 figures

We have studied the magnetic microstates arising from single-shot thermalization processes that occur during growth in artificial square spin ices. The populations of different vertex types can be controlled by the system's lattice constant, as well as by the deposition of different material underlayers. The statistics of these populations are well described by a simple model based on the canonical ensemble, which is used to infer an effective temperature for an arrested microstate. The normalized energy level spacings of the different magnetic vertex configurations are found to be very close to those predicted for a point-dipole model: this is shown to be a very good approximation to energy level spacings calculated for finite-sized cuboid magnetic bodies. States prepared with a rotating field (an athermal method commonly used to lower the energy of these systems) cannot be described by this model, showing that such a method does not induce a near-equilibrium state.

We present an experimental procedure to perform broadband microrheological measurements with optical tweezers. A generalised Langevin equation is adopted to relate the time-dependent trajectory of a particle in an imposed flow to the frequency-dependent moduli of the complex fluid. This procedure allows us to measure the material linear viscoelastic properties across the widest frequency range achievable with optical tweezers., Comment: 5 pages, 3 figures

When modelling driven steady states of matter, it is common practice either to choose transition rates arbitrarily, or to assume that the principle of detailed balance remains valid away from equilibrium. Neither of those practices is theoretically well founded. Hypothesising ergodicity constrains the transition rates in driven steady states to respect relations analogous to, but different from the equilibrium principle of detailed balance. The constraints arise from demanding that the design of any model system contains no information extraneous to the microscopic laws of motion and the macroscopic observables. This prevents over-description of the non-equilibrium reservoir, and implies that not all stochastic equations of motion are equally valid. The resulting recipe for transition rates has many features in common with equilibrium statistical mechanics., Comment: Replaced with minor revisions to introduction and conclusions. Accepted for publication in Journal of Physics A

We find analytical solutions to the Cahn-Hilliard equation for the dynamics of an interface in a system with a conserved order parameter (Model B). We show that, although steady-state solutions of Model B are unphysical in the far-field, they shed light on the local dynamics of an interface. Exact solutions are given for a particular class of order-parameter potentials, and an expandable integral equation is derived for the general case. As well as revealing some generic properties of interfaces moving under condensation or evaporation, the formalism is used to investigate two distinct modes of interface propagation in systems with a metastable potential well. Given a sufficient transient increase in the flux of material onto a condensation nucleus, the normal motion of the interface can be disrupted by interfacial unbinding, leading to growth of a macroscopic amount of a metastable phase., Comment: 23 pages, Latex, epsf