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Abstract A technique for developing convex dual variational principles for the governing PDE of nonlinear elastostatics and elastodynamics is presented. This allows the definition of notions of a variational dual solution and a dual solution corresponding to the PDEs of nonlinear elasticity, even when the latter arise as formal Euler–Lagrange equations corresponding to non-quasiconvex elastic energy functionals whose energy minimizers do not exist. This is demonstrated rigorously in the case of elastostatics for the Saint-Venant Kirchhoff material (in all dimensions), where the existence of variational dual solutions is also proven. The existence of a variational dual solution for the incompressible neo-Hookean material in 2-d is also shown. Stressed and unstressed elastostatic and elastodynamic solutions in 1 space dimension corresponding to a non-convex, double-well energy are computed using the dual methodology. In particular, we show the stability of a dual elastodynamic equilibrium solution for which there are regions of non-vanishing length with negative elastic stiffness, i.e. non-hyperbolic regions, for which the corresponding primal problem is ill-posed and demonstrates an explosive ‘Hadamard instability;’ this appears to have implications for the modeling of physically observed softening behavior in macroscopic mechanical response. 

The discovery of the fractional quantum Hall state (FQHS) in 1982 ushered a new era of research in many-body condensed matter physics. Among the numerous FQHSs, those observed at even-denominator Landau level filling factors are of particular interest as they may host quasiparticles obeying non-Abelian statistics and be of potential use in topological quantum computing. The even-denominator FQHSs, however, are scarce and have been observed predominantly in low-disorder two-dimensional (2D) systems when an excited electron Landau level is half filled. An example is the well-studied FQHS at filling factor $\mathit{\nu }=$5/2 which is believed to be a Bardeen-Cooper-Schrieffer-type, paired state of flux-particle composite fermions (CFs). Here, we report the observation of even-denominator FQHSs at $\mathit{\nu }=$3/10, 3/8, and 3/4 in the lowest Landau level of an ultrahigh-quality GaAs 2D hole system, evinced by deep minima in longitudinal resistance and developing quantized Hall plateaus. Quite remarkably, these states can be interpreted as even-denominator FQHSs of CFs, emerging from pairing of higher-order CFs when a CF Landau level, rather than an electron or a hole Landau level, is half-filled. Our results affirm enhanced interaction between CFs in a hole system with significant Landau level mixing and, more generally, the pairing of CFs as a valid mechanism for even-denominator FQHSs, and suggest the realization of FQHSs with non-Abelian anyons. 

Abstract A rigorous methodology is developed for computing elastic fields generated by experimentally observed defect structures within grains in a polycrystal that has undergone tensile extension. An example application is made using a near-field high energy x-ray diffraction microscope measurement of a zirconium sample that underwent $13.6\mathrm{\%}$tensile extension from an initially well-annealed state. (Sub)grain boundary features are identified with apparent disclination line defects in them. The elastic fields of these features identified from the experiment are calculated. 

Abstract The arrangement of solvent molecules and ions at solid–liquid interfaces determines electrochemical properties that are important in separations platforms, sensing technologies, and energy‐storage systems. Here we show that single glass and polymer pores in contact with propylene carbonate (PC) solutions of LiClO₄exhibit an effective surface potential that is modulated by the enantiomeric excess of the solvent. In particular, electrochemical and electrokinetic measurements of ionic transport through glass pipettes and polymer pores reveal that the effective surface potential is significantly lower in solutions prepared using enantiomerically pure PC than in solutions prepared using racemic PC. Both pore systems became positively charged in all racemic solutions examined in the range of LiClO₄concentrations between 1 mM and 100 mM, whereas solutions in (R)‐(+)‐PC induced a positive surface potential only at concentrations above ~5 mM. The effective surface potential is quantified through asymmetry in current–voltage curves and zeta‐potential measurements. Vibrational sum‐frequency‐generation experiments on LiClO₄solutions in racemic and enantiomerically pure PC indicate that the surface lipid‐bilayer‐like region in the former is more strongly organized than in the latter, dictating the favorable positions for lithium and perchlorate ions in each case. The more ordered molecular packing in the racemic liquid leads to accumulation of lithium ions on the outside of the bilayer, creating a higher effective positive charge. Our results highlight the extreme sensitivity of the interfacial potential on molecular organization of the solvent, and the relatively unexplored role that chirality can play in electrokinetic phenomena.