Modeling,simulation and validation of material flow on conveyor belts

In this paper a model comparison approach based on material flow systems is investigated that is divided into a microscopic and a macroscopic model scale. On the microscopic model scale particles are simulated using a model based on Newton dynamics borrowed from the engineering literature. Phenomenological observations lead to a hyperbolic partial differential equation on the macroscopic model scale. Suitable numerical algorithms are presented and both models are compared numerically and validated against real-data test settings.     

A new kernel function for SPH with applications to free surface flows

Smoothed particle hydrodynamics (SPH) is a popular meshfree Lagrangian particle method, which uses a kernel function for numerical approximations. The kernel function is closely related to the computational accuracy and stability of the SPH method. In this paper, a new kernel function is proposed, which consists of two cosine functions and is referred to as double cosine kernel function. The newly proposed double cosine kernel function is sufficiently smooth, and is associated with an adjustable support domain. It also has smaller second order momentum, and therefore it can have better accuracy in terms of kernel approximation. SPH method with this double cosine kernel function is applied to simulate a dam-break flow and water entry of a horizontal circular cylinder. The obtained SPH results agree very well with the experimental results. The double cosine kernel function is also comparatively studied with two frequently used SPH kernel functions, Gaussian and cubic spline kernel functions.     

Scheduling the hospital-wide flow of elective patients

In this paper, we address the problem of planning the patient flow in hospitals subject to scarce medical resources with the objective of maximizing the contribution margin. We assume that we can classify a large enough percentage of elective patients according to their diagnosis-related group (DRG) and clinical pathway. The clinical pathway defines the procedures (such as different types of diagnostic activities and surgery) as well as the sequence in which they have to be applied to the patient. The decision is then on which day each procedure of each patient’s clinical pathway should be done, taking into account the sequence of procedures as well as scarce clinical resources, such that the contribution margin of all patients is maximized. We develop two mixed-integer programs (MIP) for this problem which are embedded in a static and a rolling horizon planning approach. Computational results on real-world data show that employing the MIPs leads to a significant improvement of the contribution margin compared to the contribution margin obtained by employing the planning approach currently practiced. Furthermore, we show that the time between admission and surgery is significantly reduced by applying our models.     

Asymmetric flow networks

This paper provides a new model of network formation that bridges the gap between the two benchmark game-theoretic models by Bala and Goyal (2000a) – the one-way flow model, and the two-way flow model – and includes both as limiting cases. As in both the said models, a link can be initiated unilaterally by any player with any other in what we call an “asymmetric flow” network, and the flow through a link towards the player who supports it is perfect. Unlike those models, there is friction or decay in the opposite direction. When this decay is complete there is no flow and this corresponds to the one-way flow model. The limit case when the decay in the opposite direction (and asymmetry) disappears corresponds to the two-way flow model. We characterize stable and strictly stable architectures for the whole range of parameters of this “intermediate” and more general model. A study of the efficiency of these architectures shows that in general stability and efficiency do not go together. We also prove the convergence of Bala and Goyal’s dynamic model in this context.     

Boundary of Anosov dynamics and evolution equations for surfaces

We show that a compact surface of genus greater than one, without focal points and a finite number of bubbles (“good” shaped regions of positive curvature) is in the closure of Anosov metrics. Compact surfaces of nonpositive curvature and genus greater than one are in the closure of Anosov metrics, by Hamilton's work about the Ricci flow. We generalize this fact to the above surfaces without focal points admitting regions of positive curvature using a “magnetic” version of the Ricci flow, the so‐called Ricci Yang‐Mills flow.     

Robust integer programming

We provide a complexity classification of four variants of robust integer programming when the underlying Graver basis is given. We discuss applications to robust multicommodity flows and multiway statistical table problems, and describe an effective parametrization of robust integer programming.     

On front solutions of the saturation equation of two-phase flow in porous media

We investigate the existence of “front” solutions of the saturation equation of two-phase flow in porous media. By front solution we mean a monotonic solution connecting two different saturations. The Brooks–Corey and the van Genuchten models are used to describe the relative-permeability – and capillary pressure–saturation relationships. We show that two classes of front solutions exist: self-similar front solutions and travelling-wave front solutions. Self-similar front solutions exist only for horizontal displacements of fluids (without gravity). However, travelling-wave front solutions exist for both horizontal and vertical (including gravity) displacements. The stability of front solutions is confirmed numerically.     

Efficient simulation of gas–liquid pipe flows using a generalized population balance equation coupled with the algebraic slip model

The inhomogeneous generalized population balance equation, which is discretized with the direct quadrature method of moment (DQMOM), is solved to predict the bubble size distribution (BSD) in a vertical pipe flow. The proposed model is compared with a more classical approach where bubbles are characterized with a constant mean size. The turbulent two-phase flow field, which is modeled using a Reynolds-Averaged Navier–Stokes equation approach, is assumed to be in local equilibrium, thus the relative gas and liquid (slip) velocities can be calculated with the algebraic slip model, thereby accounting for the drag, lift, and lubrication forces. The complex relationship between the bubble size distribution and the resulting forces is described accurately by the DQMOM. Each quadrature node and weight represents a class of bubbles with characteristic size and number density, which change dynamically in time and space to preserve the first moments of the BSD. The predictions obtained are validated against previously published experimental data, thereby demonstrating the advantages of this approach for large-scale systems as well as suggesting future extensions to long piping systems and more complex geometries.     

A modification of the invariant imbedding method for a singular boundary value problem

We consider a dynamically-consistent analytical model of a 3D topographic vortex. The model is governed by equations derived from the classical problem of the axisymmetric Taylor–Couette flow. Using linear expansions, these equations can be reduced to a differential sixth-order equation with variable coefficients. For this differential equation, we formulate a boundary value problem, which has a number of issues for numerical solving. To avoid these issues and find the eigenvalues and eigenfunctions of the boundary value problem, we suggest a modification of the invariant imbedding method (the Riccati equation method). In this paper, we show that such a modification is necessary since the boundary conditions possess singular matrices, which sufficiently complicate the derivation of the Riccati equation. We suggest algebraic manipulations, which permit the initial problem to be reduced to a problem with regular boundary conditions. Also, we propose a method for obtaining a numerical solution of the matrix Riccati equation by means of recurrence relations, which allow us to obtain a matrizer converging to the required eigenfunction. The suggested method is tested by calculating the corresponding eigenvalues and eigenfunctions, and then, by constructing fluid particle trajectories on the basis of the eigenfunctions.