where H is the Hamiltonian (”energy”) and {. , .} is a Poisson bracket on an infinite dimensional phase space, called Poisson manifold. Unlike finite dimensional Hamiltonian systems, which are ordinary differential evolution equations on finite dimensional phase spaces, for which general existence and uniqueness theorems for solutions exist, this is not the case for PDEs. There are no general e...

The theory of differential forms began with a discovery of Poincaré who found conservation laws of a new type for Hamiltonian systems—The Integral Invariants. Even in the absence of non-trivial integrals of motion, there exist invariant differential forms: a symplectic two-form, or a contact one-form for geodesic flows. Some invariant forms can be naturally considered as “forms on the quotient....

We introduce the notion of higher dimensional transition systems as a model of concurrency providing an elementary, set-theoretic formalisation of the idea of higher dimensional transition. We show an embedding of the category of higher dimensional transition systems into that of higher dimensional automata which cuts down to an equivalence when we restrict to non-degenerate automata. Moreover,...

the performance of water flooding can be investigated by using either detail numerical modeling or simulation, or simply through the analytical buckley-leverett (bl) model. the buckley-leverett analytical technique can be applied to one-dimensional homogeneous systems. in this paper, the impact of heterogeneity on water flooding performance and fractional flow curve is investigated. first, a ba...

The spiral boundary conditions can project any two-dimensional or three-dimensional lattice onto a one-dimensional periodic chain with translational symmetry. It enables one to apply efficiently the existing techniques, such as density-matrix renormalization group (DMRG), bosonization, Jordan-Wigner transformation, etc., studies of systems in higher dimensions. Here, authors demonstrate utility...