THE STABILITY OF LINEAR MULTISTEP METHODS FOR LINEAR SYSTEMS OF NEUTRAL DIFFERENTIAL EQUATIONS

1. IntroductionFor a large class of electrical ~ks containing IOssless transmission lines the describingequations can be reduced to a system of neutral differential equations.This paper deals with the numerical solution of initial value problems for syste…     

Integral representation for powers of elements in locally <Emphasis Type="Italic">m</Emphasis>-convex algebras and applications

This paper proves a new integral representation theorem for powers of elements in locally m-convex algebras. It is shown that the conditions handled in this theorem are satisfied for any sequentially complete locally m-convex Q-algebra. Various applications of this result concerning the spectrum, the spectral radius or the numerical radius are given.      

Gas-solid interaction force from direct numerical simulation (DNS) of binary systems with extreme diameter ratios

nding the large particles becomes less in case ofa bidisperse mixture, as compared to a monodisperse system with the same volume fraction. We further investigated this discrepancy by calculating the volume per particle by means of Voronoi tessellation.     

Hillock formation on ion-irradiated graphite surfaces

Abstract

Scanning probe microscopy experiments show that ion irradiation of (0001) graphite results in the formation of isolated defects comprising of a few tens of atoms. We use molecular dynamics simulations and density-functional theory calculations to study the formation probabilities of these defects. We identify different defect structures which correspond to experimentally observed hillocks on graphite surfaces. We find that the predominant source of defects are vacancies and interlayer interstitials, and identify a three-atom carbon ring defect on the graphite surface.     

Study on the flow resistance of the dispersion system of deformable preformed particle gel in porous media using LBM-DEM-IMB method

After being injected into the porous media, the dispersion system of preformed particle gel (PPG) tends to enter high permeability regions and block water channeling passages, which forces the subsequent water to turn to the low permeability regions and thus increases sweep efficiency and enhances oil recovery. However, it is still unclear about the influence factors and the mechanisms how PPG increases water flow resistance, which limits the application of PPG in more oilfields. Therefore, the paper combines the lattice Boltzmann method (LBM), the discrete element method (DEM) and the improved immersed moving boundary (IMB) method to simulate the migration of deformable PPG in porous media. On the basis, the paper quantitatively analyzes the variation law of displacement pressure across the porous media and discusses the influence factors such as the PPG diameter, elasticity modulus and the number concentration. Results indicate that, because of the friction and retention of PPG in pore-throat, the displacement pressure across the porous media during PPG flooding is much higher than that during water flooding. In other words, the existence of PPG increases the flow resistance of injected water. Besides, the displacement pressure is always fluctuant resulting from the continuous process of PPG migration, retention, deformation and remigration. Influence factor analysis shows that the incremental value and fluctuation degree of flow resistance increase with the PPG diameter, elasticity modulus and the number concentration. The study not only provides useful reference for future PPG flooding, but also benefits the development of deformable particle flow theory.     

分散化供应链的自组织演化机制建模与仿真

供应链是一个复杂适应系统.提出了分散化供应链演化的自组织机制.在开放结构下,多企业主体为了适应外部环境,在非线性互动中涌现出供应链协作结构和协调模式.借鉴生物系统环境适应能力思想,建立了分散化供应链自组织演化模型,并采用Multi-agent技术进行仿真,证明了分散化供应链的自组织演化机制.外部环境和企业内部机制因素控制着分散化供应链的演化,其演化对初始条件高度敏感,存在着锁定、路径依赖和混沌等自组织系统特性.     

Particle Simulation of Relativistic Laser Pulse Density Channeling

Two-dimensional particle simulation is carried out to study the interaction between a high-intensity finite-size spot laser beam and a plasma with linear density profile. The laser is allowed to propagate in underdense corona until it is cut off near the critical surface. The intense laser can drive various instabilities through particle collective motion and result in electron heating,while relativistic effect and ponderomotive force can bring strong energy absorption and electron heating in the overdense region. As the laser beam is nonuniform in the transverse direction,a density channel forms and hole boring effect occurs as a result of strong ponderomotive force pushing particle outwards. These processes can be investigated well by particle simulation.     

Numerical modelling of unsteady convective–diffusive heat transfer with a control volume hybrid method

Presented in this paper is a numerical methodology for the solution of the parabolic governing partial differential equation that describes unsteady advection–diffusion heat transfer. The formulation presented here is shown to be free from the numerical oscillation commonly associated with advection–diffusion heat transfer regardless of the value of the Peclet number. The formulation involves the absorption of the advection term in the unsteady heat equation into the capacitance term. This process is achieved with the use of a control volume methodology applied to each nodal element on a finite-volume mesh. This is shown to ensure that spurious energy losses and gains are avoided and provides for consistency between temperature and energy change. This approach provides unconditional stability and it is shown that good accuracy is achievable with relatively large time-steps.     

Numerical calculation of an asymmetric supply function equilibrium with capacity constraints

Producers submit offer curves to a procurement auction, e.g. an electricity auction, before uncertain demand has been realised. In the supply function equilibrium (SFE), every firm commits to the offer curve that maximises its expected profit, given the offer curves of competitors. The equilibrium is given by a system of differential equations. In practice, it has been very difficult to find valid SFE, i.e. non-decreasing solutions, from this system, especially for asymmetric producers. This paper shows that valid SFE can be calculated by means of a shooting algorithm that combines numerical integration with an optimisation procedure that searches for an end-condition. Multiple/parallel shooting is used for ill-conditioned cases.     

Steady-state solutions in a three-dimensional nonlinear pool-boiling heat-transfer model

We consider a relatively simple model for pool-boiling processes. This model involves only the temperature distribution within the heater and describes the heat exchange with the boiling medium via a nonlinear boundary condition imposed on the fluid-heater interface. This results in a standard heat-transfer problem with a nonlinear Neumann boundary condition on part of the boundary. In a recent paper [Speetjens M, Reusken A, Marquardt W. Steady-state solutions in a nonlinear pool-boiling model. IGPM report 256, RWTH Aachen. Commun Nonlinear Sci Numer Simul, in press, doi:10.1016/j.cnsns.2006.11.002] we analysed this nonlinear heat-transfer problem for the case of two space dimensions and in particular studied the qualitative structure of steady-state solutions. The study revealed that, depending on system parameters, the model allows both multiple homogeneous and multiple heterogeneous temperature distributions on the fluid-heater interface. In the present paper we show that the analysis from Speetjens et al. (doi:10.1016/j.cnsns.2006.11.002) can be generalised to the physically more realistic case of three space dimensions. A fundamental shift-invariance property is derived that implies multiplicity of heterogeneous solutions. We present a numerical bifurcation analysis that demonstrates the multiple solution structure in this mathematical model by way of a representative case study.