Numerical study of Petrov-Galerkin formulations for the shallow water wave equations

The behavior of Petrov-Galerkin formulations for shallow water wave equations is evaluated numerically considering typical one-dimensional propagation problems. The formulations considered here use stabilizing operators to improve classical Galerkin approaches. Their advantages and disadvantages are pointed out according to the intrinsic time scale (free parameter) which has a particular importance in this kind of problem. The influence of the Courant number and the performance of the formulation in dealing with spurious oscillations are adressed.

Numerical study on mixed convection in a horizontal flow past a square porous cavity using UNIFAES scheme

Mixed convection on the flow past a heated length and past a porous cavity located in a horizontal wall bounding a saturated porous medium is numerically simulated. The cavity is heated from below. The steady-state regime is studied for several intensities of the buoyancy effects due to temperature variations. The influences of Péclet and Rayleigh numbers on the flow pattern and the temperature distributions are examined. Local and global Nusselt numbers are reported for the heated surface. The convective-diffusive fluxes at the volume boundaries are represented using the UNIFAES, Unified Finite Approach Exponential-type Scheme, with the Power-Law approximation to reduce the computing time. The conditions established by Rivas for the quadratic order of accuracy of the central differencing to be maintained in irregular grids are shown to be extensible to other quadratic schemes, including UNIFAES, so that accuracy estimates could be obtained.

On the numerical integration of rigid body nonlinear dynamics in presence of parameters singularities

One of the main complexities in the simulation of the nonlinear dynamics of rigid bodies consists in describing properly the finite rotations that they may undergo. It is well known that, to avoid singularities in the representation of the SO(3) rotation group, at least four parameters must be used. However, it is computationally expensive to use a four-parameters representation since, as only three of the parameters are independent, one needs to introduce constraint equations in the model, leading to differential-algebraic equations instead of ordinary differential ones. Three-parameter representations are numerically more efficient. Therefore, the objective of this paper is to evaluate numerically the influence of the parametrization and its singularities on the simulation of the dynamics of a rigid body. This is done through the analysis of a heavy top with a fixed point, using two three-parameter systems, Euler's angles and rotation vector. Theoretical results were used to guide the numerical simulation and to assure that all possible cases were analyzed. The two parametrizations were compared using several integrators. The results show that Euler's angles lead to faster integration compared to the rotation vector. An Euler's angles singular case, where representation approaches a theoretical singular point, was analyzed in detail. It is shown that on the contrary of what may be expected, 1) the numerical integration is very efficient, even more than for any other case, and 2) in spite of the uncertainty on the Euler's angles themselves, the body motion is well represented.

Numerical and experimental investigation of thermal louvers for space applications

Thermal louvers, using movable or rotating shutters over a radiating surface, have gained a wide acceptance as highly efficient devices for controlling the temperature of a spacecraft. This paper presents a detailed analysis of the performance of a rectangular thermal louver with movable blades. The radiative capacity of the louver, determined by its effective emittance, is calculated for different values of the blades opening angle. Experimental results obtained with a prototype of a spacecraft thermal louver show good agreement with the theoretical values.

Gas-solid two-phase flow in the riser of circulating fluidized beds: mathematical modelling and numerical simulation

A mathematical model is developed for gas-solids flows in circulating fluidized beds. An Eulerian formulation is followed based on the two-fluids model approach where both the fluid and the particulate phases are treated as a continuum. The physical modelling is discussed, including the formulation of boundary conditions and the description of the numerical methodology. Results of numerical simulation are presented and discussed. The model is validated through comparison to experiment, and simulation is performed to investigate the effects on the flow hydrodynamics of the solids viscosity.

Covalidation of Integral Transforms and Method of Lines in Nonlinear Convection-Diffusion with Mathematica

The Mathematica system (version 4.0) is employed in the solution of nonlinear difusion and convection-difusion problems, formulated as transient one-dimensional partial diferential equations with potential dependent equation coefficients. The Generalized Integral Transform Technique (GITT) is first implemented for the hybrid numerical-analytical solution of such classes of problems, through the symbolic integral transformation and elimination of the space variable, followed by the utilization of the built-in Mathematica function NDSolve for handling the resulting transformed ODE system. This approach ofers an error-controlled final numerical solution, through the simultaneous control of local errors in this reliable ODE's solver and of the proposed eigenfunction expansion truncation order. For covalidation purposes, the same built-in function NDSolve is employed in the direct solution of these partial diferential equations, as made possible by the algorithms implemented in Mathematica (versions 3.0 and up), based on application of the method of lines. Various numerical experiments are performed and relative merits of each approach are critically pointed out.

