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Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

This study aims to consider the influence of density difference integral and relative flow difference on traffic flow, a novel two-lane lattice hydrodynamic model is proposed. The stability criterion for the new model is obtained through the linear analysis method.

The modified Korteweg de Vries (KdV) (mKdV) equation is derived to describe the characteristic of traffic jams near the critical point. Numerical simulations are carried out to explore how density difference integral and relative flow difference influence traffic stability. Numerical and analytical results demonstrate that traffic congestions can be effectively relieved considering density difference integral and relative flow difference.

The traffic congestions can be effectively relieved considering density difference integral and relative flow difference.

Novel two-lane lattice hydrodynamic model is presented considering density difference integral and relative flow difference. Applying the linear stability theory, the new model’s linear stability is obtained. Through nonlinear analysis, the mKdV equation is derived. Numerical results demonstrate that the traffic flow stability can be efficiently improved by the effect of density difference integral and relative flow difference.

Discusses the 27 papers in ISEF 1999 Proceedings on the subject of electromagnetisms. States the groups of papers cover such subjects within the discipline as: induction machines; reluctance motors; PM motors; transformers and reactors; and special problems and applications. Debates all of these in great detail and itemizes each with greater in‐depth discussion of the various technical applications and areas. Concludes that the recommendations made should be adhered to.

Introduces papers from this area of expertise from the ISEF 1999 Proceedings. States the goal herein is one of identifying devices or systems able to provide prescribed performance. Notes that 18 papers from the Symposium are grouped in the area of automated optimal design. Describes the main challenges that condition computational electromagnetism’s future development. Concludes by itemizing the range of applications from small activators to optimization of induction heating systems in this third chapter.

The purpose is to present a new formal approach based on a partial integro‐differential equation, the space‐time state transition equation (STSTE), and on a set of general equations with which space‐time dynamical models of complex systems, such as social systems and ecosystems, can be built.

The STSTE provides the partial derivative of the density of a state‐variable with regard to time as a sum of time rates and space‐time rates. Time rates describe the dynamics of the system for each space‐point irrespectively of the other points, whilst space‐time rates describe this evolution as a consequence of the relation of each space‐point with a given set of other points of the space. This relation contains integrals over the accessibility domains (sets of space‐points with which each space‐point is related).

The STSTE is provided for any system of space‐coordinates and is compared with the reaction‐diffusion models (RD). The reason why it is more convenient to work with the STSTE than with the RD to model complex systems in the context of social systems and ecosystems is indicated.

An urban system (the city of Valencia, Spain) is presented as an application; an analytical solution strategy is stated under the simplest hypothesis for computing space‐time rates, and a computer program for the situation is developed to obtain numerical solutions.

A numerical comparison between the new STSTE model and the RD shows that, the STSTE model produces better results than the reaction diffusion model in validation.

A widely used approach for solving the two‐dimensional semiconductor‐device equations through the Finite‐Element method employs a linear approximation of the electric and quasi‐Fermi potentials over a triangular mesh; this approach combines the flexibility of FE method with the simplicity of a piecewise linear representation of the unknowns. Owing to the strong dependence of carrier densities on the position, a careful evaluation of integrals involving these quantities is desirable; this problem arises, for example, when the very common Galerkin's or Ritz's method are used, and is differently treated in the Literature. In this paper it is demonstrated that, if a minor approximation on the intrinsic carrier density is done, an analytical evaluation of the above integrals over each triangular element can be performed, which takes into account the correct dependence of carrier densities on the electric and quasi‐Fermi potentials; the results may be used to avoid heavy mesh refinements, which make the solution procedure costly both in CPU time and in memory storage. Practical applications to some specific devices will be shown elsewhere; the procedure and the final formulas are presented here in a rather general way, thus allowing a possible application to different problems which may be solved with FE method.

A review is made of methods for calculating parameters characterizing crack tip behaviour in non‐linear materials. Convenient methods of calculating J‐integral type quantities are reviewed, classified broadly into two groups, as domain integrals and virtual crack extension techniques. In addition to considerations of how such quantities may be calculated by finite elements, assessment methods of conducting the actual incremental analyses are described.

1.1. Logical Necessity of the Three Dimensions as a Unit of Thought The mathematician does not look kindly on the simple question of why natural space should consist of precisely three dimensions. Instead of giving an answer he assumes a silent smile and shows us a version of space with an infinity of dimensions, as if space were some kind of toy for him to fiddle with to his heart's content.

The axisymmetric steady‐state convective‐diffusive thermal field problem associated with direct‐chill, semi‐continuously cast billets has been solved using the dual reciprocity boundary element method. The solution is based on a formulation which incorporates the one‐phase physical model, Laplace equation fundamental solution weighting, and scaled augmented thin plate splines for transforming the domain integrals into a finite series of boundary integrals. Realistic non‐linear boundary conditions and temperature variation of all material properties are included. The solution is verified by comparison with the results of the classical finite volume method. Results for a 0.500[m] diameter Al 4.5 per cent Cu alloy billet at typical casting conditions are given.