A note on dominating cycles in 2-connected graphs

Let G be a 2-connected graph on n vertices such that d(x) + d(y) + d(z) n for all triples of independent vertices x, y, z. We prove that every longest cycle in G is a dominating cycle unless G is a spanning subgraph of a graph belonging to one of four easily specified classes of graphs

Constraint-consistent Runge-Kutta methods for one-dimensional incompressible multiphase flow

New time integration methods are proposed for simulating incompressible multiphase flow in pipelines described by the one-dimensional two-fluid model. The methodology is based on 'half-explicit' Runge-Kutta methods, being explicit for the mass and momentum equations and implicit for the volume constraint. These half-explicit methods are constraint-consistent, i.e., they satisfy the hidden constraints of the two-fluid model, namely the volumetric flow (incompressibility) constraint and the Poisson equation for the pressure. A novel analysis shows that these hidden constraints are present in the continuous, semi-discrete, and fully discrete equations. Next to constraint-consistency, the new methods are conservative: the original mass and momentum equations are solved, and the proper shock conditions are satisfied; efficient: the implicit constraint is rewritten into a pressure Poisson equation, and the time step for the explicit part is restricted by a CFL condition based on the convective wave speeds; and accurate: achieving high order temporal accuracy for all solution components (masses, velocities, and pressure). High-order accuracy is obtained by constructing a new third order Runge-Kutta method that satisfies the additional order conditions arising from the presence of the constraint in combination with time-dependent boundary conditions. Two test cases (Kelvin-Helmholtz instabilities in a pipeline and liquid sloshing in a cylindrical tank) show that for time-independent boundary conditions the half-explicit formulation with a classic fourth-order Runge-Kutta method accurately integrates the two-fluid model equations in time while preserving all constraints. A third test case (ramp-up of gas production in a multiphase pipeline) shows that our new third order method is preferred for cases featuring time-dependent boundary conditions

Modelling, screening, and solving of optimisation problems: Application to industrial metal forming processes

Coupling Finite Element (FEM) simulations to mathematical optimisation techniques provides a high potential to improve industrial metal forming processes. In order to optimise these processes, all kind of optimisation problems need to be mathematically modelled and subsequently solved using an appropriate optimisation algorithm. Although the modelling part greatly determines the final outcome of optimisation, the main focus in most publications until now was on the solving part of mathematical optimisation, i.e. algorithm development. Modelling is generally performed in an arbitrary way. In this paper, we propose an optimisation strategy for metal forming processes using FEM. It consists of three stages: a structured methodology for modelling optimisation problems, screening for design variable reduction, and a generally applicable optimisation algorithm. The strategy is applied to solve manufacturing problems for an industrial deep drawing process

Pancyclicity of Hamiltonian line graphs

Let f(n) be the smallest integer such that for every graph G of order n with minimum degree 3(G)>f(n), the line graph L(G) of G is pancyclic whenever L(G) is hamiltonian. Results are proved showing that f(n) = ®(n 1/3)

Global and local conservation of mass, momentum and kinetic energy in the simulation of compressible flow

The spatial discretization of convective terms in compressible flow equations is studied from an abstract viewpoint, for finite-difference methods and finite-volume type formulations with cell-centered numerical fluxes. General conditions are sought for the local and global conservation of primary (mass and momentum) and secondary (kinetic energy) invariants on Cartesian meshes. The analysis, based on a matrix approach, shows that sharp criteria for global and local conservation can be obtained and that in many cases these two concepts are equivalent. Explicit numerical fluxes are derived in all finite-difference formulations for which global conservation is guaranteed, even for non-uniform Cartesian meshes. The treatment reveals also an intimate relation between conservative finite-difference formulations and cell-centered finite-volume type approaches. This analogy suggests the design of wider classes of finite-difference discretizations locally preserving primary and secondary invariants

Parabolic interface reconstruction for 2D volume of fluid methods

For capillary driven flow the interface curvature is essential in the modelling of surface tension via the imposition of the Young–Laplace jump condition. We show that traditional geometric volume of fluid (VOF) methods, that are based on a piecewise linear approximation of the interface, do not lead to an interface curvature which is convergent under mesh refinement in time-dependent problems. Instead, we propose to use a piecewise parabolic approximation of the interface, resulting in a class of piecewise parabolic interface calculation (PPIC) methods. In particular, we introduce the parabolic LVIRA and MOF methods, PLVIRA and PMOF, respectively. We show that a Lagrangian remapping method is sufficiently accurate for the advection of such a parabolic interface. It is numerically demonstrated that the newly proposed PPIC methods result in an increase of reconstruction accuracy by one order, convergence of the interface curvature in time-dependent advection problems and Weber number independent convergence of a droplet translation problem, where the advection method is coupled to a two-phase Navier–Stokes solver. The PLVIRA method is applied to the simulation of a 2D rising bubble, which shows good agreement to a reference solution.</p

Developing a shared supplier with endogenous spillovers

Firms who buy from suppliers often engage in supplier development to reduce the supplier's production cost. Being aware that their efforts may benefit a rival firm when there is a shared supplier, some buyers only invest in “specific supplier development,” that is, in those processes or technologies where spillover cannot occur. Other buyers willingly accept the spillover that arises from supplier development, and invest in “generic supplier development.” Our game-theoretic model captures a buyer's choice to invest in these distinct supplier development types as a way to endogenize spillovers. In contrast to the literature, this paper considers the benefits of investing in a combination (i.e., portfolio) of cost-reducing generic and specific supplier development. We demonstrate how supplier development affects a shared supplier's wholesale pricing decisions; whereas generic supplier development lowers wholesale prices equally across buyers, specific supplier development only lowers the wholesale price of the investing party. Our model shows that buyers should treat the spillovers from generic supplier development as an investment opportunity rather than a threat. In equilibrium, a buyer will always invest in a portfolio of both supplier development types, and having a better generic than specific investment capability may even make generic supplier development the most prevalent option for him, depending on the level of competition. Moreover, even if the buyers can commit to only investing in specific supplier investment, the resulting equilibrium gives lower buyer profits than a portfolio that includes generic investments. We also find that the presence of specific investments may raise generic supplier development, benefiting all supply chain actors. However, incorporating specific supplier development into a supplier development portfolio or a commitment to investment in only specific supplier development can lead to a prisoner's dilemma in terms of buyer profits. We show how investment capabilities and competitive intensity drive the buyers' investment decisions and supply chain actors' profits. The paper's main results also hold for asymmetric generic investment capabilities, though we highlight that the least capable buyer will free-ride on his rival's investments, consequently making him earn higher profits

Evaluating the power capability of a typical Dutch MV grid incorporating sustainable technologies

This paper describes the power capability of a typical Dutch medium voltage (MV) distribution grid when future generation and load technologies are applied. Therefore reference networks are selected which are representative for of a larger group of networks. The application of the future technologies is simulated in these reference networks. A methodology is presented to calculate the penetration degrees for these future technologies. A sensitivity analysis is then performed on changes in the power profiles of the technologies