Generalized Langevin equations for a driven tracer in dense soft colloids: construction and applications

We describe a tracer in a bath of soft Brownian colloids by a particle coupled to the density field of the other bath particles. From the Dean equation, we derive an exact equation for the evolution of the whole system, and show that the density field evolution can be linearized in the limit of a dense bath. This linearized Dean equation with a tracer taken apart is validated by the reproduction of previous results on the mean-field liquid structure and transport properties. Then, the tracer is submitted to an external force and we compute the density profile around it, its mobility and its diffusion coefficient. Our results exhibit effects such as bias enhanced diffusion that are very similar to those observed in the opposite limit of a hard core lattice gas, indicating the robustness of these effects. Our predictions are successfully tested against molecular dynamics simulations.Comment: 21 pages, 7 figure

From microstructural features to effective toughness in disordered brittle solids

The relevant parameters at the microstructure scale that govern the macroscopic toughness of disordered brittle materials are investigated theoretically. We focus on planar crack propagation and describe the front evolution as the propagation of a long-range elastic line within a plane with random distribution of toughness. Our study reveals two regimes: in the collective pinning regime, the macroscopic toughness can be expressed as a function of a few parameters only, namely the average and the standard deviation of the local toughness distribution and the correlation lengths of the heterogeneous toughness field; in the individual pinning regime, the passage from micro to macroscale is more subtle and the full distribution of local toughness is required to be predictive. Beyond the failure of brittle solids, our findings illustrate the complex filtering process of microscale quantities towards the larger scales into play in a broad range of systems governed by the propagation of an elastic interface in a disordered medium.Comment: 7 pages, 4 figure

Effect of disorder geometry on the critical force in disordered elastic systems

We address the effect of disorder geometry on the critical force in disordered elastic systems. We focus on the model system of a long-range elastic line driven in a random landscape. In the collective pinning regime, we compute the critical force perturbatively. Not only our expression for the critical force confirms previous results on its scaling with respect to the microscopic disorder parameters, it also provides its precise dependence on the disorder geometry (represented by the disorder two-point correlation function). Our results are successfully compared to the results of numerical simulations for random field and random bond disorders.Comment: 18 pages, 7 figure

Roadmap to the morphological instabilities of a stretched twisted ribbon

We address the mechanics of an elastic ribbon subjected to twist and tensile load. Motivated by the classical work of Green and a recent experiment that discovered a plethora of morphological instabilities, we introduce a comprehensive theoretical framework through which we construct a 4D phase diagram of this basic system, spanned by the exerted twist and tension, as well as the thickness and length of the ribbon. Different types of instabilities appear in various "corners" of this 4D parameter space, and are addressed through distinct types of asymptotic methods. Our theory employs three instruments, whose concerted implementation is necessary to provide an exhaustive study of the various parameter regimes: (i) a covariant form of the F\"oppl-von K\'arm\'an (cFvK) equations to the helicoidal state - necessary to account for the large deflection of the highly-symmetric helicoidal shape from planarity, and the buckling instability of the ribbon in the transverse direction; (ii) a far from threshold (FT) analysis - which describes a state in which a longitudinally-wrinkled zone expands throughout the ribbon and allows it to retain a helicoidal shape with negligible compression; (iii) finally, we introduce an asymptotic isometry equation that characterizes the energetic competition between various types of states through which a twisted ribbon becomes strainless in the singular limit of zero thickness and no tension.Comment: Submitted to Journal of Elasticity, themed issue on ribbons and M\"obius band

Cylinder morphology of a stretched and twisted ribbon

A rich zoology of shapes emerges from a simple stretched and twisted elastic ribbon. Despite a lot of interest, all these shape are not understood, in particular the shape that prevails at large tension and twist and that emerges from a transverse instability of the helicoid. Here, we propose a simple description for this cylindrical shape. By comparing its energy to the energy of other configurations, we are able to determine its location on the phase diagram. The theoretical predictions are in good agreement with our experimental results

Mechanics of large folds in thin interfacial films

A thin film at a liquid interface responds to uniaxial confinement by wrinkling and then by folding; its shape and energy have been computed exactly before self contact. Here, we address the mechanics of large folds, i.e. folds that absorb a length much larger than the wrinkle wavelength. With scaling arguments and numerical simulations, we show that the antisymmetric fold is energetically favorable and can absorb any excess length at zero pressure. Then, motivated by puzzles arising in the comparison of this simple model to experiments on lipid monolayers and capillary rafts, we discuss how to incorporate film weight, self-adhesion and energy dissipation.Comment: 5 pages, 3 figure

Thermal Casimir drag in fluctuating classical fields

A uniformly moving inclusion which locally suppresses the fluctuations of a classical thermally excited field is shown to experience a drag force which depends on the dynamics of the field. It is shown that in a number of cases the linear friction coefficient is dominated by short distance fluctuations and takes a very simple form. Examples where this drag can occur are for stiff objects, such as proteins, nonspecifically bound to more flexible ones such as polymers and membranes.Comment: 4 pages RevTex, 2 figure