We investigate buckling of soft elastic capsules under negative pressure or for reduced capsule volume. Based on nonlinear shell theory and the assumption of a hyperelastic capsule membrane, shape equations for axisymmetric and initially spherical capsules are derived and solved numerically. A rich bifurcation behavior is found, which is presented in terms of bifurcation diagrams. The energetically preferred stable configuration is deduced from a least-energy principle both for prescribed volume and prescribed pressure. We find that buckled shapes are energetically favorable already at smaller negative pressures and larger critical volumes than predicted by the classical buckling instability. By preventing self-intersection for strongly reduced volume, we obtain a complete picture of the buckling process and can follow the shape from the initial undeformed state through the buckling instability into the fully collapsed state. Interestingly, the sequences of bifurcations and stable capsule shapes differ for prescribed volume and prescribed pressure. In the buckled state, we find a relation between curvatures at the indentation rim and the bending modulus, which can be used to determine elastic moduli from experimental shape analysis.

Elastic capsules, prepared from droplets or bubbles attached to a capillary (as in a pendant drop tensiometer), can be deflated by suction through the capillary. We study this deflation and show that a combined analysis of the shape and wrinkling characteristics enables us to determine the elastic properties in situ. Shape contours are analyzed and fitted using shape equations derived from nonlinear membrane-shell theory to give the elastic modulus, Poisson ratio and stress distribution of the membrane. We include wrinkles, which generically form upon deflation, within the shape analysis. Measuring the wavelength of wrinkles and using the calculated stress distribution gives the bending stiffness of the membrane. We compare this method with previous approaches using the Laplace-Young equation and illustrate the method on two very different capsule materials: polymerized octadecyltrichlorosilane (OTS) capsules and hydrophobin (HFBII) coated bubbles. Our results are in agreement with the available rheological data. For hydrophobin coated bubbles, the method reveals an interesting nonlinear behavior consistent with the hydrophobin molecules having a rigid core surrounded by a softer shell.

The stability of a vortex glass phase with quasi-long-range positional order is examined for a disordered layered superconductor. The role of topological defects is investigated using a detailed scaling argument, supplemented by a variational calculation. The results indicate that topological order is preserved for a wide range of parameters in the vortex glass phase. The extent of the stability regime is given in terms of a simple Lindemann-like criterion.

We develop a theory for dislocation-mediated structural transitions in the vortex lattice which allows for a unified description of phase transitions between the three phases, the elastic vortex glass, the amorphous vortex glass, and the vortex liquid, in terms of a free energy functional for the dislocation density. The origin of a critical endpoint of the melting line at high magnetic fields, which has been recently observed experimentally, is explained.