Related papers: The pinning effect of dilute defects
We derive a residual a posteriori estimator for the Kirchhoff plate bending problem. We consider the problem with a combination of clamped, simply supported and free boundary conditions subject to both distributed and concentrated (point…
In this paper we discuss a level set approach for the identification of an unknown boundary in a computational domain. The problem takes the form of a Bernoulli problem where only the Dirichlet datum is known on the boundary that is to be…
We study the critical point of directed pinning/wetting models with quenched disorder. The distribution K(.) of the location of the first contact of the (free) polymer with the defect line is assumed to be of the form…
In the presence of boundaries, the entanglement entropy in lattice models is known to exhibit oscillations with the (parity of the) length of the subsystem, which however decay to zero with increasing distance from the edge. We point out in…
Vertical loads acting on the surface of a half-space made of discrete and elastic particles are supported by a network of force chains that changes with the specific realization of the packing. These force chains can be transformed into…
The impact of liquid drops on a rigid surface is central in cleaning, cooling and coating processes in both nature and industrial applications. However, it is not clear how details of pores, roughness and texture on the solid surface…
In this article, we study the impact of a change in the type of boundary conditions of an elliptic boundary value problem. In the context of the conductivity equation we consider a reference problem with mixed homogeneous Dirichlet and…
The spatial inhomogeneities are expected to affect nucleation process in an essential way. These effects are studied theoretically by considering the case of the depinning of the charge density wave as a typical example. The threshold field…
For shape optimization problems, governed by elliptic equations with Dirichlet boundary condition and random coefficients, we utilize a penalization technique to get the approximate problem. We consider that uncertainties exists in the…
Motivated by recent experiments, we consider theoretically the compression of droplets pinned at the bottom on a surface of finite area. We show that if the droplet is sufficiently compressed at the top by a surface, it will always develop…
We illustrate how boundary states are recovered when going from a noncommutative manifold to a commutative one with a boundary. Our example is the noncommutative plane with a defect, whose commutative limit was found to be a punctured plane…
We investigate the effect of correlated disorder on the localization transition undergone by a renewal sequence with loop exponent $\alpha$ > 0, when the correlated sequence is given by another independent renewal set with loop exponent…
In the present work, we derive functional upper bounds for the potential error arising from finite-element boundary-element coupling formulations for a nonlinear Poisson-type transmission problem. The proposed a posteriori error estimates…
The capillary energy landscape for particles on curved fluid interfaces is strongly influenced by the particle wetting conditions. Contact line pinning has now been widely reported for colloidal particles, but its implications in capillary…
We give improved estimates for the size of the singular set of minimizing capillary hypersurfaces: the singular set is always of codimension at least $4$, and this estimate improves if the capillary angle is close to $0$, $\frac{\pi}{2}$,…
In this paper we rigorously investigate the emergence of defects on Nematic Shells with genus different from one. This phenomenon is related to a non trivial interplay between the topology of the shell and the alignment of the director…
We study minimizing singular cones with free boundary associated with the capillarity problem. Precisely, we provide a stability criterion $\`a$ la Jerison-Savin for capillary hypersurfaces and show that, in dimensions up to $4$, minimizing…
We consider the Bernoulli bond percolation process $\mathbb{P}_{p,p'}$ on the nearest-neighbor edges of $\mathbb{Z}^d$, which are open independently with probability $p<p_c$, except for those lying on the first coordinate axis, for which…
We investigate the collision of a new class of topological defects that tends to become compact as a control parameter increases to larger and larger values These new compactlike defects have, in general, more than one internal discrete…
In this paper, we introduce a modification of the free boundary problem related to optimal stopping problems for diffusion processes. This modification allows the application of this PDE method in cases where the usual regularity…