Abrikosov’s solution of the linearized Ginzburg-Landau theory describing a periodic lattice of vortex lines in type-II superconductors at large inductions, is generalized to non-periodic vortex arrangements, e.g., to lattices with a vacancy surrounded by relaxing vortices and to periodically distorted lattices that are needed in the nonlocal theory of elasticity of the vortex lattice. Generaliz...

We have studied patterns of electrically-driven convective vortices in thin freely-suspended lms of smectic liquid crystal at and above the onset of con-vection. We present measurements of the convective amplitude above onset, the spatial variation of the amplitude due to the presence of end walls, and the relaxation of the amplitude following a sudden change in the experimental control paramet...

We prove the Doran–Harder–Thompson conjecture in the case of elliptic curves by using ideas from SYZ mirror symmetry. The conjecture claims that when a Calabi– Yau manifold X degenerates to a union of two quasi-Fano manifolds (Tyurin degeneration), a mirror Calabi–Yau manifold of X can be constructed by gluing the two mirror Landau– Ginzburg models of the quasi-Fano manifolds. The two crucial i...

We show that the theta representations on certain covers of general linear groups support certain types of unique functionals. The proof involves two types of Fourier coefficients. The first are semi-Whittaker coefficients, which generalize coefficients introduced by Bump and Ginzburg for the double cover. The covers for which these coefficients vanish identically (resp. do not vanish for some ...