Different implementations on a massively parallel computer system of a semi-Lagrangian method within the numerical weather forecast model HIRLAM are presented. In principle semi-Lagrangian methods on massively parallel architectures result in irregular communications, i.e., communications between arbitrary processors. It is shown that the fastest implementationincreases the total execution time...

An isometric immersion f : Mn → M̃n from a Riemannian nmanifold Mn into a Kähler n-manifold M̃n is called Lagrangian if the complex structure J of the ambient manifold M̃n interchanges each tangent space of Mn with the corresponding normal space. In this paper, we completely classify spherical Lagrangian submanifolds in complex Euclidean spaces. In this paper, we also provide two corresponding cla...

Laser plasma is modeled by Lagrangian hydrodynamical equations including heat conductivity and laser absorption. The hyperbolic part of the model is treated by Arbitrary Lagrangian Eulerian (ALE) method which avoids moving mesh distortion and parabolic heat conductivity part is treated by splitting and mimetic method. High velocity laser accelerated disc impact problems for which standard Lagra...

This is a continuation of part I in the series (in progress) of the papers on Lagrangian Floer theory on toric manifolds. Using the deformations of Floer cohomology by the ambient cycles, which we call bulk deformations, we find a continuum of non-displaceable Lagrangian fibers on some compact toric manifolds. We also provide a method of finding all those fibers in arbitrary compact toric manif...

We study a large class of Poisson manifolds, derived from Manin triples, for which we construct explicit partitions into regular Poisson submanifolds by intersecting certain group orbits. Examples include all varieties L of Lagrangian subalgebras of reductive quadratic Lie algebras d with Poisson structures defined by Lagrangian splittings of d. In the special case of g ⊕ g, where g is a comple...

We study a class of Poisson manifolds for which intersections of certain group orbits give partitions into regular Poisson submanifolds. Examples are the varieties L of Lagrangian subalgebras of reductive quadratic Lie algebras with the Poisson structures defined by Lagrangian splittings. In the special case of g⊕g, where g is a complex semi-simple Lie algebra, we explicitly compute the ranks o...

We study a class of Poisson manifolds for which intersections of certain group orbits give partitions into regular Poisson submanifolds. Examples are the varieties L of Lagrangian subalgebras of reductive quadratic Lie algebras with Poisson structures defined by Lagrangian splittings. In the special case of g ⊕ g, where g is a complex semi-simple Lie algebra, we explicitly compute the ranks of ...

The surface flows on a droplet in an oscillating pressure field are simulated numerically by solving the Navier-Stokes equations using the Arbitrary Lagrangian-Eulerian and level set coupled method. Detailed transient flow fields in and around the droplet are calculated by performing parallel computations, and the flow phenomena in a thin layer around the droplet surface are discussed. The reci...

The subject of low energy photon-photon scattering is considered in arbitrary dimensional space-time and the interaction is widened to include scattering events involving an arbitrary number of photons. The effective interaction Lagrangian for these processes in QED has been determined in a manifestly invariant form. This generalisation resolves the structure of the weak-field Euler-Heisenberg ...

We construct, for a homogeneous Lagrangian of arbitrary order in two independent variables, a differential 2-form with the property that it is closed precisely when the Lagrangian is null. This is similar to the property of the ‘fundamental Lepage equivalent’ associated with first-order Lagrangians defined on jets of sections of a fibred manifold.