A transform method for linear evolution PDEs on a finite interval

We study initial boundary value problems for linear scalar evolutionpartial differential equations, with spatial derivatives ofarbitrary order, posed on the domain {t > 0, 0 < x <L}. We show that the solution can be expressed as an integralin the complex k-plane. This integral is defined in terms ofan x-transform of the initial condition and a t-transform ofthe boundary conditions. The derivation of this integral representationrelies on the analysis of the global relation, which is an algebraicrelation defined in the complex k-plane coupling all boundaryvalues of the solution. For particular cases, such as the case of periodic boundaryconditions, or the case of boundary value problems for even-orderPDEs, it is possible to obtain directly from the global relationan alternative representation for the solution, in the formof an infinite series. We stress, however, that there existinitial boundary value problems for which the only representationis an integral which cannot be written as an infinite series.An example of such a problem is provided by the linearized versionof the KdV equation. Similarly, in general the solution of odd-orderlinear initial boundary value problems on a finite intervalcannot be expressed in terms of an infinite series.     

Banana-shaped mesogens: a new homologous series of compounds exhibiting the B7 mesophase

The synthesis and characterization of a new homologous series of compounds, the 2-cyano-1,3-phenylene bis[4-(4-n-alkoxyphenyliminomethyl)benzoates] derived from 2-cyanoresorcinol is reported. All the compounds are enantiotropic mesogens and exhibit the fascinating B₇ mesophase. The characterization of the mesophase was performed using polarizing optical microscopy, differential scanning calorimetry, X-ray diffraction and electro-optical studies.     

Fractional Derivatives Applied to Phase-Space Reconstructions

The concept and application of phase-space reconstructions are reviewed. Fractional derivatives are then proposed for the purpose of reconstructing dynamics from a single observed time history. A procedure is presented in which the fractional derivatives of time series data are obtained in the frequency domain. The method is applied to the Lorenz system. The ability of the method to unfold the data is assessed by the method of global false nearest neighbors. The reconstructed data is used to compute recurrences and correlation dimensions. The reconstruction is compared to the commonly used method of delays in order to assess the choice of reconstruction parameters, and also the quality of results.     

An improved numerical simulator for multiphase flow in porous media

In basin modelling the thermodynamics of a multicomponent multiphase fluid flux are computationally too expensive when derived from an equation of state and the Gibbs equality constraints. In this article we present a novel implicit molar mass formulation technique using binary mixture thermodynamics. The two proposed solution methods, with and without cross derivative terms between components, are based on a preconditioned Newton‐GMRES scheme for each time‐step with analytical computation of the derivatives. These new algorithms reduce significantly the numerical effort for the computation of the molar masses, and we illustrate the behavior of these methods with numerical computations. Copyright © 2004 John Wiley & Sons Ltd.     

Assessment of two‐equation turbulence modelling for high Reynolds number hydrofoil flows

This paper presents an evaluation of the capability of turbulence models available in the commercial CFD code FLUENT 6.0 for their application to hydrofoil turbulent boundary layer separation flow at high Reynolds numbers. Four widely applied two‐equation RANS turbulence models were assessed through comparison with experimental data at Reynolds numbers of 8.284×106 and 1.657×107. They were the standard k–εmodel, the realizable k–εmodel, the standard k–ωmodel and the shear‐stress‐transport (SST) k–ωmodel. It has found that the realizable k–εturbulence model used with enhanced wall functions and near‐wall modelling techniques, consistently provides superior performance in predicting the flow characteristics around the hydrofoil. Copyright © 2004 John Wiley & Sons, Ltd.     

Robust handling of non‐linear constraints for GA optimization of aerodynamic shapes

A new approach to the robust handling of non‐linear constraints for GAs (genetic algorithms) optimization is proposed. A specific feature of the approach consists of the change in the conventional search strategy by employing search paths which pass through both feasible and infeasible points (contrary to the traditional approach where only feasible points may be included in a path). The method (driven by full Navier–Stokes computations) was applied to the problem of multiobjective optimization of aerodynamic shapes subject to various geometrical and aerodynamic constraints. The results demonstrated that the method retains high robustness of conventional GAs while keeping CFD computational volume to an acceptable level, which allowed the algorithm to be used in a demanding engineering environment. Copyright © 2004 John Wiley & Sons, Ltd.     

Free boundary viscous flows at micro and mesolevel during liquid composites moulding process

Numerical simulation aspects, related to low Reynolds number free boundary viscous flows at micro and mesolevel during the resin impregnation stage of the liquid composite moulding process (LCM), are presented in this article. A free boundary program (FBP), developed by the authors, is used to track the movement of the resin front accurately by accounting for the surface tension effects at the boundary. Issues related to the global and local mass conservation (GMC and LMC) are identified and discussed. Unsuitable conditions for LMC and consequently GMC are uncovered at low capillary numbers, and hence a strategy for the numerical simulation of such flows is suggested. FBP encompasses a set of subroutines that are linked to modules in ANSYS. FBP can capture the void formation dynamics based on the analysis developed. We present resin impregnation dynamics in two dimensions. Extension to three dimensions is a subject for further research. Several examples are shown and efficiency of different stabilization techniques are compared. Copyright © 2004 John Wiley & Sons, Ltd.     

Photoinitiators with functional groups. VII. Covalently bonded camphorquinone—amines

Camphorquinone (CQ), a widely used photoinitiator (PI) in dental applications, was covalently bonded to aromatic amines to enhance the rate of electron and proton transfer effect due to the close vicinity of the diketone and the amine group. 10‐bromocamphorquinone and 10‐bromomethylcamphorquinone were selected as suitable precursors for esterification with the carboxyl group containing aromatic amines based on 4‐dimethylaminobenzoic acid. Properties of the new photoinitiating systems were investigated by UV spectroscopy and differential scanning photocalorimetry in lauryl acrylate. Compared to physical mixtures, in all cases similar or even better performance was obtained. Surprisingly, 10‐acetyl derivatives 7 – 9 and 18 especially, were found to be highly reactive. Compared to CQ/ethyl 4‐dimethylaminobenzoate, the rate of photopolymerization was increased by a factor of up to 2. Intramolecular reaction was confirmed by photo‐differential scanning calorimetry experiments with varying PI concentrations. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 4948–4963, 2004