Related papers: The one-dimensional model for d-cones revisited
The equations of a planar elastica under pressure can be rewritten in a useful form by parametrising the variables in terms of the local orientation angle, $\theta$, instead of the arc length. This ``$\theta$-formulation'' lends itself to a…
A statistical study of crumpled paper is allowed by a minimal 1D model: a self-avoiding line bent at sharp angles -- in which resides the elastic energy -- put in a confining potential. Many independent equilibrium configurations are…
The dynamics of symmetry-breaking after a quench is numerically simulated on a lattice for the (2+1)-dimensional O(3) model. In addition to the standard sigma-model with temperature-dependent Phi^4-potential the energy functional includes a…
Energies and equilibrium equations for thin elastic plates are discussed, with emphasis on several issues pertinent to recent approaches in soft condensed matter. Consequences of choice of basis, choice of invariant strain measures, and of…
We present a simple torsional potential for graphene to accurately describe its out-of-plane deformations. The parameters of the potential are derived through appropriate fitting with suitable DFT calculations regarding the deformation…
We study the $p$-variational capacity of interior condensers in a bounded open set $\Omega\subset\mathbb R^n$ when both plates are determined by a single phase $\theta:\Omega\to\mathbb R$ in $W^{1,\infty}(\Omega)$ through sublevel and…
We consider the problem of minimizing Euler's elastica energy for simple closed curves confined to the unit disk. We approximate a simple closed curve by the zero level set of a function with values +1 on the inside and -1 on the outside of…
Differential growth processes play a prominent role in shaping leaves and biological tissues. Using both analytical and numerical calculations, we consider the shapes of closed, elastic strips which have been subjected to an inhomogeneous…
In materials science, wedge disclinations are defects caused by angular mismatches in the crystallographic lattice. To describe such disclinations, we introduce an atomistic model in planar domains. This model is given by a…
We study 2d vortex sheets with unbounded support. First we show a version of the Biot- Savart law related to a class of objects including such vortex sheets. Next, we give a formula associating the kinetic energy of a very general class of…
This paper is devoted to describe the deformations and the elastic energy for structures made of straight rods of thickness $2\delta$ when $\delta$ tends to 0. This analysis relies on the decomposition of the large deformation of a single…
We compute roughness exponents of elastic d-dimensional manifolds in (d+1)-dimensional embedding spaces at the depinning transition for d=1,...,4. Our numerical method is rigorously based on a Hamiltonian formulation; it allows to determine…
The elastic energy of a planar convex body is defined by $E(\Om)=\frac 12\,\int\_{\partial\Om} k^2(s)\,ds$where $k(s)$ is the curvature of the boundary. In this paper we are interested in the minimization problemof $E(\Om)$ with a…
Nematic elastomers and glasses deform spontaneously when subjected to temperature changes. This property can be exploited in the design of heterogeneously patterned thin sheets that deform into a non-trivial shape when heated or cooled. In…
Using the spherical geometry, we introduce a novel model to study excitons confined in a three-dimensional space, which offers unparalleled mathematical simplicity while retaining much of the key physics. This new model consists of an…
We study a simple model of interacting bosons on a d-dimensional cubic lattice whose dynamics conserves both total boson number and total boson dipole moment. This model provides a simple framework in which several remarkable consequences…
We investigate the formation dynamics of plastic creases in thin elasto-plastic sheets. In contrast to the commonly accepted description of crumpled thin sheets, which asserts that creases form only by elastic interaction between two…
In this paper we use the angular deficit scheme [V. Borrelli, F. Cazals, and J.-M. Morvan, {\sl Computer Aided Geometric Design} {\bf 20}, 319 (2003)] to determine the distribution of Gaussian curvature in developable cones (d-cones) [E.…
We consider the axial compression of a thin elastic cylinder placed about a hard cylindrical core. Treating the core as an obstacle, we prove upper and lower bounds on the minimum energy of the cylinder that depend on its relative thickness…
We address the inverse problem of recovering a degeneracy point within the diffusion coefficient of a one-dimensional complex parabolic equation by observing the normal derivative at one point of the boundary. The strongly degenerate case…