Related papers: Symmetry breaking in indented elastic cones
Reviewing work done in collaboration with Jennifer Hodgdon, we derive the most general crack growth law allowed by symmetry for mixed-mode three-dimensional fracture. We do so using the system developed in condensed matter physics to derive…
A general framework is developed to study the deformation and stress response in F{\"o}ppl-von K{\'a}rm{\'a}n shallow shells for a given distribution of defects, such as dislocations, disclinations, and interstitials, and metric anomalies,…
One may impose to a system with spontaneous broken symmetry, boundary conditions which correspond to different pure states at two ends of a sample. For a discrete Ising-like broken symmetry, boundary conditions with opposite spins in two…
For a fast rotating condensate in a harmonic trap, we investigate the structure of the vortex lattice using wave functions minimizing the Gross Pitaveskii energy in the Lowest Landau Level. We find that the minimizer of the energy in the…
We prove convergence of critical points $u^h$ of the nonlinear elastic energies $E^h$ of thin incompressible plates $\Omega^h=\Omega \times (-h/2, h/2)$, which satisfy the von K\'arm\'an scaling: $E^h(u^h)\leq Ch^4$, to critical points of…
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…
Consideration is given to a non-convex variational model for a shear experiment in the framework of single-crystal linearised plasticity with infinite cross-hardening. The rectangular shear sample is clamped at each end, and is subjected to…
We review the symmetry energy in the context of AdS/CFT correspondence. After constructing $D$ brane configurations corresponding to dense system in boundary theory, we calculate the symmetry energy by solving DBI action of $D$ branes in…
Addition energy spectra at 0 T of circular and ellipsoidally deformed few-electron vertical quantum dots are measured and compared to results of model calculations within spin-density functional theory. Because of the rotational symmetry of…
In this paper we study the effects of simultaneous homogenization and dimension reduction in the context of convergence of stationary points for thin nonhomogeneous rods under the assumption of the von K\'arm\'an scaling. Assuming…
In this note we present a scaling theory for the elasticity of olympic gels, i.e., gels where the elasticity is a consequence of topology only. It is shown that two deformation regimes exist. The first is the non affine deformation regime…
In the direct approach to continua in reduced space dimensions, a thin shell is described as a mathematical surface in three-dimensional space. An exploratory kinematic study of such surfaces could be very valuable, especially if conducted…
In the limit of vanishing lattice spacing we provide a rigorous variational coarse-graining result for a next-to-nearest neighbor lattice model of a simple crystal. We show that the $\Gamma$-limit of suitable scaled versions of the model…
We show that electrons in coupled quantum dots characterized by high aspect ratios undergo abrupt density rotations when the dots are biased into an asymmetric confinement configuration. Density rotations occur with electron transfer to a…
A circular twist disclination is a nontrivial example of a defect in an elastic continuum that causes large deformations. The minimal potential energy and the corresponding displacement field is calculated by solving the…
Deep indentation of soft materials is ubiquitous across scales in nature and engineering, yet accurate predictions of contact behaviors under extreme deformations ($\delta/R > 1$) remain elusive due to geometric and material nonlinearities.…
We propose a scaling ansatz for the elastic energy of a system near the critical jamming transition in terms of three relevant fields: the compressive strain $\Delta \phi$ relative to the critical jammed state, the shear strain $\epsilon$,…
In this work, we consider a Bose-Einstein condensate in the self-focusing regime, confined transversely by a funnel-like potential and axially by a double-well potential formed by the combination of two inverted P\"oschl-Teller potentials.…
We study the $\Gamma$-limit of sequences of variational problems for straight, transversely curved shallow shells, as the width of the planform $\varepsilon$ goes to zero. The energy is of von K\'arm\'an type for shallow shells under…
We deduce a 1D model of elastic planar rods starting from the F\"{o}ppl--von K\'{a}rm\'{a}n model of thin shells. Such model is enhanced by additional kinematical descriptors that keep explicit track of the compatibility condition requested…