The nonlinear Schrödinger (NLS) equation describing the propagation of weakly rotational wave packets in an infinitely deep fluid in Lagrangian coordinates has been derived. The vorticity is assumed to be an arbitrary function of Lagrangian coordinates and quadratic in the small parameter proportional to the wave steepness. The vorticity effects manifest themselves in a shift of the wave number...

In numerical simulations of fluid flow, the choice of the computational mesh is crucial. Traditionally, there have been two viewpoints, utilizing the Lagrangian or the Eulerian framework, each with its own advantages and disadvantages. In a pioneering paper [1], Hirt et al. developed the formalism for a mesh whose motion could be determined as an independent degree of freedom, and showed that t...

The importance of explicit examples of Lagrangian submanifolds of moduli spaces is revealed by papers such as [9, 25]: given a 3-manifold M with boundary ∂M = Σ, Dostoglou and Salamon use such examples to obtain a proof of the Atiyah-Floer conjecture relating the symplectic Floer homology of the representation space Hom(π1(Σ = ∂M), U)/U (associated to an explicit pair of Lagrangian submanifolds...

We perform a general study of primordial scalar non-Gaussianities in single field inflationary models. We consider models where the inflaton Lagrangian is an arbitrary function of the scalar field and its first derivative, and the sound speed is arbitrary. We find that under reasonable assumptions, the non-Gaussianity is completely determined by 5 parameters. In special limits of the parameter ...

A Lorentz-covariant regularization scheme for effective field theories with an arbitrary number of propagating heavy and light particles is given. This regularization scheme leaves the low-energy analytic structure of Greens functions intact and preserves all the symmetries of the underlying Lagrangian. The power divergences of regularized loop integrals are controlled by the low-energy kinemat...

We investigate the theory of particles with arbitrary spin and anomalous magnetic moment in the Lorentz representation (0, s) ⊕ (s, 0), in an external constant and uniform electromagnetic field. We obtain the density matrix of free particles in pure spin states. The differential probability of pair producing particles with arbitrary spin by an external constant uniform electromagnetic field has...

We study the problem of instability inhomogeneous radiation universes in quadratic lagrangian theories gravity written as a system evolution equations with constraints. construct formal series expansions and show that resulting solutions have smaller number arbitrary functions than required general solution. These results continue to hold for more polynomial extensions relativity.

the purpose of this paper is to investigate the egm method and the behavior of a solid particle suspended in a twodimensional rectangular cavity due to conjugate natural convection. a thermal lattice boltzmann bgk model is implemented to simulate the two dimensional natural convection and the particle phase was modeled using the lagrangian–lagrangian approach where the solid particles are treat...

A finite element scheme to compute the dynamics of insoluble surfactant on a deforming free surface is presented. The free surface is tracked by the arbitrary Lagrangian–Eulerian (ALE) approach, whereas the surfactant concentration transport equation is approximated in a Lagrangian manner. Since boundary resolved moving meshes are used in the ALE approach, the surface tension, which may be a li...

I describe a mathematical framework for the efficient processing of very large sets Feynman diagrams contributing to scattering many particles. reexpress established numerical methods recursive construction elements as operations on compact abstract data types. This allows perturbative computations in arbitrary models, long they can be described by an effective, not necessarily local, Lagrangian.