Numerical Simulation of the Cavitation in the Hydrodynamic Lubrication of Journal Bearings: a Parallel Algorithm

In this paper we present an algorithm for the numerical simulation of the cavitation in the hydrodynamic lubrication of journal bearings. Despite the fact that this physical process is usually modelled as a free boundary problem, we adopted the equivalent variational inequality formulation. We propose a two-level iterative algorithm, where the outer iteration is associated to the penalty method, used to transform the variational inequality into a variational equation, and the inner iteration is associated to the conjugate gradient method, used to solve the linear system generated by applying the finite element method to the variational equation. This inner part was implemented using the element by element strategy, which is easily parallelized. We analyse the behavior of two physical parameters and discuss some numerical results. Also, we analyse some results related to the performance of a parallel implementation of the algorithm.

Numerical study of wedge supported oblique shock wave-oblique detonation wave transitions

The results of a numerical study of premixed Hydrogen-air flows ignition by an oblique shock wave (OSW) stabilized by a wedge are presented, in situations when initial and boundary conditions are such that transition between the initial OSW and an oblique detonation wave (ODW) is observed. More precisely, the objectives of the paper are: (i) to identify the different possible structures of the transition region that exist between the initial OSW and the resulting ODW and (ii) to evidence the effect on the ODW of an abrupt decrease of the wedge angle in such a way that the final part of the wedge surface becomes parallel to the initial flow. For such a geometrical configuration and for the initial and boundary conditions considered, the overdriven detonation supported by the initial wedge angle is found to relax towards a Chapman-Jouguet detonation in the region where the wedge surface is parallel to the initial flow. Computations are performed using an adaptive, unstructured grid, finite volume computer code previously developed for the sake of the computations of high speed, compressible flows of reactive gas mixtures. Physico-chemical properties are functions of the local mixture composition, temperature and pressure, and they are computed using the CHEMKIN-II subroutines.

Numerical Simulation of Stochastic Di erential Equations

Stochastic differential equation (SDE) is a differential equation in which some of the terms and its solution are stochastic processes. SDEs play a central role in modeling physical systems like finance, Biology, Engineering, to mention some. In modeling process, the computation of the trajectories (sample paths) of solutions to SDEs is very important. However, the exact solution to a SDE is generally difficult to obtain due to non-differentiability character of realizations of the Brownian motion. There exist approximation methods of solutions of SDE. The solutions will be continuous stochastic processes that represent diffusive dynamics, a common modeling assumption for financial, Biology, physical, environmental systems. This Masters' thesis is an introduction and survey of numerical solution methods for stochastic differential equations. Standard numerical methods, local linearization methods and filtering methods are well described. We compute the root mean square errors for each method from which we propose a better numerical scheme. Stochastic differential equations can be formulated from a given ordinary differential equations. In this thesis, we describe two kind of formulations: parametric and non-parametric techniques. The formulation is based on epidemiological SEIR model. This methods have a tendency of increasing parameters in the constructed SDEs, hence, it requires more data. We compare the two techniques numerically.

Modal testing and numerical modeling of the dynamic properties of layered sheet-steel structure

Recently, due to the increasing total construction and transportation cost and difficulties associated with handling massive structural components or assemblies, there has been increasing financial pressure to reduce structural weight. Furthermore, advances in material technology coupled with continuing advances in design tools and techniques have encouraged engineers to vary and combine materials, offering new opportunities to reduce the weight of mechanical structures. These new lower mass systems, however, are more susceptible to inherent imbalances, a weakness that can result in higher shock and harmonic resonances which leads to poor structural dynamic performances. The objective of this thesis is the modeling of layered sheet steel elements, to accurately predict dynamic performance. During the development of the layered sheet steel model, the numerical modeling approach, the Finite Element Analysis and the Experimental Modal Analysis are applied in building a modal model of the layered sheet steel elements. Furthermore, in view of getting a better understanding of the dynamic behavior of layered sheet steel, several binding methods have been studied to understand and demonstrate how a binding method affects the dynamic behavior of layered sheet steel elements when compared to single homogeneous steel plate. Based on the developed layered sheet steel model, the dynamic behavior of a lightweight wheel structure to be used as the structure for the stator of an outer rotor Direct-Drive Permanent Magnet Synchronous Generator designed for high-power wind turbines is studied.

