Problem of the Motion of an Elastic Medium Formed at the Solidification Front

The following self-similar problem is considered. At the initial instant of time, a phase transformation front starts moving at constant velocity from a certain plane (which will be called a wall or a piston, depending on whether it is assumed to be fixed or movable); at this front, an elastic medium is formed as a result of solidification from a medium without tangential stresses. On the wall, boundary conditions are defined for the components of velocity, stress, or strain. Behind the solidification front, plane nonlinear elastic waves can propagate in the medium formed, provided that the velocities of these waves are less than the velocity of the front. The medium formed is assumed to be incompressible, weakly nonlinear, and with low anisotropy. Under these assumptions, the solution of the self-similar problem is described qualitatively for arbitrary parameters appearing in the statement of the problem. The study is based on the authors’ previous investigation of solidification fronts whose structure is described by the Kelvin–Voigt model of a viscoelastic medium.     

Influence of electromagnetic stirrer position on fluid flow and solidification in continuous casting mold

A computational study of the effect of stirrer position on fluid flow and solidification in a continuous casting billet mold with in-mold electromagnetic stirring has been carried out. The numerical investigation uses a full coupling method in which alternating magnetic field equations are solved simultaneously with the governing equations of fluid flow and heat transfer. An enthalpy-porosity technique is used for the solidification analysis while the magnetohydrodynamics technique is used for studying the fluid flow behavior under the electromagnetic field. The streamline, liquid fraction, and solid shell thickness at the mold wall have been predicted with and without EMS application at different positions along the length of the mold. Recirculation loops are seen to be formed above and below the stirrer position when fluid flow and electromagnetic field equations were solved, without incorporating the solidification model. Application of the solidification model interestingly resulted in the reduction of the size of the recirculation loops formed. The tangential component of velocity of the fluid near the solidification front, stirring intensity and the effective length of stirring below the stirrer decrease as the stirrer position is moved downwards. Significant changes in characteristics of solid shell formation like delay in initiation of solidification at the mold wall and formation of a gap in the re-solidified shell have been observed with change in stirrer position.     

A numerical method to compute solidification and melting processes

This paper deals with thermodynamically consistent numerical predictions of solidification and melting processes of pure materials using moving grids. Till date, enthalpy-porosity-based formulations of numerical codes have been generally the popular choice, although because of an artificial numerical smearing of the interface, it is virtually impossible to reproduce a sharp melting/solidification front that is supposed to exist for phase changes of pure substances. Numerical techniques based on moving grid methods have been relatively less used as they rely on complex and time-consuming adaptive grid generations. Using the moving grid approach, the authors present a method to solve solidification and melting problems. A simple linear interpolation is used to slide grid nodes along the interface to handle the otherwise obtained grid skewness near the interface. The numerical approach employed is validated with standard test cases available in the literature. The capability of capturing very complex flow field structures and the superiority of the present approach over enthalpy-porosity-based formulations is discussed. The authors also demonstrate the ability of the set-up computer code to solve complex thermofluid processes such as occur during crystal growth in Czochralski reactors.     

On ordered categories as a framework for fuzzification of algebraic and topological structures

Using the framework of ordered categories, the paper considers a generalization of the fuzzification machinery of algebraic structures introduced by Rosenfeld as well as provides a new approach to fuzzification of topological structures, which amounts to fuzzifying the underlying “set” of a structure in a suitably compatible way, leaving the structure itself crisp. The latter machinery allows the so-called “double fuzzification”, i.e., a fuzzification of something that is already fuzzified.     

Link formation in cooperative situations

In this paper we study the endogenous formation of cooperation structures or communication graphs between players in a superadditive TU game. For each cooperation structure that is formed, the payoffs to the players are determined by an exogenously given solution. We model the process of cooperation structure formation as a game in strategic form. It is shown that several equilibrium refinements predict the formation of the complete cooperation structure or some structure which is payoff-equivalent to the complete structure. These results are obtained for a large class of solutions for cooperative games with cooperation structures. Received September 1995/Revised version I October 1996/Revised version II April 1997/Final version September 1997     

A three-dimensional fluid flow model for puddle formation in the single-roll rapid solidification process

