An alternating boundary integral based method for a Cauchy problem for the Laplace equation in semi-infinite regions

We consider a Cauchy problem for the Laplace equation in a two-dimensional semi-infinite region with a bounded inclusion, i.e. the region is the intersection between a half-plane and the exterior of a bounded closed curve contained in the half-plane. The Cauchy data are given on the unbounded part of the boundary of the region and the aim is to construct the solution on the boundary of the inclusion. In 1989, Kozlov and Maz'ya [10] proposed an alternating iterative method for solving Cauchy problems for general strongly elliptic and formally self-adjoint systems in bounded domains. We extend their approach to our setting and in each iteration step mixed boundary value problems for the Laplace equation in the semi-infinite region are solved. Well-posedness of these mixed problems are investigated and convergence of the alternating procedure is examined. For the numerical implementation an efficient boundary integral equation method is proposed, based on the indirect variant of the boundary integral equation approach. The mixed problems are reduced to integral equations over the (bounded) boundary of the inclusion. Numerical examples are included showing the feasibility of the proposed method.

An iterative method based on boundary integrals for elliptic Cauchy problems in semi-infinite domains

In this study, we investigate the problem of reconstruction of a stationary temperature field from given temperature and heat flux on a part of the boundary of a semi-infinite region containing an inclusion. This situation can be modelled as a Cauchy problem for the Laplace operator and it is an ill-posed problem in the sense of Hadamard. We propose and investigate a Landweber-Fridman type iterative method, which preserve the (stationary) heat operator, for the stable reconstruction of the temperature field on the boundary of the inclusion. In each iteration step, mixed boundary value problems for the Laplace operator are solved in the semi-infinite region. Well-posedness of these problems is investigated and convergence of the procedures is discussed. For the numerical implementation of these mixed problems an efficient boundary integral method is proposed which is based on the indirect variant of the boundary integral approach. Using this approach the mixed problems are reduced to integral equations over the (bounded) boundary of the inclusion. Numerical examples are included showing that stable and accurate reconstructions of the temperature field on the boundary of the inclusion can be obtained also in the case of noisy data. These results are compared with those obtained with the alternating iterative method.

Some Computational Aspects of the Consistent Mass Finite Element Method for a (semi-)periodic Eigenvalue Problem

We consider a model eigenvalue problem (EVP) in 1D, with periodic or semi–periodic boundary conditions (BCs). The discretization of this type of EVP by consistent mass finite element methods (FEMs) leads to the generalized matrix EVP Kc = λ M c, where K and M are real, symmetric matrices, with a certain (skew–)circulant structure. In this paper we fix our attention to the use of a quadratic FE–mesh. Explicit expressions for the eigenvalues of the resulting algebraic EVP are established. This leads to an explicit form for the approximation error in terms of the mesh parameter, which confirms the theoretical error estimates, obtained in [2].

A Unified Group-Theoretic Method on Improper Partial Semi-Bilateral Generating Functions

2000 Mathematics Subject Classification: 33A65, 33C20.

An Examination of Qualitative Empirical Studies at the AHRD from 1999-2003: Method, Rationale for Method, Data Collection, Sampling Strategies, and Integrity Measures

The paper examines the nature of qualitative empirical studies published in the AHRD proceedings from 1999-2003 and discusses findings on method, rationale for method, data collection, sampling strategies, and integrity measures.

Empirical aspects of a mixed method approach to economic network analysis

We discuss the interactions among the various phases of network research design in the context of our current work using Mixed Methods and SNA on networks and rural economic development. We claim that there are very intricate inter-dependencies among the various phases of network research design - from theory and formulation of research questions right through to modes of analysis and interpretation. Through examples drawn from our work we illustrate how choices about methods for Sampling and Data Collection are influenced by these interdependencies.