Proteolytic release and partial characterization of human sperm-surface glycopeptides

Sperm-surface glycopeptides were obtained from intact sperm membranes after proteolytic release by different enzymatic treatments such as autoproteolysis, trypsin, papain and pronase. Glycopeptides were isolated, their properties and composition were examined, and their monosaccharide and amino acid constituents were characterized. The monosaccharides identified were fucose, mannose, galactose, N-acetylglucosamine, and N-acetylgalactosamine, which form part of more than one type of oligosaccharide units. Autoproteolytic treatment mainly provided O-glycosidic type oligosaccharides, while a mixture of O- and N-glycosidic oligosaccharides was obtained in variable proportions when treated with trypsin, papain or pronase. The highest degree of peptide cleavage was obtained with pronase. Despite the higher yields reached with trypsin, these glycopeptides contain the lowest percentage of oligosaccharide chains. Proteolytic treatment provides a simple, rapid procedure for the isolation of glycopeptides from the sperm surface

Partial recovery of erythrocyte glycogen in diabetic rats treated with phenobarbital

Erythrocytes may play a role in glucose homeostasis during the postprandial period. Erythrocytes from diabetic patients are defective in glucose transport and metabolism, functions that may affect glycogen storage. Phenobarbital, a hepatic enzyme inducer, has been used in the treatment of patients with non-insulin-dependent diabetes mellitus (NIDDM), increasing the insulin-mediated glucose disposal. We studied the effects of phenobarbital treatment in vivo on glycemia and erythrocyte glycogen content in control and alloxan-diabetic rats during the postprandial period. In control rats (blood glucose, 73 to 111 mg/dl in femoral and suprahepatic veins) the erythrocyte glycogen content was 45.4 ± 1.1 and 39.1 ± 0.8 µg/g Hb (mean ± SEM, N = 4-6) in the femoral artery and vein, respectively, and 37.9 ± 1.1 in the portal vein and 47.5 ± 0.9 in the suprahepatic vein. Diabetic rats (blood glucose, 300-350 mg/dl) presented low (P<0.05) erythrocyte glycogen content, i.e., 9.6 ± 0.1 and 7.1 ± 0.7 µg/g Hb in the femoral artery and vein, respectively, and 10.0 ± 0.7 and 10.7 ± 0.5 in the portal and suprahepatic veins, respectively. After 10 days of treatment, phenobarbital (0.5 mg/ml in the drinking water) did not change blood glucose or erythrocyte glycogen content in control rats. In diabetic rats, however, it lowered (P<0.05) blood glucose in the femoral artery (from 305 ± 18 to 204 ± 45 mg/dl) and femoral vein (from 300 ± 11 to 174 ± 48 mg/dl) and suprahepatic vein (from 350 ± 10 to 174 ± 42 mg/dl), but the reduction was not sufficient for complete recovery. Phenobarbital also stimulated the glycogen synthesis, leading to a partial recovery of glycogen stores in erythrocytes. In treated rats, erythrocyte glycogen content increased to 20.7 ± 3.8 µg/g Hb in the femoral artery and 30.9 ± 0.9 µg/g Hb in the suprahepatic vein (P<0.05). These data indicate that phenobarbital activated some of the insulin-stimulated glucose metabolism steps which were depressed in diabetic erythrocytes, supporting the view that erythrocytes participate in glucose homeostasis

Cloning, expression and purification of recombinant streptokinase: partial characterization of the protein expressed in Escherichia coli

