Related papers: Elasticae and inradius
We consider a one-dimensional variational problem arising in connection with a model for cholesteric liquid crystals. The principal feature of our study is the assumption that the twist deformation of the nematic director incurs much higher…
In this paper we consider a minimization problem of the type $$ I_{\beta,p}(D;\Omega)=\inf\biggl\{\int_\Omega \lvert{D\phi}\rvert^pdx+\beta \int_{\partial^* \Omega}\lvert{\phi}\rvert^pd\mathcal{H}^{n-1},\; \phi \in W^{1,p}(\Omega),\;\phi…
We study convexity properties of energy functions in plane nonlinear elasticity of incompressible materials and show that rank-one convexity of an objective and isotropic elastic energy $W$ on the special linear group $\mathrm{SL}(2)$…
The elastic scattering amplitude (ESA) is obtained in the one-loop approximation of the 2+1 dimensional quantum electrodynamics (QED$_{2+1}$) for planar charged fermions in an external constant magnetic field. We obtain the elastic…
An eigenvalue problem arising in optimal insulation related to the minimization of the heat decay rate of an insulated body is adapted to enforce a positive lower bound imposed on the distribution of insulating material. We prove the…
We derive the effective energy density of thin membranes of liquid crystal elastomers as the Gamma-limit of a widely used bulk model. These membranes can display fine-scale features both due to wrinkling that one expects in thin elastic…
Using classical differential geometry, the problem of elastic curves and surfaces in the presence of long-range interactions $\Phi$, is posed. Starting from a variational principle, the balance of elastic forces and the corresponding…
We present a simple discrete formula for the elastic energy of a bilayer. The formula is convenient for rapidly computing equilibrium configurations of actuated bilayers of general initial shapes. We use maps of principal curvatures and…
We consider problems of static equilibrium in which the primary unknown is the stress field and the solutions maximize a complementary energy subject to equilibrium constraints. A necessary and sufficient condition for the sequential…
The elastic energy of a bending-resistant interface depends both on its geometry and its material composition. We consider such a heterogeneous interface in the plane, modeled by a curve equipped with an additional density function. The…
Using a geometrically motivated 8-parameter ansatz through the thickness, we reduce a three-dimensional shell-like geometrically nonlinear Cosserat material to a fully two-dimensional shell model. Curvature effects are fully taken into…
Modeling the internal structure of self-gravitating solid and liquid bodies presents a challenge, as existing approaches are often limited to either overly simplistic constant-density approximations or more complex numerical equations of…
Consider the energy per particle on the lattice given by $\min_{ \Lambda }\sum_{ \mathbb{P}\in \Lambda} \left|\mathbb{P}\right|^4 e^{-\pi \alpha \left|\mathbb{P}\right|^2 }$, where $\alpha >0$ and $\Lambda$ is a two dimensional lattice. We…
We study the three-dimensional compressible elastic Navier-Stokes-Poisson equations induced by a new bipolar viscoelastic model derived here, which model the motion of the compressible electrically conducting fluids. The various boundary…
We develop a theory of existence of minimizers of energy functionals in vectorial problems based on a nonlocal gradient under Dirichlet boundary conditions. The model shares many features with the peridynamics model and is also applicable…
In this article, we derive a mathematical model for a shell (i.e. a thin elastic body) bonded to an elastic foundation by modifying Koiter's linear shell equations. We prove the existence and the uniqueness of solutions, and we explicitly…
We study the effective elastic behavior of incompatibly prestrained plates, where the prestrain is independent of thickness as well as uniform through the thickness. We model such plates as three-dimensional elastic bodies with a prescribed…
We consider a viscoelastic body occupying a smooth bounded domain of $R^3$ under the effects of volumic traction forces. Inertial effects are considered: hence, the equation describing the evolution of displacements is of the second order…
The elastica is a curve in $\R^3$ that is stationary under variations of the integral of the square of the curvature. Elastica is viewed as a dynamical system that arises from the second order calculus of variations, and its quantization is…
We first review the phenomenology of viscous liquids and the standard models used for explaining the non-Arrhenius average relaxation time. Then the focus is turned to the so-called elastic models, arguing that these models are all…