A Survey on the Numerics and Computations for the Landau-Lifshitz Equation of Micromagnetism

The Landau-Lifshitz (LL)equation of micromagnetism governs rich variety of the evolution of magnetization patterns in ferromagnetic media. This is due to the complexity of physical quantities appearing in the LL equation. This complexity causes also an interesting mathematical properties of the LL equation: nonlocal character for some quantities,nonconvex side-constraints, strongly nonlinear terms. These effects influence also the numerical approximations. In this work, recent developments on the approximation of weak solutions, together with the overview of well-known methods for strong solutions,are addressed. Author is supported by the Fund for Scientific Research - Flanders FWO (Belgium).     

具有厚大断面的大型球墨铸铁铸件的生产

首先通过电炉—LF精炼炉—VD精炼炉—包内球化的工艺路线获得了足够的优质铁液,然后通过选取合适的分型面、设置合理的浇注系统、设计专用的冷铁、安放足够大的保温冒口和上表面加大加工余量来去除夹渣等措施,成功生产了具有厚大断面的大型球墨铸铁铸件。     

The Transformation of Carbides during Austenization and Its Effect on the Wear Resistance of High Speed Steel Rolls

The transformation of carbides with austenization time of a high speed steel (HSS) roll material, manufactured by a centrifugal casting method, has been studied. The correlation between wear resistance and the type, morphology, volume fraction, and distribution of the carbides has also been investigated. Microstructural observations, X-ray diffraction (XRD) analysis, hardness measurements, and energy dispersive spectroscopy (EDS) have been used to characterize the carbides. The type and volume fraction of carbides were found to change with austenizing time. During austenization, the transformation of the M₃C carbides can be postulated as M₃C + γ-Fe → M₂C, with much finer nodular and rodlike MC carbides also forming through a solid-state transformation. The M₂C carbide decomposes as M₂C + γ-Fe → MC + M₇C₃ + M₆C. The decomposed carbide substantially maintains a platelike shape until the end of decomposition. The most important finding of this study is that austenization results in changes in the type, morphology, volume fraction, and distribution of carbides and that it can be controlled to produced a homogeneous distribution of hard carbides, resulting in an improvement in the wear resistance of HSS rolls. This finding may be of great use for the industrial production of HSS rolls.     

The Growth of a Single Cell/Dendrite in a Directional Solidification Process

Following the original model for a single cell/dendrite growth by Hunt,[5] systematic numerical simulations are carried out with focus on cell shape evolution and tip radius selection in a directional solidification process conducted in a capillary tube. Computations indicate that the anisotropy of solid/liquid interfacial energy and the diameter of a capillary tube have significant influences on the selection of a tip shape. The anisotropy in dilute SCN-salol alloys has been determined through the equilibrium droplet shape method and its value is 1.09 pct. The calculated cell/dendrite shapes with this value of anisotropy agree with experimental observations where a single cell/dendrite of SCN-salol alloys grows in a capillary tube.     

External-Memory Algorithms for Processing Line Segments in Geographic Information Systems

In the design of algorithms for large-scale applications it is essential to consider the problem of minimizing I/O communication. Geographical information systems (GIS) are good examples of such large-scale applications as they frequently handle huge amounts of spatial data. In this paper we develop efficient external-memory algorithms for a number of important problems involving line segments in the plane, including trapezoid decomposition, batched planar point location, triangulation, red--blue line segment intersection reporting, and general line segment intersection reporting. In GIS systems the first three problems are useful for rendering and modeling, and the latter two are frequently used for overlaying maps and extracting information from them.     

Train Tracks and Confluent Drawings

Confluent graphs capture the connection properties of train tracks, offering a very natural generalization of planar graphs, and—as the example of railroad maps shows—are an important tool in graph visualization. In this paper we continue the study of confluent graphs, introducing strongly confluent graphs and tree-confluent graphs. We show that strongly confluent graphs can be recognized in NP (the complexity of recognizing confluent graphs remains open). We also give a natural elimination ordering characterization of tree-confluent graphs, and we show that this class coincides with the (6,2)-chordal bipartite graphs. Finally, we define outerconfluent graphs and identify the bipartite permutation graphs as a natural subclass.     

怀念建筑设计大师张开济先生

虽然国内正值“十一”黄金周,但是新华社的一则唁电却给中国建筑界带来了一个噩耗。中国建筑界泰斗、全国建筑设计大师、第一届梁思成奖获得者、北京市建筑设计研究院顾问总建筑师张开济,因病医治无效,于9月28日零时5分在北