The single-roll rapid solidification process (SRRSP) is considered to be a process of perspective to produce a Fe-Si-B ribbon of amorphous microstructure and near net shape products such as thin strips of stainless steel. The condition of a melt puddle between the nozzle and rotating wheel in the single-roll rapid solidification process significantly affects the quality and dimensional uniformity of the products as well as the smoothness of the operation. The purpose of this study was to develop a three-dimensional fluid flow analysis system to model the formation of puddle and flow conditions of molten metal in the puddle for the single-roll rapid solidification processes which include the planar flow casting (PFC) process and the single-roll strip casting process. The model is based on a computational fluid dynamics technique called the SOLA-VOF scheme, which possesses the capability of treating transient fluid flow problems with the evolution of free boundaries. Furthermore, the SOLA-VOF scheme is extended from two dimensions to three dimensions. The simulated results reveal how the melt puddle is formed between the nozzle and the rotating substrate and its corresponding fluid flow behavior for the PFC process as well as the single-roll strip casting process. The test results also demonstrate that two-dimensional analysis cannot properly consider the actual flow condition in the puddle.     

A multi-structural framework for adaptive supply chain planning and operations control with structure dynamics considerations

A trend in up-to-date developments in supply chain management (SCM) is to make supply chains more agile, flexible, and responsive. In supply chains, different structures (functional, organizational, informational, financial, etc.) are (re)formed. These structures interrelate with each other and change in dynamics. The paper introduces a new conceptual framework for multi-structural planning and operations of adaptive supply chains with structure dynamics considerations. We elaborate a vision of adaptive supply chain management (A-SCM), a new dynamic model and tools for the planning and control of adaptive supply chains. SCM is addressed from perspectives of execution dynamics under uncertainty. Supply chains are modelled in terms of dynamic multi-structural macro-states, based on simultaneous consideration of the management as a function of both states and structures. The research approach is theoretically based on the combined application of control theory, operations research, and agent-based modelling. The findings suggest constructive ways to implement multi-structural supply chain management and to transit from a “one-way” partial optimization to the feedback-based, closed-loop adaptive supply chain optimization and execution management for value chain adaptability, stability and crisis-resistance. The proposed methodology enhances managerial insight into advanced supply chain management.     

Stringlike structures in Kerr-Schild geometry: The N=2 string, twistors, and the Calabi-Yau twofold

The four-dimensional Kerr-Schild geometry contains two stringy structures. The first is the closed string formed by the Kerr singular ring, and the second is an open complex string obtained in the complex structure of the Kerr-Schild geometry. The real and complex Kerr strings together form a membrane source of the over-rotating Kerr-Newman solution without a horizon, a = J/m ? m. It was also recently found that the principal null congruence of the Kerr geometry is determined by the Kerr theorem as a quartic in the projective twistor space, which corresponds to an embedding of the Calabi-Yau twofold into the bulk of the Kerr geometry. We describe this embedding in detail and show that the four sheets of the twistorial K3 surface represent an analytic extension of the Kerr congruence created by antipodal involution.     

Solidification modelling with a control volume method on domains subjected to viscoplastic deformation

The rise in importance of semi-solid based products has created a need for accurate modelling approaches to coupled solidification and deformation. Current approaches to solidification modelling, using the finite element method (FEM), are principally founded on capacitance methods. Unfortunately they suffer from a major drawback in that energy is not correctly transported through elements, so providing a source of inaccuracy. This paper is concerned with the development and application of a control volume capacitance method (CVCM) to problems where viscoplastic deformation and solidification are combined. The approach adopted is founded on the theory that describes energy transfer through a control volume (CV) moving relative to the deforming mass. This essentially arbitrary Lagrangian–Eulerian (ALE) method facilitates the accurate treatment of discontinuities. The CV approach is tested against known analytical solutions and is shown to be accurate, stable and computationally competitive.     

On the stabilization mechanisms in liquid metallic foams

Metal foams are porous structures made up of conventional metals such as aluminium. Their advantageous density to stiffness ratio leads to a variety of applications especially in automotive industry, where they have gained interest as material used in shock absorbers and light weight construction parts. Solid metal foams are usually produced by solidification of a liquid metallic foam. The latter is generated by the introduction of gas into a melt analogous to aqueous foams. Depending on the parameters of the production process, porous structures with relative densities down to 10% of the original metal can be achieved. However, while the mechanisms leading to stable aqueous foams are quite well understood, this is not the case for metallic foams. In contrast for example to soap foams, no surface active or polar substances are present in liquid metals. It is merely known empirically that solid particles have a major influence on the stability of a liquid metallic foam. In this paper we present experimental observations showing that the stability and structure of metallic foams produced via a melt route are predominantly governed by interface rather than drainage effects. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

