Theoretical and numerical analyses of convective instability in porous media with upward throughflow

Exact analytical solutions have been obtained for a hydrothermal system consisting of a horizontal porous layer with upward throughflow. The boundary conditions considered are constant temperature, constant pressure at the top, and constant vertical temperature gradient, constant Darcy velocity at the bottom of the layer. After deriving the exact analytical solutions, we examine the stability of the solutions using linear stability theory and the Galerkin method. It has been found that the exact solutions for such a hydrothermal system become unstable when the Rayleigh number of the system is equal to or greater than the corresponding critical Rayleigh number. For small and moderate Peclet numbers (Pe less than or equal to 6), an increase in upward throughflow destabilizes the convective flow in the horizontal layer. To confirm these findings, the finite element method with the progressive asymptotic approach procedure is used to compute the convective cells in such a hydrothermal system. Copyright (C) 1999 John Wiley & Sons, Ltd.

A two-dimensional analytical solution of groundwater responses to tidal loading in an estuary and ocean

Previous studies on tidal dynamics of coastal aquifers have focussed on the inland propagation of oceanic tides in the cross-shore direction, a configuration that is essentially one-dimensional. Aquifers at natural coasts can also be influenced by tidal waves in nearby estuaries, resulting in a more complex behaviour of head fluctuations in the aquifers. We present an analytical solution to the two-dimensional depth-averaged groundwater flow equation for a semi-infinite aquifer subject to oscillating head conditions at the boundaries. The solution describes the tidal dynamics of a coastal aquifer that is adjacent to a cross-shore estuary. Both the effects of oceanic and estuarine tides on the aquifer are included in the solution. The analytical prediction of the head fluctuations is verified by comparison with numerical solutions computed using a standard finite-difference method. An essential feature of the present analytical solution is the interaction between the cross- and along-shore tidal waves in the aquifer area near the estuary's entry. As the distance from the estuary or coastline increases, the wave interaction is weakened and the aquifer response is reduced, respectively, to the one-dimensional solution for oceanic tides or the solution of Sun (Sun H. A two-dimensional analytical solution of groundwater response to tidal loading in an estuary, Water Resour Res 1997;33:1429-35) for two-dimensional non-interacting tidal waves. (C) 2000 Elsevier Science Ltd. All rights reserved.

A numerical study of flexural buckling of foliated rock slopes

The occurrence of foliated rock masses is common in mining environment. Methods employing continuum approximation in describing the deformation of such rock masses possess a clear advantage over methods where each rock layer and each inter-layer interface (joint) is explicitly modelled. In devising such a continuum model it is imperative that moment (couple) stresses and internal rotations associated with the bending of the rock layers be properly incorporated in the model formulation. Such an approach will lead to a Cosserat-type theory. In the present model, the behaviour of the intact rock layer is assumed to be linearly elastic and the joints are assumed to be elastic-perfectly plastic. Condition of slip at the interfaces are determined by a Mohr-Coulomb criterion with tension cut off at zero normal stress. The theory is valid for large deformations. The model is incorporated into the finite element program AFENA and validated against an analytical solution of elementary buckling problems of a layered medium under gravity loading. A design chart suitable for assessing the stability of slopes in foliated rock masses against flexural buckling failure has been developed. The design chart is easy to use and provides a quick estimate of critical loading factors for slopes in foliated rock masses. It is shown that the model based on Euler's buckling theory as proposed by Cavers (Rock Mechanics and Rock Engineering 1981; 14:87-104) substantially overestimates the critical heights for a vertical slope and underestimates the same for sub-vertical slopes. Copyright (C) 2001 John Wiley & Sons, Ltd.