Model reduction for nonlinear aerodynamics and aeroelasticity using a Discrete Empirical Interpolation Method

A novel surrogate model is proposed in lieu of Computational Fluid Dynamics (CFD) solvers, for fast nonlinear aerodynamic and aeroelastic modeling. A nonlinear function is identified on selected interpolation points by
a discrete empirical interpolation method (DEIM). The flow field is then reconstructed using a least square approximation of the flow modes extracted
by proper orthogonal decomposition (POD). The aeroelastic reduce order
model (ROM) is completed by introducing a nonlinear mapping function
between displacements and the DEIM points. The proposed model is investigated to predict the aerodynamic forces due to forced motions using
a N ACA 0012 airfoil undergoing a prescribed pitching oscillation. To investigate aeroelastic problems at transonic conditions, a pitch/plunge airfoil
and a cropped delta wing aeroelastic models are built using linear structural models. The presence of shock-waves triggers the appearance of limit
cycle oscillations (LCO), which the model is able to predict. For all cases
tested, the new ROM shows the ability to replicate the nonlinear aerodynamic forces, structural displacements and reconstruct the complete flow
field with sufficient accuracy at a fraction of the cost of full order CFD
model.

Simulation of Oil Shale Semi-Coke Particle Cold Transportation in a Spouted Bed Using CPFD Method

The spouted bed was widely used due to its good mixing of particles and effective phase transferability between the gas and solid phase. In this paper, the transportation process of particles in a 3D spouted bed was studied using the Computational Particle Fluid Dynamics (CPFD) numerical method. Experiments were conducted to verify the validity of the simulation results. Distributions of the pressure, velocities and particle concentration of transportation devices were investigated. The motion state and characteristics of multiphase flows in the transportation device were demonstrated under various operating conditions. The results showed that a good consistency was obtained between the simulated results and the experimental results. The motion characteristics of the gas-solid two-phase flow in the device was effectively predicted, which could assist the optimal operating condition estimation for the spouted transportation process.

Model reduction for nonlinear aeroelasticity using the Discrete Empirical Interpolation Method

A novel surrogate model is proposed in lieu of computational fluid dynamic (CFD) code for fast nonlinear aerodynamic modeling. First, a nonlinear function is identified on selected interpolation points defined by discrete empirical interpolation method (DEIM). The flow field is then reconstructed by a least square approximation of flow modes extracted by proper orthogonal decomposition (POD). The proposed model is applied in the prediction of limit cycle oscillation for a plunge/pitch airfoil and a delta wing with linear structural model, results are validate against a time accurate CFD-FEM code. The results show the model is able to replicate the aerodynamic forces and flow fields with sufficient accuracy while requiring a fraction of CFD cost.

A semi-Lagrangian finite volume method for solving viscoelastic flow problems

Recently, there has been considerable interest in solving viscoelastic problems in 3D particularly with the improvement in modern computing power. In many applications the emphasis has been on economical algorithms which can cope with the extra complexity that the third dimension brings. Storage and computer time are of the essence. The advantage of the finite volume formulation is that a large amount of memory space is not required. Iterative methods rather than direct methods can be used to solve the resulting linear systems efficiently.

Viability of irrigation by porous capsule method in arid and semi-arid regions.

This paper presents the results of four field experiments carried out with the objetive of evaluating the feaibility of irrigation by porous capsule method, from 1979 to 1983, at Bebedouro Experiment Station, EMBRAPA-CPATSA, Petrolina, PE, Brazil. The irrigation system consisted of fulcrum of cone shaped porous capsules, interconnected with conduit pipe and installed in the soil at equidistance and 0.10 m deep along contour lines. The hydrostatic pressures studies did not significantly influence the crop yield, but influenced, at 0.10 level, the daily water release from porous unit. The mean yields for watermelon (Citrullus vulgaris Shard), var. Charleston Gray, for muskmelon (Cucumis melo L.) var. Valenciano Amarelo, and for maize (Zea mays L.), var. Centralmex, estimated in ton/2,500 units/ha or in cobs/2,500 units/ha, were 28.5, 10 and 17,500, respectively. The water consumption for watermelon, musk melon and maize was, respectively, 60 mm, 60 mm and 100 mm in a deep sandy yellow-red latosol. The cost of the system was US$ 1.677,41/ha.

