MODEL SHIFT AND STRANGE ATTRACTOR ON MBIUS STRIP

A new model shift mapping was given in bilateral symbol space. It is topologically conjugate with the traditional shift mapping. Similar to Smale Horseshoe, a model was constructed correspondent to the model shift mapping, i.e., a class of mapping on Mbius strip was given. Its attractors’ structure and dynamical behaviour were described.     

Convective instability in a rapidly rotating fluid layer in the presence of a non-uniform magnetic field

Magnetoconvective instabilities in a rapidly rotating, electrically conducting fluid layer heated from below in the presence of a non-uniform, horizontal magnetic field are investigated. It was first shown by Chandrasekhar that an overall minimum of the Rayleigh number may be reached at the onset of magnetoconvection when a uniform basic magnetic field is imposed. In this paper, we show that the properties of instability can be quite different when a non-uniform basic magnetic field is applied. It is shown that there is an optimum value of the Elsasser number provided that the basic magnetic field is a monotonically decreasing or increasing function of the vertical coordinate. However, there exist no optimum values of the Elsasser number that can give rise to an overall minimum of the Rayleigh number at the onset of magnetoconvection if the imposed basic magnetic field has an inflexion point. The project supported by the National Natural Science Foundation of China (40174026 and 40074041)     

Computer computation of the method of multiple scales—dirichlet problem for a class of system of nonlinear differential equations

The method of boundary layer with multiple scales and computer algebra were applied to study the asymptotic behavior of solution of boundary value problems for a class of system of nonlinear differential equations. The asymptotic expansions of solution were constructed. The remainders were estimated. And an example was analysed. It provides a new foreground for the application of the method of boundary layer with multiple scales. Contributed by Jiang Fu-ru, Original Member of Editorial Committe, AMM Biography: Xie La-bing (1976∼); Jiang Fu-ru(1927∼)     

Parametric identification of nonlinear systems using multiple trials

It is observed that the harmonic balance (HB) method of parametric identification of nonlinear system may not give right identification results for a single test data. A multiple-trial HB scheme is suggested to obtain improved results in the identification, compared with a single sample test. Several independent tests are conducted by subjecting the system to a range of harmonic excitations. The individual data sets are combined to obtain the matrix for inversion. This leads to the mean square error minimization of the entire set of periodic orbits. It is shown that the combination of independent test data gives correct results even in the case where the individual data sets give wrong results.     

Numerical simulation of effects of flow maldistribution on heat and mass transfer in a PEM fuel cell stack

A 3D numerical study was carried out to analyze flow, heat and mass transfer first in a single half-cell cathode channel of proton exchange membrane (PEM) fuel cell. From practical point of view, it is necessary to put the appropriate number of cells in a stack. Hence, the above study on a single half-cell is extended to a stack of channels. Due to stacking, the assumption of uniform flow distribution would no longer hold true. Therefore, the channel flow-maldistribution is considered. The water formed at the active surface due to the electrochemical reaction diffuses through the porous layer and eventually enters the gas flow duct. The higher gas velocities in the duct result in faster water vapour removal which leads to a lower value of water vapour into the duct and hence a lower Nusselt number.     

Regularization of Discontinuous Vector Fields on $${\mathbb{R}^3}$$ via Singular Perturbation

Singular perturbations problems in dimension three which are approximations of discontinuous vector fields are studied in this paper. The main result states that the regularization process developed by Sotomayor and Teixeira produces a singular problem for which the discontinuous set is a center manifold. Moreover, the definition of sliding vector field coincides with the reduced problem of the corresponding singular problem for a class of vector fields.      

Pore space network characterization with sub-voxel definition

Morphological measurements in 3D for pore space characterization (connectivity pore-body/throat classification, shape factors, virtual fluid intrusion) are based on computed intensive digital-thinning operations for skeletonization and medial axis extraction from 3D digital images. We present an alternative method that is measurably faster and allows sub-voxel definition of the pore space network. The method allows extracting—based on morphological considerations only—the centered and shortest stream-lines—i.e., the paths—to follow in order to go through the pore space from one given point to another and to exit. In addition the method penalizes long and narrow pore-throats in favor of short stubby/ones—i.e., it has a built-in exemplification capacity. It exploits well-established mathematical methods successfully applied in medical endoscopy.     

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.     

Convective heat transfer in the thermal entrance region of finned double-pipe

Numerical simulation of the steady and laminar convection in the thermal entry region of the finned annulus is carried out for the case of hydrodynamically fully developed flow when subjected to uniform heat flux thermal boundary condition. Finite difference based marching procedure is used to compute the numerical solution of the energy equation. The results to be presented include Nusselt number, as a function of dimensionless axial length and thermal entrance length for various configurations of the finned double-pipe. The numerical results show that Nusselt number has complex dependence on the geometric variables like ratio of radii, fin height, and number of fins. A comparison of the computed results for certain limiting cases with the results available in the literature validates the numerical procedure used in this work.     

Boiling Stability in a Porous Medium Heated From Below

Boiling in a porous layer heated from below at constant heat flux and cooled at constant temperature from the upper permeable surface leads below the critical flux of appearance of a vapor zone at the bottom in the approximation of dominated reservoirs to two solutions: a liquid-dominated one and a vapor-dominated one. The stability of these two situations is analyzed. The approach allows to understand the respective roles played by the gravitational instability, natural convection in the liquid upper layer, and movement of the interface between the two regions. Taking into account the confinement allows the comparison of these theoretical results with experimental results obtained in the laboratory.