轻质热防护系统多层材料组合结构的热应力分析

提出了轻质热防护系统外面板使用多层结构的概念,设计了2种热防护材料组合构成的3种铺层方案．通过模拟飞行器再入大气层时受到的机械和热载荷条件,数值计算得到了层间剪切力、底部温度和y方向位移．计算结果发现,层间剪切力发生在边缘部位且呈反对称分布;选用高热导率和高热容材料能够减少材料内的温度梯度,进而有效地降低结构的热应力和热变形;在均匀温度场情况下,两种材料的热膨胀系数之差越小,则层间剪切力越小．该研究表明不同的材料组合和铺层次序的多层结构,可以满足不同设计要求,具有优化设计潜力．     

基于分子动力学模拟的金属构件的弹-塑性分解方法

针对金属多晶材料构件的分子动力学（MD）模拟,本文提出了一种新的弹-塑性分解方法.文章将MD运动轨迹分解为结构变形和热振动,给出了计算结构变形的方法和近似公式;针对金属多晶材料构件的当前构型,给出了基于FCC|BCC晶胞和四原子占位的四面体单元相组合的连续变形函数及计算变形梯度的算法;利用原子-连续关联模型,发展了计算当前构型应力场和弹性张量的算法.分析了当构件承受过大载荷后在材料内部所产生的微观缺陷,并将其分类标定为位错、层错、挛晶界、晶界和空位等;对于层错和挛晶界讨论了在弹性卸载过程中应满足的刚体运动约束方程;利用极小势能原理构造了基于当前构型的弹性卸载算法,进而给出了完整的基于MD模拟的计算弹-塑性应变的算法.最后,针对单晶铜纳米线拉伸的MD模拟,计算了弹-塑性应变场,验证了本文方法的合理性.
本文提出的基于MD模拟的弹-塑性分解方法,为从微观到宏观的多尺度和多模型耦合计算提供了算法支撑.     

Minimum cost spanning tree games

We consider the problem of cost allocation among users of a minimum cost spanning tree network. It is formulated as a cooperative game in characteristic function form, referred to as a minimum cost spanning tree (m.c.s.t.) game. We show that the core of a m.c.s.t. game is never empty. In fact, a point in the core can be read directly from any minimum cost spanning tree graph associated with the problem. For m.c.s.t. games with efficient coalition structures we define and construct m.c.s.t. games on the components of the structure. We show that the core and the nucleolus of the original game are the cartesian products of the cores and the nucleoli, respectively, of the induced games on the components of the efficient coalition structure.This paper is a revision of [4].     

Solving two-phase freezing Stefan problems: Stability and monotonicity

The two-phase Stefan problems with phase formation and depletion are special cases of moving boundary problems with interest in science and industry. In this work, we study a solidification problem, introducing a front-fixing transformation. The resulting non-linear partial differential system involves singularities, both at the beginning of the freezing process and when the depletion is complete, that are treated with special attention in the numerical modelling. The problem is decomposed in three stages, in which implicit and explicit finite difference schemes are used. Numerical analysis reveals qualitative properties of the numerical solution spatial monotonicity of both solid and liquid temperatures and the evolution of the solidification front. Numerical experiments illustrate the behaviour of the temperatures profiles with time, as well as the dynamics of the solidification front.     

Biaxial orientation of amorphous linear polymers

The dependence of the birefringence and orientation stress on the biaxial stretch ratio and orientation conditions has been experimentally investigated. The temperature dependence of these characteristics is explained in terms of the network structure of amorphous polymers. It is shown that the transformations of the supermolecular structures in the process of biaxial orientation depend on the orientation temperature — at higher temperatures better organized structures are formed. There is a formal relationship between the effect of orientation temperature on supermolecular structure formation and on the relaxation process responsible for the formation of a more thermally stable molecular network.Moscow. Translated from Mekhanika Polimerov, No. 5, pp. 17–23, January–February, 1971.     

Waves in periodic structures with imperfections

The study of wave propagation in structures and media has a significant history which follows from the examination of the dynamics of atomic and molecular lattices. Relatively recently, some of these ideas have been transferred and applied to the dynamic behavior of engineered structures. In particular, structures with periodic and almost periodic topologies and material properties have been extensively studied and important conclusions drawn regarding their energy-transmission properties. The attraction to wave propagation models is due to the efficient nature of the analytical tools available to study how energies of different frequency content are propagated or filtered by the structure. Such properties of a structure are profoundly affected by any imperfections or “near-periodicities”. It has been found that imperfections will have the effect of localizing energies about them, thus not allowing the development of normal modes of vibration as would be observed when assuming a perfect structure. It is envisioned that such understanding will permit the analyst to take advantage of localization effects to isolate locations experiencing loading. Additional applications possibly include the modeling of composite and layered structures and cracks. Also, one expects that structures with periodic boundary conditions will experience some sort of localization of energies in certain frequency ranges.     

