On disjoint configurations in infinite graphs

For a graph A and a positive integer n, let nA denote the union of n disjoint copies of A; similarly, the union of ?₀ disjoint copies of A is referred to as ?₀A. It is shown that there exist (connected) graphs A and G such that nA is a minor of G for all n??, but ?₀A is not a minor of G. This supplements previous examples showing that analogous statements are true if, instead of minors, isomorphic embeddings or topological minors are considered. The construction of A and G is based on the fact that there exist (infinite) graphs G₁, G₂,… such that G_i is not a minor of G_j for all i ≠ j. In contrast to previous examples concerning isomorphic embeddings and topological minors, the graphs A and G presented here are not locally finite. The following conjecture is suggested: for each locally finite connected graph A and each graph G, if nA is a minor of G for all n ? ?, then ?₀A is a minor of G, too. If true, this would be a far‐reaching generalization of a classical result of R. Halin on families of disjoint one‐way infinite paths in graphs. © 2002 Wiley Periodicals, Inc. J Graph Theory 39: 222–229, 2002; DOI 10.1002/jgt.10016     

Dynamics of liquid membranes. II: Adaptive finite difference methods

Two domain-adaptive finite difference methods are presented and applied to study the dynamic response of incompressible, inviscid, axisymmetric liquid membranes subject to imposed sinusoidal pressure oscillations. Both finite difference methods map the time-dependent physical domain whose downstream boundary is unknown onto a fixed computational domain. The location of the unknown time-dependent downstream boundary of the physical domain is determined from the continuity equation and results in an integrodifferential equation which is non-linearly coupled with the partial differential equations which govern the conservation of mass and linear momentum and the radius of the liquid membrane. One of the finite difference methods solves the non-conservative form of the governing equations by means of a block implicit iterative method. This method possesses the property that the Jacobian matrix of the convection fluxes has an eigenvalue of algebraic multiplicity equal to four and of geometric multiplicity equal to one. The second finite difference procedure also uses a block implicit iterative method, but the governing equations are written in conservation law form and contain an axial velocity which is the difference between the physical axial velocity and the grid speed. It is shown that these methods yield almost identical results and are more accurate than the non-adaptive techniques presented in Part I. It is also shown that the actual value of the pressure coefficient determined from linear analyses can be exceeded without affecting the stability and convergence of liquid membranes if the liquid membranes are subjected to sinusoidal pressure variations of sufficiently high frequencies.     

Resolvent estimates in W−1,p related to strongly coupled‐linear parabolic systems with coupled nonsmooth capacities

We investigate linear parabolic systems with coupled nonsmooth capacities and mixed boundary conditions. We prove generalized resolvent estimates in W^{?1, p} spaces. The method is an appropriate modification of a technique introduced by Agmon to obtain L^p estimates for resolvents of elliptic differential operators in the case of smooth boundary conditions. Moreover, we establish an existence and uniqueness result. Copyright © 2007 John Wiley & Sons, Ltd.     

高俘获效率电子辐照加速器的设计研究

加速管是一台加速器的核心部分. 一般电子辐照加速器的俘获效率在50%左右, 一半的电子都损失在加速管内. 丢失的电子打在加速管内壁, 产生轫致辐射、腔体发热量增加、真空变坏等许多负面影响. 采用一段等梯度加速结构, 相速沿加速管呈线形增加,调整相速变化规律及加速管腔体的尺寸参数, 设计出的加速管最终的俘获效率提高到90%以上, 同时平均加速梯度没有因此降低, 加速管总长度没有增加.     

Time Asymptotic Behaviour for a One-Velocity Transport Operator with Maxwell Boundary Condition

This paper is concerned with the spectral analysis of a one-velocity transport operator with Maxwell boundary condition in L ₁-space. After a detailed spectral analysis it is shown that the associated Cauchy problem is governed by a C ₀-semigroup. Next, we discuss the irreducibility of the transport semigroup. In particular, we show that the transport semigroup is irreducible. Finally, a spectral decomposition of the solutions into an asymptotic term and a transient one which will be estimated for smooth initial data is given.     

A Particle-Mesh Method for the Shallow Water Equations Near Geostrophic Balance

In this paper we outline a new particle-mesh method for rapidly rotating shallow water flows based on a set of regularized equations of motion. The time-stepping method uses an operator splitting of the equations into an Eulerian gravity wave part and a Lagrangian advection part. An essential ingredient is the advection of absolute vorticity by means of translated radial basis functions. We show that this implies exact conservation of enstrophy. The method is tested on two model problems based on the qualitative features of the solutions obtained (i.e., dispersion or smoothness of potential vorticity contours) as well as on the increase in mean divergence level.     

Numerical treatment of an asset price model with non-stochastic uncertainty

In contrast to stochastic differential equation models used for the calculation of the term structure of interest rates, we develop an approach based on linear dynamical systems under non-stochastic uncertainty with perturbations. The uncertainty is described in terms of known feasible sets of varying parameters. Observations are used in order to estimate these parameters by minimizing the maximum of the absolute value of measurement errors, which leads to a linear or nonlinear semi-infinite programming problem. A regularized logarithmic barrier method for solving (ill-posed) convex semi-infinite programming problems is suggested. In this method a multi-step proximal regularization is coupled with an adaptive discretization strategy in the framework of an interior point approach. A special deleting rule permits one to use only a part of the constraints of the discretized problems. Convergence of the method and its stability with respect to data perturbations in the cone of convexC ¹-functions are studied. On the basis of the solutions of the semi-infinite programming problems a technical trading system for future contracts of the German DAX is suggested and developed. Supported by the Stiftung Rheinland/Pfalz für Innovation, No. 8312-386261/307.     

The Photochemical Synthesis of Fine Chemicals with Sunlight

The light of the sun can be used directly for changing chemical structures photochemically. Any industrial application must conform to the limitations imposed by the spectral distribution of the photons from the sun, the interruptions to the radiation due to the day/night rhythm, and the weather. In this review, we describe the photochemical potential of the sun, give a fundamental treatment of the concept of photoreactors driven by sunlight (abbreviated to solar photoreactors), and give an account of the realization of this concept in the first pilot plant on the “Plataforma Solar de Almeria” in southern Spain and in other activities in this field. Based on experimental data from photochemical investigations on the pilot plant scale, possibilities, limitations, and the potential growth of solar photochemistry are described. Solar photochemistry, in our opinion, is a technique which could make a contribution to the chemistry of the future because of its photochemical synthesis potential, the avoidance of waste products, and the direct utilization of the sun, not only as a primary energy source, but also as a reaction partner.     

A note on stability of the Douglas splitting method

In this note some stability results are derived for the Douglas splitting method. The relevance of the theoretical results is tested for an advection-reaction equation.

     

Differential–algebraic equations in multibody system modeling

Numerical methods for the efficient integration of both stiff and nonstiff equations of motion of multibody systems having the form of differential-algebraic equations (DAE) of index 3 are discussed. Linear multi-step ABM and BDF methods are considered for the non-iterational integration of nonstiff DAE. The Park method is proposed for integration of stiff equations. This revised version was published online in June 2006 with corrections to the Cover Date.