We show that for almost every translation surface the number of pairs saddle connections with bounded magnitude cross product has asymptotic growth like cR2 where constant c depends only on area and connected component stratum. The proof techniques combine classical results counting crucial result Siegel–Veech transform is in L2. In order to capture information about connections, we consider si...

The identification of discontinuous parameters in elliptic systems is formulated as a constrained minimization problem combining the output least squares and the equation error method. The minimization problem is then proved to be equivalent to the saddle-point problem of an augmented Lagrangian. The finite element method is used to discretize the saddle-point problem, and the convergence of th...

The partition function of a two-dimensional quantum gauge theory in the large-N limit is expressed as the functional integral over some scalar field. The large-N saddle point equation is presented and solved. The free energy is calculated as the function of the area and of the Euler characteristic. There is no non-trivial saddle point at genus g > 0. The existence of a non-trivial saddle point ...

In vector field analysis, saddle points have two different types of invariant manifolds, namely stable ones and unstable ones. The invariant manifolds represent separatrices that partition the domain of trajectories into invariant regions of different dynamics. In this work, we analyze the basins of attraction of two different stable nodes by reconstructing the separatrices of a saddle point. T...

Noise-induced transition in the solutions of the Kuramoto–Sivashinsky (K–S) equation is investigated using the minimum action method derived from the large deviation theory. This is then used as a starting point for exploring the configuration space of the K–S equation. The particular example considered here is the transition between a stable fixed point and a stable travelling wave. Five saddl...

Abstract Arcades of flare loops form as a consequence magnetic reconnection powering solar flares and eruptions. We analyze the morphology evolution arcades that formed during five well-known eruptive flares. show have common saddle-like shape. The saddles occur despite fact were different classes (C to X), occurred in environments, observed various projections. are related presence longer, rel...