Nowhere‐Zero 5‐Flows On Cubic Graphs with Oddness 4

Tutte's 5‐flow conjecture from 1954 states that every bridgeless graph has a nowhere‐zero 5‐flow. It suffices to prove the conjecture for cyclically 6‐edge‐connected cubic graphs. We prove that every cyclically 6‐edge‐connected cubic graph with oddness at most 4 has a nowhere‐zero 5‐flow. This implies that every minimum counterexample to the 5‐flow conjecture has oddness at least 6.     

On Preconditioning of Incompressible Non-Newtonian Flow Problems

This paper deals with fast and reliable numerical solution methods for the incompressible non-Newtonian Navier-Stokes equations. To handle the nonlinearity of the governing equations, the Picard and Newton methods are used to linearize these coupled partial differential equations. For space discretization we use the finite element method and utilize the two-by-two block structure of the matrices in the arising algebraic systems of equations. The Krylov subspace iterative methods are chosen to solve the linearized discrete systems and the development of computationally and numerically efficient preconditioners for the two-by-two block matrices is the main concern in this paper. In non-Newtonian flows, the viscosity is not constant and its variation is an important factor that affects the performance of some already known preconditioning techniques. In this paper we examine the performance of several preconditioners for variable viscosity applications, and improve them further to be robust with respect to variations in viscosity.     

系统数值优化方法的研究与应用

大系统具有结构复杂、功能综合、因素众多等特点,相应的规划和决策问题的求解是非常困难的。我们针对大系统工程规划和决策的特点,结合运筹学的原理,提出了大系统数值优化概念,建立了优化模型,给出了优化问题的求解方法;并选择了中石油的DS-1油田作为应用实例,进行了油田采油工程数值优化,取得了很好的效果。为一般的复杂工程系统的规划和决策提供了一个新方法。     

Nonlocal Interaction Equations in Environments with Heterogeneities and Boundaries

We study well-posedness of a class of nonlocal interaction equations with spatially dependent mobility. We also allow for the presence of boundaries and external potentials. Such systems lead to the study of nonlocal interaction equations on subsets ? of ? ^d endowed with a Riemannian metric g. We obtain conditions, relating the interaction potential and the geometry, which imply existence, uniqueness and stability of solutions. We study the equations in the setting of gradient flows in the space of probability measures on ? endowed with Riemannian 2-Wasserstein metric.     

Long Time Behavior of the Cahn-Hilliard Equation with Irregular Potentials and Dynamic Boundary Conditions

The Cahn-Hilliard equation with irregular potentials and dynamic boundary conditions is considered.The existence of the global attractor is proved and the long time behavior of the trajectories,namely,the convergence to steady states,is studied.     

Maximum flow problem on dynamic generative network flows with time-varying bounds

This paper considers a new class of network flows, called dynamic generative network flows in which, the flow commodity is dynamically generated at a source node and dynamically consumed at a sink node and the arc-flow bounds are time dependent. Then the maximum dynamic flow problem in such networks for a pre-specified time horizon T is defined and mathematically formulated in both arc flow and path flow presentations. By exploiting the special structure of the problem, an efficient algorithm is developed to solve the general form of the dynamic problem as a minimum cost static flow problem.     

Comparison of turbulence models in simulating swirling pipe flows

Swirling flow is a common phenomenon in engineering applications. A numerical study of the swirling flow inside a straight pipe was carried out in the present work with the aid of the commercial CFD code fluent. Two-dimensional simulations were performed, and two turbulence models were used, namely, the RNG k–ε model and the Reynolds stress model. Results at various swirl numbers were obtained and compared with available experimental data to determine if the numerical method is valid when modeling swirling flows. It has been shown that the RNG k–ε model is in better agreement with experimental velocity profiles for low swirl, while the Reynolds stress model becomes more appropriate as the swirl is increased. However, both turbulence models predict an unrealistic decay of the turbulence quantities for the flows considered here, indicating the inadequacy of such models in simulating developing pipe flows with swirl.     

Robust optimization of internal transports at a parcel sorting center operated by Deutsche Post World Net

Competitiveness in global markets requires the ongoing identification and full utilization of improvement potential. To cut costs by means of process optimization, logistics service providers need to focus on efficient planning — not only for external but also for internal transports. This contribution will demonstrate that significant reductions in internal transports at one of the Deutsche Post World Net’s main parcel sorting centers can be achieved by applying the robust solution of a modified three-dimensional linear assignment model.     

Study of a finite element method for the time-dependent generalized Stokes system associated with viscoelastic flow

A three-field finite element scheme designed for solving systems of partial differential equations governing time-dependent viscoelastic flows is studied. Once a classical backward Euler time discretization is performed, the resulting three-field system of equations allows for a stable approximation of velocity, pressure and extra stress tensor, by means of continuous piecewise linear finite elements, in both two- and three- dimensional space. This is proved to hold for the linearized form of the system. An advantage of the new formulation is the fact that it provides an algorithm for the explicit iterative resolution of system nonlinearities. Convergence in an appropriate sense applying to these three flow fields is demonstrated.     

A low-Mach number model for time-harmonic acoustics in arbitrary flows

This paper concerns the finite element simulation of the diffraction of a time-harmonic acoustic wave in the presence of an arbitrary mean flow. Considering the equation for the perturbation of displacement (due to Galbrun), we derive a low-Mach number formulation of the problem which is proved to be of Fredholm type and is therefore well suited for discretization by classical Lagrange finite elements. Numerical experiments are done in the case of a potential flow for which an exact approach is available, and a good agreement is observed.