Semi-implicit method for thermodynamically linked equations in phase change problems (SIMTLE)

Thermodynamic coupling of temperature and composition fields in phase-change problems has been a challenge for decades. A compromise has been always desired between numerical efficiency and detailed physical consideration, toward a general scheme. In the present work, a macro–micro numerical method is proposed to link the conservation equations of energy and species with the thermodynamics of the solidification problems. Firstly, the basic structure of the method, simplified with a local equilibrium assumption, is presented. The method is then extended to a multi-phase model, demonstrating a three-phase approach to the solidification of a eutectic binary alloy. Relaxing the limitations imposed by the equilibrium assumption, non-equilibrium and microscale considerations was also included subsequently by a suggested modification to the macroscopic mathematical model. Advantages gained through the general algorithm proposed are concerned with two features of the method; (a) consistency with the energy and species equations. (b) No need of a predefined solidification path; that allows for the usage of raw phase diagram curves and offers simplicity and generality for extension through complex problems (i.e. microscopic, multi-phase or non-equilibrium). A benchmark problem was employed to test the performance of the proposed method in two cases of local equilibrium and Scheil-like solidification. The obtained results were validated in comparison with available semi-analytical solution.     

Two-stage search algorithm for the inbound container unloading and stacking problem

This study focuses on the inbound container unloading and stacking problem at container terminals and achieves both a reasonable unloading sequence and the optimal yard stacking distribution. A formulation is proposed as the relational expression between the expected number of rehandles and the stacking height. Based on the formulation, an integer programming model is established to both find the optimal stacking distribution and unloading sequence and attempt to minimize the expected number of rehandles. The model can be solved by the commercial solver for small-scale instances. To solve for large-scale instances in the real world, a two-stage search algorithm is designed, therein incorporating an initial stage for generating the feasible solution and a neighborhood search stage for finding the optimal solution. The algorithm can find an optimal solution in polynomial time, which is proved by theoretical methods and evidenced by numerical experiments.     

Multiscale analysis of depth images from natural scenes: Scaling in the depth of the woods

We analyze an ensemble of images from outdoor natural scenes and consisting of pairs of a standard gray-level luminance image associated with a depth image of the same scene, delivered by a recently introduced low-cost sensor for joint imaging of depth and luminance. We specially focus on statistical analysis of multiscale and fractal properties in the natural images. Two methodologies are implemented for this purpose, and examining the distribution of contrast upon coarse-graining at increasing scales, and the orientationally averaged power spectrum tied to spatial frequencies. Both methodologies confirm, on another independent dataset here, the presence of fractal scale invariance in the luminance natural images, as previously reported. Both methodologies here also reveal the presence of fractal scale invariance in the novel data formed by depth images from natural scenes. The multiscale analysis is confronted on luminance images and on the novel depth images together with an analysis of their statistical correlation. The results, especially the new results on the multiscale analysis of depth images, consolidate the importance and extend the multiplicity of aspects of self-similarity and fractal scale invariance properties observable in the constitution of images from natural scenes. Such results are useful to better understanding and modeling of the (multiscale) structure of images from natural scenes, with relevance to image processing algorithms and to visual perception. The approach also contains potentialities for the fractal characterization of three-dimensional natural structures and their interaction with light.     

Numerical modelling of melt-conditioned direct-chill casting

Melt conditioned direct-chill (MC-DC) casting is a novel technology which combines direct-chill (DC) casting with a high shear device directly immersed in the sump for in situ microstructural control. A numerical model of melt-conditioned direct-chill casting (MC-DC) is presented in this paper. This model is based on a finite volume continuum model using a moving reference frame (MRF) to enforce fluid rotation inside the rotor-stator region and is numerically stable within the range of processing conditions. The boundary conditions for the heat transfer include the effects of the hot-top, the aluminium mould, and the direct chill. This model is applied to the casting of two alloys: aluminium-based A6060 and magnesium-based AZ31. Results show that MC-DC casting modifies the temperature profile in the sump, resulting in a larger temperature gradient at the solidification front and a shorter local solidification time. The increased heat extraction rate due to forced convection in the sump is expected to contribute to a finer, more uniform grain structure in the as-cast billet.