Theoretical and numerical analyses of convective instability in porous media with temperature-dependent viscosity

Exact analytical solutions of the critical Rayleigh numbers have been obtained for a hydrothermal system consisting of a horizontal porous layer with temperature-dependent viscosity. The boundary conditions considered are constant temperature and zero vertical Darcy velocity at both the top and bottom of the layer. Not only can the derived analytical solutions be readily used to examine the effect of the temperature-dependent viscosity on the temperature-gradient driven convective flow, but also they can be used to validate the numerical methods such as the finite-element method and finite-difference method for dealing with the same kind of problem. The related analytical and numerical results demonstrated that the temperature-dependent viscosity destabilizes the temperature-gradient driven convective flow and therefore, may affect the ore body formation and mineralization in the upper crust of the Earth. Copyright (C) 2003 John Wiley Sons, Ltd.

Numerical simulation of double-diffusion driven convective flow and rock alteration in three-dimensional fluid-saturated geological fault zones

Numerical methods are used to simulate the double-diffusion driven convective pore-fluid flow and rock alteration in three-dimensional fluid-saturated geological fault zones. The double diffusion is caused by a combination of both the positive upward temperature gradient and the positive downward salinity concentration gradient within a three-dimensional fluid-saturated geological fault zone, which is assumed to be more permeable than its surrounding rocks. In order to ensure the physical meaningfulness of the obtained numerical solutions, the numerical method used in this study is validated by a benchmark problem, for which the analytical solution to the critical Rayleigh number of the system is available. The theoretical value of the critical Rayleigh number of a three-dimensional fluid-saturated geological fault zone system can be used to judge whether or not the double-diffusion driven convective pore-fluid flow can take place within the system. After the possibility of triggering the double-diffusion driven convective pore-fluid flow is theoretically validated for the numerical model of a three-dimensional fluid-saturated geological fault zone system, the corresponding numerical solutions for the convective flow and temperature are directly coupled with a geochemical system. Through the numerical simulation of the coupled system between the convective fluid flow, heat transfer, mass transport and chemical reactions, we have investigated the effect of the double-diffusion driven convective pore-fluid flow on the rock alteration, which is the direct consequence of mineral redistribution due to its dissolution, transportation and precipitation, within the three-dimensional fluid-saturated geological fault zone system. (c) 2005 Elsevier B.V. All rights reserved.

A new wavelet-based method for the solution of the population balance equation

A new wavelet-based method for solving population balance equations with simultaneous nucleation, growth and agglomeration is proposed, which uses wavelets to express the functions. The technique is very general, powerful and overcomes the crucial problems of numerical diffusion and stability that often characterize previous techniques in this area. It is also applicable to an arbitrary grid to control resolution and computational efficiency. The proposed technique has been tested for pure agglomeration, simultaneous nucleation and growth, and simultaneous growth and agglomeration. In all cases, the predicted and analytical particle size distributions are in excellent agreement. The presence of moving sharp fronts can be addressed without the prior investigation of the characteristics of the processes. (C) 2001 Published by Elsevier Science Ltd.

Solution techniques for transport problems involving steep concentration gradients: application to noncatalytic fluid solid reactions

Some efficient solution techniques for solving models of noncatalytic gas-solid and fluid-solid reactions are presented. These models include those with non-constant diffusivities for which the formulation reduces to that of a convection-diffusion problem. A singular perturbation problem results for such models in the presence of a large Thiele modulus, for which the classical numerical methods can present difficulties. For the convection-diffusion like case, the time-dependent partial differential equations are transformed by a semi-discrete Petrov-Galerkin finite element method into a system of ordinary differential equations of the initial-value type that can be readily solved. In the presence of a constant diffusivity, in slab geometry the convection-like terms are absent, and the combination of a fitted mesh finite difference method with a predictor-corrector method is used to solve the problem. Both the methods are found to converge, and general reaction rate forms can be treated. These methods are simple and highly efficient for arbitrary particle geometry and parameters, including a large Thiele modulus. (C) 2001 Elsevier Science Ltd. All rights reserved.

