We show that Lagrangian and Legendre varieties associated with matrix singularities and singularities of composite functions are stable in a sense which is a natural modification of Givental’s notion of stability of Lagrangian projections. The study of singular Lagrangian and Legendre varieties was initiated about twenty five years ago by Arnold when he was investigating singularities in the va...

The breathing-mode isoscalar giant monopole resonance (GMR) is investigated using the generator coordinate method within the relativistic mean-field (RMF) theory. Employing the Lagrangian models of the nonlinear-σ model (NLσ), the scalarvector interaction model (SVI) and the σ-ω coupling model (SIGO), we show that each Lagrangian model exhibits a distinctly different GMR response. Consequently,...

The Lagrangian dispersion of fluid particles in inhomogeneous turbulence is investigated by a direct numerical simulation of turbulent channel flow. Lagrangian velocity and acceleration along a particle trajectory are computed by employing several interpolation schemes. Among the schemes tested, the four-point Hermite interpolation in the homogeneous directions combined with Chebyshev polynomia...

We consider the separable nonlinear and strictly convex single-commodity network flow problem (SSCNFP). We develop a computational scheme for generating a primal feasible solution from any Lagrangian dual vector; this is referred to as “early primal recovery”. It is motivated by the desire to obtain a primal feasible vector before convergence of a Lagrangian scheme; such a vector is not availab...

The single-particle dispersion, Lagrangian structure functions and Lagrangian energy spectra characteristic of two-dimensional incompressible turbulent flows are investigated theoretically and numerically. The domain of validity of the classical asymptotic estimates is extended; it is shown in particular that the asymptotic behavior of the single-particle dispersion at small times remains valid...

A hierarchical structure model is developed for anomalous scaling of the Lagrangian velocity structure functions in fully developed turbulence. This model is an extension of the Eulerian hierarchical structure model of She and Leveque [Phys. Rev. Lett. 72, 366 (1994)] to the Lagrangian velocity structure functions, where the straining and sweeping hypotheses are used to build up the relationshi...

We construct some examples of special Lagrangian submanifolds and Lagrangian self-similar solutions in almost Calabi–Yau cones over toric Sasaki manifolds. For example, for any integer g ≥ 1, we can construct a real 6-dimensional Calabi–Yau cone Mg and a 3-dimensional special Lagrangian submanifold F 1 g : L 1 g → Mg which is diffeomorphic to Σg ×R and a compact Lagrangian self-shrinker F 2 g :...

Recently an effective Lagrangian for the interactions of photons, Nambu-Goldstone bosons and superfluid phonons in dense quark matter has been derived using anomaly matching arguments. In this paper we illuminate the nature of certain anomalous terms in this Lagrangian by an explicit microscopic calculation. We also generalize the corresponding construction to introduce the axion field. We deri...