Related papers: Pinning for the critical and supercritical membran…
We study the case of contact angle hysteresis, when a solid defect is quasi-statically pulled out and pushed into a liquid, in the presence of gravity. We solve the problem analytically in an approximation which, in the case of a truncated…
We consider a model of an elastic manifold driven on a disordered energy landscape, with generalized long range elasticity. Varying the form of the elastic kernel by progressively allowing for the existence of zero-modes, the model…
We report on the modeling of the dynamics of confined lipid membranes. We derive a thin film model in the lubrication limit which describes an inextensible liquid membrane with bending rigidity confined between two adhesive walls. The…
Understanding the role played by the microstructure of materials on their macroscopic failure properties is an important challenge in solid mechanics. Indeed, when a crack propagates at a heterogeneous brittle interface, the front is…
We present a minimal model of plasma membrane heterogeneity that combines criticality with connectivity to cortical cytoskeleton. Our model is motivated by recent observations of micron-sized critical fluctuations in plasma membrane…
In this note, we show how the penalization method, introduced in order to describe some non-trivial changes of the Wiener measure, can be applied to the study of some simple polymer models such as the pinning model. The bulk of the analysis…
The depinning of a contact line is studied as a dynamical critical phenomenon by a functional renormalization group technique. In $D=2-\epsilon$ interface dimensions, the roughness exponent is $\zeta=\epsilon/3$ to all orders in…
In this paper, we consider the discrete membrane model in four dimensions. We confirm the existence of the scaling limit of the intermediate (i.e., a multiple of the expected maximum) level-sets of the model, and show that it is equal in…
We consider the dimer model in cylindrical domains $\Omega_\delta$ on square grids of mesh size $\delta$ with two Temperleyan boundary components of different colors. Assuming that the $\Omega_\delta$ approximate a cylindrical domain…
We apply a recently advocated simulation scheme that employs a local order-parameter pinning field to study quantum critical phenomena in the two-dimensional square-lattice bilayer quantum Heisenberg model. Using a world-line quantum Monte…
We derive a continuum model for incompatible elasticity as a variational limit of a family of discrete nearest-neighbor elastic models. The discrete models are based on discretizations of a smooth Riemannian manifold $(M,\mathfrak{g})$,…
We use a macroscopic Hamiltonian approach to study the pinning of a solid--liquid--vapour contact line on an array of equidistant stripes of obstacles perpendicular to the liquid. We propose an estimate of the density of pinning stripes for…
The three-dimensional frustrated anisotropic XY model with point disorder is studied with both Monte Carlo simulations and resistively-shunted-junction dynamics to model the dynamics of a type-II superconductor with quenched point pinning…
The shape of a liquid-air interface advancing on a heterogeneous surface was studied experimentally, together with the force induced by the pinning of the contact line to surface defects. Different surfaces were considered with circular…
Vortex pinning is a crucial factor that determines the critical current of practical superconductors and enables their diverse applications. However, the underlying mechanism of vortex pinning has long been elusive, lacking a clear…
Consider balls $\Lambda_n$ of growing volumes in the $d$-dimensional hierarchical lattice, and place edges independently between each pair of vertices $x\neq y\in\Lambda_n$ with probability $1-\exp(-\beta J(x, y) )$ where $J(x, y) \asymp \|…
The vortex-lattice melting line in three-dimensional type-II superconductors with pinning is derived by equating the free energies of the vortex system in the solid and liquid phases. We account for the elastic and pinning energies and the…
We formulate and analyze interior penalty discontinuous Galerkin methods for coupled elliptic PDEs modeling excitable tissue, represented by intracellular and extracellular domains sharing a common interface. The PDEs are coupled through a…
Dissipation-free current transport in type II superconductors requires vortices to be pinned by defects in the underlying material. The pinning capacity of a defect is quantified by the Labusch parameter $\kappa \sim f_p/\xi\bar{C}$,…
We consider the scaling limit of a generic ferromagnetic system with a continuous phase transition, on the half plane with boundary conditions leading to the equilibrium of two different phases below criticality. We use general properties…