A recent variant of the inflationary paradigm is that the “primordial” curvature perturbations come from quantum fluctuations of a scalar field, subdominant and effectively massless during inflation, called the “curvaton”, instead of the fluctuations of the inflaton field. We consider a cosmological scenario which mixes the standard and variant versions, i.e. where primordial curvature perturba...

The Jacobi curve of an extremal of optimal control problem is a curve in a Lagrangian Grassmannian defined up to a symplectic transformation and containing all information about the solutions of the Jacobi equations along this extremal. In our previous works we constructed the canonical bundle of moving frames and the complete system of symplectic invariants, called curvature maps, for parametr...

The authors construct a mechanical analog of an Ising antiferromagnet by inserting square array locally dilated sites into 2D crystalline membrane. Past buckling threshold, these dilations become bistable, and buckle either above or below the host lattice. When lattice is planar, neighboring prefer to be antialigned, but cylindrical can bias away from center curvature. They show that curvature ...