We cloned the streptokinase (STK) gene of Streptococcus equisimilis in an expression vector of Escherichia coli to overexpress the profibrinolytic protein under the control of a tac promoter. Almost all the recombinant STK was exported to the periplasmic space and recovered after gentle lysozyme digestion of induced cells. The periplasmic fraction was chromatographed on DEAE Sepharose followed by chromatography on phenyl-agarose. Active proteins eluted between 4.5 and 0% ammonium sulfate, when a linear gradient was applied. Three major STK derivatives of 47.5 kDa, 45 kDa and 32 kDa were detected by Western blot analysis with a polyclonal antibody. The 32-kDa protein formed a complex with human plasminogen but did not exhibit Glu-plasminogen activator activity, as revealed by a zymographic assay, whereas the 45-kDa protein showed a Km = 0.70 µM and kcat = 0.82 s-1, when assayed with a chromogen-coupled substrate. These results suggest that these proteins are putative fragments of STK, possibly derived from partial degradation during the export pathway or the purification steps. The 47.5-kDa band corresponded to the native STK, as revealed by peptide sequencing

Partial sequence and toxic effects of granulitoxin, a neurotoxic peptide from the sea anemone Bunodosoma granulifera

A neurotoxic peptide, granulitoxin (GRX), was isolated from the sea anemone Bunodosoma granulifera. The N-terminal amino acid sequence of GRX is AKTGILDSDGPTVAGNSLSGT and its molecular mass is 4958 Da by electrospray mass spectrometry. This sequence presents a partial degree of homology with other toxins from sea anemones such as Bunodosoma caissarum, Anthopleura fuscoviridis and Anemonia sulcata. However, important differences were found: the first six amino acids of the sequence are different, Arg-14 was replaced by Ala and no cysteine residues were present in the partial sequence, while two cysteine residues were present in the first 21 amino acids of other toxins described above. Purified GRX injected ip (800 µg/kg) into mice produced severe neurotoxic effects such as circular movements, aggressive behavior, dyspnea, tonic-clonic convulsion and death. The 2-h LD50 of GRX was 400 ± 83 µg/kg.

Effects of the partial removal of wood hemicelluloses on the properties of kraft pulp

The objective of this work was to study the effects of partial removal of wood hemicelluloses on the properties of kraft pulp.The work was conducted by extracting hemicelluloses (1) by a softwood chip pretreatment process prior to kraft pulping, (2) by alkaline extraction from bleached birch kraft pulp, and (3) by enzymatic treatment, xylanase treatment in particular, of bleached birch kraft pulp. The qualitative and quantitative changes in fibers and paper properties were evaluated. In addition, the applicability of the extraction concepts and hemicellulose-extracted birch kraft pulp as a raw material in papermaking was evaluated in a pilot-scale papermaking environment. The results showed that each examined hemicellulose extraction method has its characteristic effects on fiber properties, seen as differences in both the physical and chemical nature of the fibers. A prehydrolysis process prior to the kraft pulping process offered reductions in cooking time, bleaching chemical consumption and produced fibers with low hemicellulose content that are more susceptible to mechanically induced damages and dislocations. Softwood chip pretreatment for hemicellulose recovery prior to cooking, whether acidic or alkaline, had an impact on the physical properties of the non-refined and refined pulp. In addition, all the pretreated pulps exhibited slower beating response than the unhydrolyzed reference pulp. Both alkaline extraction and enzymatic (xylanase) treatment of bleached birch kraft pulp fibers indicated very selective hemicellulose removal, particularly xylan removal. Furthermore, these two hemicellulose-extracted birch kraft pulps were utilized in a pilot-scale papermaking environment in order to evaluate the upscalability of the extraction concepts. Investigations made using pilot paper machine trials revealed that some amount of alkalineextracted birch kraft pulp, with a 24.9% reduction in the total amount of xylan, could be used in the papermaking stock as a mixture with non-extracted pulp when producing 75 g/m2 paper. For xylanase-treated fibers there were no reductions in the mechanical properties of the 180 g/m2 paper produced compared to paper made from the control pulp, although there was a 14.2% reduction in the total amount of xylan in the xylanase-treated pulp compared to the control birch kraft pulp. This work emphasized the importance of the hemicellulose extraction method in providing new solutions to create functional fibers and in providing a valuable hemicellulose co-product stream. The hemicellulose removal concept therefore plays an important role in the integrated forest biorefinery scenario, where the target is to the co-production of hemicellulose-extracted pulp and hemicellulose-based chemicals or fuels.