Poisson integrators

An overview of Hamiltonian systems with noncanonical Poisson structures is given. Examples of bi-Hamiltonian ode's, pde's and lattice equations are presented. Numerical integrators using generating functions, Hamiltonian splitting, symplectic Runge-Kutta methods are discussed for Lie-Poisson systems and Hamiltonian systems with a general Poisson structure. Nambu-Poisson systems and the discrete gradient methods are also presented.Comment: 30 page

Destruction of the family of steady states in the planar problem of Darcy convection

The natural convection of incompressible fluid in a porous medium causes for some boundary conditions a strong non-uniqueness in the form of a continuous family of steady states. We are interested in the situation when these boundary conditions are violated. The resulting destruction of the family of steady states is studied via computer experiments based on a mimetic finite-difference approach. Convection in a rectangular enclosure is considered under different perturbations of boundary conditions (heat sources, infiltration). Two scenario of the family of equilibria are found: the transformation to a limit cycle and the formation of isolated convective patterns.Comment: 12 pages, 6 figure

Poisson integrators for Volterra lattice equations

The Volterra lattice equations are completely integrable and possess bi-Hamiltonian structure. They are integrated using partitioned Lobatto IIIA-B methods which preserve the Poisson structure. Modified equations are derived for the symplectic Euler and second order Lobatto IIIA-B method. Numerical results confirm preservation of the corresponding Hamiltonians, Casimirs, quadratic and cubic integrals in the long-term with different orders of accuracy.Comment: 9 pages, 2 figure

Staggered grids discretization in three-dimensional Darcy convection

We consider three-dimensional convection of an incompressible fluid saturated in a parallelepiped with a porous medium. A mimetic finite-difference scheme for the Darcy convection problem in the primitive variables is developed. It consists of staggered nonuniform grids with five types of nodes, differencing and averaging operators on a two-nodes stencil. The nonlinear terms are approximated using special schemes. Two problems with different boundary conditions are considered to study scenarios of instability of the state of rest. Branching off of a continuous family of steady states was detected for the problem with zero heat fluxes on two opposite lateral planes.Comment: 20 pages, 9 figure

Portrait of a Consortium: ANKOS (Anatolian University Libraries Consortium)

[No abstract available

Feature cluster "advances in continuous optimization"

[No abstract available

Non-linearly stable reduced-order models for incompressible flow with energy-conserving finite volume methods

A novel reduced-order model (ROM) formulation for incompressible flows is presented with the key property that it exhibits non-linearly stability, independent of the mesh (of the full order model), the time step, the viscosity, and the number of modes. The two essential elements to non-linear stability are: (1) first discretise the full order model, and then project the discretised equations, and (2) use spatial and temporal discretisation schemes for the full order model that are globally energy-conserving (in the limit of vanishing viscosity). For this purpose, as full order model a staggered-grid finite volume method in conjunction with an implicit Runge-Kutta method is employed. In addition, a constrained singular value decomposition is employed which enforces global momentum conservation. The resulting `velocity-only' ROM is thus globally conserving mass, momentum and kinetic energy. For non-homogeneous boundary conditions, a (one-time) Poisson equation is solved that accounts for the boundary contribution. The stability of the proposed ROM is demonstrated in several test cases. Furthermore, it is shown that explicit Runge-Kutta methods can be used as a practical alternative to implicit time integration at a slight loss in energy conservation

Does Urquhart’s Law Hold for Consortial Use of Electronic Journals?

This paper tests the validity of Urquhart’s Law (“the inter-library loan demand for a periodical is as a rule a measure of its total use”). It compares the use of print journals at the Turkish Academic Network and Information Center (ULAKBIM) with the consortial use of the same journals in their electronic form by the individual libraries making up the Consortium of Turkish University Libraries (ANKOS). It also compares the on-site use of electronic journals at ULAKBIM with their consortial use at ANKOS. About 700 thousand document delivery, in-house and on-site use data and close to 28 million consortial use data representing seven years’ worth of downloads of full-text journal articles were used. Findings validate Urquhart’s Law in that a positive correlation was observed between the use of print journals at ULAKBIM and the consortial use of their electronic copies at ANKOS. The on-site and consortial use of electronic journals was also highly correlated. Both print and electronic journals that were used most often at ULAKBIM tend to get used heavily by the member libraries of ANKOS consortium, too. Findings can be used in developing consortial collection management policies and negotiate better consortial licence agreements

Numerical Studies on a bi-Hamiltonian Hénon-Heiles System

An integrable two-degree of freedom Hénon-Heiles system in biHamiltonian form is integrated by reversible, symplectic and integral preserving methods. The methods are compared by presenting numerical results for long time behavior of the Hamiltonians and Poincaré sections