Related papers: Spacetime diffeomorphisms and the geodesic approxi…
Computational anatomy (CA) has introduced the idea of anatomical structures being transformed by geodesic deformations on groups of diffeomorphisms. Among these geometric structures, landmarks and image outlines in CA are shown to be…
Some first results are presented regarding the behavior of invariant correlations in simplicial gravity, with an action containing both a bare cosmological term and a lattice higher derivative term. The determination of invariant…
We approximate the quasi-static equation of linear elasticity in translation invariant spaces on the torus. This unifies different FFT-based discretisation methods into a common framework and extends them to anisotropic lattices. We analyse…
We present a collective coordinate approximation to model the dynamics of two interacting nonlinear Schr\"odinger (NLS) solitons. We discuss the accuracy of this approximation by comparing our results to those of the full numerical…
Nonrelativistic Newton and Schroedinger equations remain correct not only under holonomic but also under nonholonomic transformations of the spacetime coordinates. Here we study the properties of transformations which are holonomic in the…
The main theme of the paper is the dynamics of Hamiltonian diffeomorphisms of ${\mathbb C}{\mathbb P}^n$ with the minimal possible number of periodic points (equal to $n+1$ by Arnold's conjecture), called here Hamiltonian pseudo-rotations.…
In this paper we present a Hamiltonian formulation of multisymplectic type of an invariant variational problem on smooth submanifold of dimension $p$ in a smooth manifold of dimension $n$ with $p<n$.
Dilaton gravities in two dimensions can be formulated as particular Poisson sigma models. Target space diffeomorphisms map different models to each other and establish a one-to-one correspondence between their classical solutions. We obtain…
Pseudospectral collocation methods and finite difference methods have been used for approximating an important family of soliton like solutions of the mKdV equation. These solutions present a structural instability which make difficult to…
We study the implications of a change of coordinatization of momentum space for theories with curved momentum space. We of course find that after a passive diffeomorphism the theory yields the same physical predictions, as one would expect…
The quantum fluctuations of the geodesic deviation equation in a flat background spacetime are discussed. We calculate the resulting mean squared fluctuations in the relative velocity and separation of test particles. The effect of these…
We construct a self-consistent relativistic Newtonian analogue corresponding to gravitational static spherical symmetric spacetime geometries, staring directly from a generalized scalar relativistic gravitational action in Newtonian…
We bring together those systems of hydrodynamical type that can be written as geodesic equations on diffeomorphism groups or on extensions of diffeomorphism groups with right invariant $L^2$ or $H^1$ metrics. We present their formal…
We exhibit isomorphisms of Grassmann spaces and their relationship with collineations and embeddings of the underlying projective spaces.
We consider a quantum test particle in the background of a Newtonian gravitational field in the framework of Cartan's formulation of nonrelativistic spacetimes. We have proposed a novel quantization of a point particle which amounts to…
We describe how to approximate the Riemann curvature tensor as well as sectional curvatures on possibly infinite-dimensional shape spaces that can be thought of as Riemannian manifolds. To this end, we extend the variational time…
We propose a coordinate-invariant geometric formulation of the GENERIC stochastic differential equation, unifying reversible Hamiltonian and irreversible dissipative dynamics within a differential-geometric framework. Our construction…
Some aspects of the connection between differential geometry and multidimensional soliton equations are discussed.
We consider a Navier-Stokes model for compressible fluids in one space dimension. We show that it can be approximated by a time-discrete scheme combining the discretization of a trivial stochastic differential equation and the application…
The kinematics on spatially flat FLRW space-times is presented for the first time in co-moving local charts with physical coordinates, i. e. the cosmic time and Painlev\' e-type Cartesian space coordinates. It is shown that there exists a…