Fast, scalable master equation solution algorithms. III. Direct time propagation accelerated by a diffusion approximation preconditioned iterative solver

In this paper we propose a novel fast and linearly scalable method for solving master equations arising in the context of gas-phase reactive systems, based on an existent stiff ordinary differential equation integrator. The required solution of a linear system involving the Jacobian matrix is achieved using the GMRES iteration preconditioned using the diffusion approximation to the master equation. In this way we avoid the cubic scaling of traditional master equation solution methods and maintain the low temperature robustness of numerical integration. The method is tested using a master equation modelling the formation of propargyl from the reaction of singlet methylene with acetylene, proceeding through long lived isomerizing intermediates. (C) 2003 American Institute of Physics.

Surgical correction of scoliosis: Numerical analysis and optimization of the procedure

A previously developed model is used to numerically simulate real clinical cases of the surgical correction of scoliosis. This model consists of one-dimensional finite elements with spatial deformation in which (i) the column is represented by its axis; (ii) the vertebrae are assumed to be rigid; and (iii) the deformability of the column is concentrated in springs that connect the successive rigid elements. The metallic rods used for the surgical correction are modeled by beam elements with linear elastic behavior. To obtain the forces at the connections between the metallic rods and the vertebrae geometrically, non-linear finite element analyses are performed. The tightening sequence determines the magnitude of the forces applied to the patient column, and it is desirable to keep those forces as small as possible. In this study, a Genetic Algorithm optimization is applied to this model in order to determine the sequence that minimizes the corrective forces applied during the surgery. This amounts to find the optimal permutation of integers 1, ... , n, n being the number of vertebrae involved. As such, we are faced with a combinatorial optimization problem isomorph to the Traveling Salesman Problem. The fitness evaluation requires one computing intensive Finite Element Analysis per candidate solution and, thus, a parallel implementation of the Genetic Algorithm is developed.

Numerical Uncertainty and Its Implications

Copyright © 2014 António F. Rodrigues, Nuno O. Martins. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In accordance of the Creative Commons Attribution License all Copyrights © 2014 are reserved for SCIRP and the owner of the intellectual property António F. Rodrigues, Nuno O. Martins. All Copyright © 2014 are guarded by law and by SCIRP as a guardian.

Spectral solution for the air stripping pollutants removal dynamic model with non linear steady state conditions

This work deals with the numerical simulation of air stripping process for the pre-treatment of groundwater used in human consumption. The model established in steady state presents an exponential solution that is used, together with the Tau Method, to get a spectral approach of the solution of the system of partial differential equations associated to the model in transient state.

Explicit series solution for a glucose-induced electrical activity model of pancreatic beta-cells

In this work, we present the explicit series solution of a specific mathematical model from the literature, the Deng bursting model, that mimics the glucose-induced electrical activity of pancreatic beta-cells (Deng, 1993). To serve to this purpose, we use a technique developed to find analytic approximate solutions for strongly nonlinear problems. This analytical algorithm involves an auxiliary parameter which provides us with an efficient way to ensure the rapid and accurate convergence to the exact solution of the bursting model. By using the homotopy solution, we investigate the dynamical effect of a biologically meaningful bifurcation parameter rho, which increases with the glucose concentration. Our analytical results are found to be in excellent agreement with the numerical ones. This work provides an illustration of how our understanding of biophysically motivated models can be directly enhanced by the application of a newly analytic method.

Electrophoretic protein patterns and numerical analysis of Candida albicans from the oral cavities of healthy children