An empirical investigation of the impact of global energy transition on Nigerian oil and gas exports

18 months embargo on the thesis and check appendix for copy right materials

A screening method for detection of hexavalent chromium levels in soils

A rapid and low cost method to determine Cr(VI) in soils based upon alkaline metal extraction at room temperature is proposed as a semi-quantitative procedure to be performed in the field. A color comparison with standards with contents of Cr(VI) in the range of 10 to 150 mg kg-1 was used throughout. For the different types of soils studied, more than 75% of the fortified soluble Cr(VI) were recovered for all levels of spike tested for both the proposed and standard methods. Recoveries of 83 and 99% were obtained for the proposed and the standard methods, respectively, taking into account the analysis of a heavily contaminated soil sample.

Rapid detection of bovine coronavirus by a semi-nested RT-PCR

Bovine coronavirus (BCoV) is a member of the group 2 of the Coronavirus (Nidovirales: Coronaviridae) and the causative agent of enteritis in both calves and adult bovine, as well as respiratory disease in calves. The present study aimed to develop a semi-nested RT-PCR for the detection of BCoV based on representative up-to-date sequences of the nucleocapsid gene, a conserved region of coronavirus genome. Three primers were designed, the first round with a 463bp and the second (semi-nested) with a 306bp predicted fragment. The analytical sensitivity was determined by 10-fold serial dilutions of the BCoV Kakegawa strain (HA titre: 256) in DEPC treated ultra-pure water, in fetal bovine serum (FBS) and in a BCoV-free fecal suspension, when positive results were found up to the 10-2, 10-3 and 10-7 dilutions, respectively, which suggests that the total amount of RNA in the sample influence the precipitation of pellets by the method of extraction used. When fecal samples was used, a large quantity of total RNA serves as carrier of BCoV RNA, demonstrating a high analytical sensitivity and lack of possible substances inhibiting the PCR. The final semi-nested RT-PCR protocol was applied to 25 fecal samples from adult cows, previously tested by a nested RT-PCR RdRp used as a reference test, resulting in 20 and 17 positives for the first and second tests, respectively, and a substantial agreement was found by kappa statistics (0.694). The high sensitivity and specificity of the new proposed method and the fact that primers were designed based on current BCoV sequences give basis to a more accurate diagnosis of BCoV-caused diseases, as well as to further insights on protocols for the detection of other Coronavirus representatives of both Animal and Public Health importance.

An EFG method for the nonlinear analysis of plates undergoing arbitrarily large deformations

The applicability of a meshfree approximation method, namely the EFG method, on fully geometrically exact analysis of plates is investigated. Based on a unified nonlinear theory of plates, which allows for arbitrarily large rotations and displacements, a Galerkin approximation via MLS functions is settled. A hybrid method of analysis is proposed, where the solution is obtained by the independent approximation of the generalized internal displacement fields and the generalized boundary tractions. A consistent linearization procedure is performed, resulting in a semi-definite generalized tangent stiffness matrix which, for hyperelastic materials and conservative loadings, is always symmetric (even for configurations far from the generalized equilibrium trajectory). Besides the total Lagrangian formulation, an updated version is also presented, which enables the treatment of rotations beyond the parameterization limit. An extension of the arc-length method that includes the generalized domain displacement fields, the generalized boundary tractions and the load parameter in the constraint equation of the hyper-ellipsis is proposed to solve the resulting nonlinear problem. Extending the hybrid-displacement formulation, a multi-region decomposition is proposed to handle complex geometries. A criterium for the classification of the equilibrium`s stability, based on the Bordered-Hessian matrix analysis, is suggested. Several numerical examples are presented, illustrating the effectiveness of the method. Differently from the standard finite element methods (FEM), the resulting solutions are (arbitrary) smooth generalized displacement and stress fields. (c) 2007 Elsevier Ltd. All rights reserved.