Related papers: Volterra's realization of the KM-system
The recently re-discovered multipole vector approach to understanding the harmonic decomposition of the cosmic microwave background traces its roots to Maxwell's Treatise on Electricity and Magnetism. Taking Maxwell's directional derivative…
Recently much attention has been paid to the restriction of KP to the submanifold of operators which can be represented as a ratio of two purely differential operators L=AB^{-1}. Whereas most of the aspects concerning this reduced…
For a separable Hamiltonian, there are two fundamental, time-symmetric, second-order velocity-Verlet (VV) and position-Verlet (PV) symplectic integrators. Similarly, there are two VV and PV version of exact energy conserving algorithms for…
Many PDEs (Burgers' equation, KdV, Camassa-Holm, Euler's fluid equations,...) can be formulated as infinite-dimensional Lie-Poisson systems. These are Hamiltonian systems on manifolds equipped with Poisson brackets. The Poisson structure is…
A Poisson structure on the time-extended space R x M is shown to be appropriate for a Hamiltonian formalism in which time is no more a privileged variable and no a priori geometry is assumed on the space M of motions. Possible geometries…
Numerical simulation of compressible fluid flows is performed using the Euler equations. They include the scalar advection equation for the density, the vector advection equation for the velocity and a given pressure dependence on the…
The three integrable two-dimensional Henon-Heiles systems and their integrable perturbations are revisited. A family of new integrable perturbations is found, and N-dimensional completely integrable generalizations of all these systems are…
A plane algebraic curve whose Newton polygone contains d lattice points can be given by d points it passes through. Then the coefficients of its equation Poisson commute having been regarded as functions of coordinates of those points. It…
We study translative integral formulas for certain translation invariant functionals on convex polytopes and discuss local extensions and applications to Poisson processes and Boolean models.
We compare a relativistic and a nonrelativistic version of Ostrogradsky's method for higher-time derivative theories extended to scalar field theories and consider as an alternative a multi-field variant. We apply the schemes to space-time…
In this paper we develop a general framework for constructing and analysing coupled Markov chain Monte Carlo samplers, allowing for both (possibly degenerate) diffusion and piecewise deterministic Markov processes. For many performance…
Reciprocal space methods for solving Poisson's equation for finite charge distributions are investigated. Improvements to previous proposals are presented, and their performance is compared in the context of a real-space density functional…
This work gathers new results concerning the semi-geostrophic equations: existence and stability of measure valued solutions, existence and uniqueness of solutions under certain continuity conditions for the density, convergence to the…
On the basis of the explicit formulae for the action of the unitary group of exponentials corresponding to almost solvable extensions of a given closed symmetric operator with equal deficiency indices, we derive a new representation for the…
We formulate one dimensional many-body integrable systems in terms of a new set of phase space variables involving exchange operators. The hamiltonian in these variables assumes a decoupled form. This greatly simplifies the derivation of…
We propose a new theoretical framework that exploits convolution kernels to transform a Volterra-type path-dependent (non-Markovian) stochastic process into a standard (Markovian) diffusion process. Remarkably, it is also possible to go…
A new object, called the velocity tensor, is introduced. It allows to formulate a generally covariant mechanics. Some properties of the velocity tensor are derived.
In this paper we provide a matched pair decomposition of the space of symmetric contravariant tensors $\mathfrak{T}\mathcal{Q}$. From this procedure two complementary Lie subalgebras of $\mathfrak{T}\mathcal{Q}$ under \textit{mutual}…
On a (pseudo-) Riemannian manifold of dimension n > 2, the space of tensors which transform covariantly under Weyl rescalings of the metric is built. This construction is related to a Weyl-covariant operator D whose commutator [D,D] gives…
Let $M$ be a smooth closed orientable manifold and $\mathcal{P}(M)$ the space of Poisson structures on $M$. We construct a Poisson bracket on $\mathcal{P}(M)$ depending on a choice of volume form. The Hamiltonian flow of the bracket acts on…