The aim of this research was to evaluate the protein polymorphism degree among seventy-five C. albicans strains from healthy children oral cavities of five socioeconomic categories from eight schools (private and public) in Piracicaba city, São Paulo State, in order to identify C. albicans subspecies and their similarities in infantile population groups and to establish their possible dissemination route. Cell cultures were grown in YEPD medium, collected by centrifugation, and washed with cold saline solution. The whole-cell proteins were extracted by cell disruption, using glass beads and submitted to SDS-PAGE technique. After electrophoresis, the protein bands were stained with Coomassie-blue and analyzed by statistics package NTSYS-pc version 1.70 software. Similarity matrix and dendrogram were generated by using the Dice similarity coefficient and UPGMA algorithm, respectively, which made it possible to evaluate the similarity or intra-specific polymorphism degrees, based on whole-cell protein fingerprinting of C. albicans oral isolates. A total of 13 major phenons (clusters) were analyzed, according to their homogeneous (socioeconomic category and/or same school) and heterogeneous (distinct socioeconomic categories and/or schools) characteristics. Regarding to the social epidemiological aspect, the cluster composition showed higher similarities (0.788 < S D < 1.0) among C. albicans strains isolated from healthy children independent of their socioeconomic bases (high, medium, or low). Isolates of high similarity were not found in oral cavities from healthy children of social stratum A and D, B and D, or C and E. This may be explained by an absence of a dissemination route among these children. Geographically, some healthy children among identical and different schools (private and public) also are carriers of similar strains but such similarity was not found among other isolates from children from certain schools. These data may reflect a restricted dissemination route of these microorganisms in some groups of healthy scholars, which may be dependent of either socioeconomic categories or geographic site of each child. In contrast to the higher similarity, the lower similarity or higher polymorphism degree (0.499 < S D < 0.788) of protein profiles was shown in 23 (30.6%) C. albicans oral isolates. Considering the social epidemiological aspect, 42.1%, 41.7%, 26.6%, 23.5%, and 16.7% were isolates from children concerning to socioeconomic categories A, D, C, B, and E, respectively, and geographically, 63.6%, 50%, 33.3%, 33.3%, 30%, 25%, and 14.3% were isolates from children from schools LAE (Liceu Colégio Albert Einstein), MA (E.E.P.S.G. "Prof. Elias de Melo Ayres"), CS (E.E.P.G. "Prof. Carlos Sodero"), AV (Alphaville), HF (E.E.P.S.G. "Honorato Faustino), FMC (E.E.P.G. "Prof. Francisco Mariano da Costa"), and MEP (E.E.P.S.G. "Prof. Manasses Ephraim Pereira), respectively. Such results suggest a higher protein polymorphism degree among some strains isolated from healthy children independent of their socioeconomic strata or geographic sites. Complementary studies, involving healthy students and their families, teachers, servants, hygiene and nutritional habits must be done in order to establish the sources of such colonization patterns in population groups of healthy children. The whole-cell protein profile obtained by SDS-PAGE associated with computer-assisted numerical analysis may provide additional criteria for the taxonomic and epidemiological studies of C. albicans.

Exploring the potentialities of a new type of CFRP laminate for the simultaneous flexural and shear strengthening of RC beams: numerical research

This study aims to develop an innovative carbon fibre reinforced polymer (CFRP) laminate with a U configuration to address strengthening interventions, where the increment of both flexural and shear capacity of reinforced concrete (RC) elements is required. This strengthening solution combines the near surface mounted (NSM) and embedded through section (ETS) techniques in the same application, since these techniques have already evidenced high performance on flexural and shear strengthening of RC beams using FRP systems, respectively. In fact, the proposed hybrid technique aims to mobilize the advantages provided by these two strengthening techniques by using an innovative CFRP laminate. The strengthening efficacy of this new hybrid NSM/ETS technique was numerically assessed and compared to the corresponding efficiency of NSM and ETS techniques applied separately for the flexural and shear strengthening of RC beams, respectively. The numerical models are described and the main relevant results are presented and discussed.

Analytical and numerical study of the electro-osmotic annular flow of viscoelastic fluids

In this work we present semi-analytical solutions for the electro-osmotic annular flow of viscoelastic fluids modeled by the Linear and Exponential PTT models. The viscoelastic fluid flows in the axial direction between two concentric cylinders under the combined influences of electrokinetic and pressure forcings. The analysis invokes the Debye-Hückel approximation and includes the limit case of pure electro-osmotic flow. The solution is valid for both no slip and slip velocity at the walls and the chosen slip boundary condition is the linear Navier slip velocity model. The combined effects of fluid rheology, electro-osmotic and pressure gradient forcings on the fluid velocity distribution are also discussed.