A mathematical model and a numerical model for hyperbolic mass transport in compressible flows

A number of contributions have been made during the last decades to model pure-diffusive transport problems by using the so-called hyperbolic diffusion equations. These equations are used for both mass and heat transport. The hyperbolic diffusion equations are obtained by substituting the classic constitutive equation (Fick’s and Fourier’s law, respectively), by a more general differential equation, due to Cattaneo (C R Acad Sci Ser I Math 247:431–433, 1958). In some applications the use of a parabolic model for diffusive processes is assumed to be accurate enough in spite of predicting an infinite speed of propagation (Cattaneo, C R Acad Sci Ser I Math 247:431–433, 1958). However, the use of a wave-like equation that predicts a finite velocity of propagation is necessary in many other calculations. The studies of heat or mass transport with finite velocity of propagation have been traditionally limited to pure-diffusive situations. However, the authors have recently proposed a generalization of Cattaneo’s law that can also be used in convective-diffusive problems (Gómez, Technical Report (in Spanish), University of A Coruña, 2003; Gómez et al., in An alternative formulation for the advective-diffusive transport problem. 7th Congress on computational methods in engineering. Lisbon, Portugal, 2004a; Gómez et al., in On the intrinsic instability of the advection–diffusion equation. Proc. of the 4th European congress on computational methods in applied sciences and engineering (CDROM). Jyväskylä, Finland, 2004b) (see also Christov and Jordan, Phys Rev Lett 94:4301–4304, 2005). This constitutive equation has been applied to engineering problems in the context of mass transport within an incompressible fluid (Gómez et al., Comput Methods Appl Mech Eng, doi: 10.1016/j.cma.2006.09.016, 2006). In this paper we extend the model to compressible flow problems. A discontinuous Galerkin method is also proposed to numerically solve the equations. Finally, we present some examples to test out the performance of the numerical and the mathematical model.     

An Experimental Evaluation of a Scatter Search for the Linear Ordering Problem

Scatter search is a population-based method that has recently been shown to yield promising outcomes for solving combinatorial and nonlinear global optimization problems. Based on formulations originally proposed in the 1960s for combining decision rules and problem constraints, such as in generating surrogate constraints, scatter search uses strategies for combining solution vectors that have proved effective in a variety of problem settings. In this paper, we present a scatter search implementation designed to find high quality solutions for the NP-hard linear ordering problem, which has a significant number of applications in practice. The LOP, for example, is equivalent to the so-called triangulation problem for input-output tables in economics. Our implementation incorporates innovative mechanisms to combine solutions and to create a balance between quality and diversification in the reference set. We also use a tracking process that generates solution statistics disclosing the nature of combinations and the ranks of antecedent solutions that produced the best final solutions. Extensive computational experiments with more than 300 instances establishes the effectiveness of our procedure in relation to approaches previously identified to be best.     

Reactions of 6‐aminopyrimidines with 2‐dimethylaminomethylenetetralone. Regiospecific Synthesis Of 5,6‐Dihydrobenzo [h]pyrimido [4,5‐b] quinolines

Benzo[h]pyrimido[4,5‐b]quinolines ( 3 ) have been synthesized via a regiospecific cyclocondensation reaction between 6‐aminopyrimidines ( 1 ) and 2‐dimethylaminomethylentetralone hydrochloride ( 2 ). The linear structure of the final compounds were determined by nmr measurements, especially by ¹H,¹H, ¹H,¹³C COSY and DEPT experiments.     

Methyl 2‐methyl‐6‐methyl­thio‐1,3‐dioxo‐4‐[(2,3,4,6‐tetra‐O‐acetyl‐β‐d‐gluco­pyran­osyl)­amino]‐2,3‐di­hydro‐1H‐pyrrolo­[3,4‐c]­pyridine‐7‐carboxyl­ate

The title compound, C₂₅H₂₉N₃O₁₃S, has peripheral acetyl and carbo­methoxy groups which show disorder. The absolute structure, although known from the starting materials, was confirmed by the analysis. There are no intermolecular hydrogen bonds. This structure is of importance because it elucidates the pathway for hetero‐Diels–Alder reactions between di­methyl acetyl­enedi­carboxyl­ate and 6‐amino­pyridin‐4(3H)‐one derivatives catalyzed by tri­fluoro­acetic acid.     

Analysis of the Solid-State Rearrangementof Hydrido-Alkynyl Ruthenium Complexesto their Vinylidene Tautomers

Summary.  The solid-state tautomerization of the hydrido-alkynyl derivatives [Cp ^*RuH(C&*CR)-(dippe)][BPh₄] (Cp^* = C₅Me₅; R = SiMe₃, Ph, H; dippe = 1,2-bis-(diisopropylphosphino)-ethane) to their vinylidene isomers [Cp ^*Ru*C*CHR(dippe)][BPh₄] was studied by IR spectroscopy. Characteristic isothermic αvs. t curves for each individual rearrangement process were recorded. Their shape, and hence the isomerization mechanism, depends strongly on the nature of the substituent R. The kinetic analysis of the above curves using the Avrami-Erofeev provided some mechanistic information about the isomerization process in the solid. Received July 7, 2000. Accepted August 29, 2000     

Viscosity in discontinuous Galerkin methods

The Discontinuous Galerkin (DG) discretisation technique proposes a higher order alternative to current state of the art Finite Volume (FV) methods of second order accuracy in space. DG features higher order on unstructured grids without reconstruction, highly local data access patterns and excellent parallelisation properties. However, viscosity does not fit seamlessly into DG, but is indispensable for nearly every technical aeronautical simulation. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stability of reduced electric arc models

An energy equation coupled to the eddy-current Maxwell equations with nonlinear material coefficients gives a reduced electric arc model with interesting existence and stability behaviour. Applications are arcs in industrial plasma flows. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

How to Approximate the Heat Equation with Neumann Boundary Conditions by Nonlocal Diffusion Problems

We present a model for nonlocal diffusion with Neumann boundary conditions in a bounded smooth domain prescribing the flux through the boundary. We study the limit of this family of nonlocal diffusion operators when a rescaling parameter related to the kernel of the nonlocal operator goes to zero. We prove that the solutions of this family of problems converge to a solution of the heat equation with Neumann boundary conditions.