Introduction to numerical analysis.

Mode of access: Internet.

Current United States practice for numerical analysis of dams : a report /

"February 1985."

Numerical Analysis on a Dual-Loop Waste Heat Recovery System Coupled with an ORC for Vehicle Applications

The internal combustion (IC) engines exploits only about 30% of the chemical energy ejected through combustion, whereas the remaining part is rejected by means of cooling system and exhausted gas. Nowadays, a major global concern is finding sustainable solutions for better fuel economy which in turn results in a decrease of carbon dioxide (CO2) emissions. The Waste Heat Recovery (WHR) is one of the most promising techniques to increase the overall efficiency of a vehicle system, allowing the recovery of the heat rejected by the exhaust and cooling systems. In this context, Organic Rankine Cycles (ORCs) are widely recognized as a potential technology to exploit the heat rejected by engines to produce electricity. The aim of the present paper is to investigate a WHR system, designed to collect both coolant and exhausted gas heats, coupled with an ORC cycle for vehicle applications. In particular, a coolant heat exchanger (CLT) allows the heat exchange between the water coolant and the ORC working fluid, whereas the exhausted gas heat is recovered by using a secondary circuit with diathermic oil. By using an in-house numerical model, a wide range of working conditions and ORC design parameters are investigated. In particular, the analyses are focused on the regenerator location inside the ORC circuits. Five organic fluids, working in both subcritical and supercritical conditions, have been selected in order to detect the most suitable configuration in terms of energy and exergy efficiencies.

Numerical analysis of the relation between interactions and structure in a molecular fluid

Coarse graining is a popular technique used in physics to speed up the computer simulation of molecular fluids. An essential part of this technique is a method that solves the inverse problem of determining the interaction potential or its parameters from the given structural data. Due to discrepancies between model and reality, the potential is not unique, such that stability of such method and its convergence to a meaningful solution are issues.rnrnIn this work, we investigate empirically whether coarse graining can be improved by applying the theory of inverse problems from applied mathematics. In particular, we use the singular value analysis to reveal the weak interaction parameters, that have a negligible influence on the structure of the fluid and which cause non-uniqueness of the solution. Further, we apply a regularizing Levenberg-Marquardt method, which is stable against the mentioned discrepancies. Then, we compare it to the existing physical methods - the Iterative Boltzmann Inversion and the Inverse Monte Carlo method, which are fast and well adapted to the problem, but sometimes have convergence problems.rnrnFrom analysis of the Iterative Boltzmann Inversion, we elaborate a meaningful approximation of the structure and use it to derive a modification of the Levenberg-Marquardt method. We engage the latter for reconstruction of the interaction parameters from experimental data for liquid argon and nitrogen. We show that the modified method is stable, convergent and fast. Further, the singular value analysis of the structure and its approximation allows to determine the crucial interaction parameters, that is, to simplify the modeling of interactions. Therefore, our results build a rigorous bridge between the inverse problem from physics and the powerful solution tools from mathematics. rn

Computer-Assisted Numerical Analysis for Oxygen and Carbon Dioxide Mass Transfer in Blood Oxygenators

A two-dimensional numeric simulator is developed to predict the nonlinear, convective-reactive, oxygen mass exchange in a cross-flow hollow fiber blood oxygenator. The numeric simulator also calculates the carbon dioxide mass exchange, as hemoglobin affinity to oxygen is affected by the local pH value, which depends mostly on the local carbon dioxide content in blood. Blood pH calculation inside the oxygenator is made by the simultaneous solution of an equation that takes into account the blood buffering capacity and the classical Henderson-Hasselbach equation. The modeling of the mass transfer conductance in the blood comprises a global factor, which is a function of the Reynolds number, and a local factor, which takes into account the amount of oxygen reacted to hemoglobin. The simulator is calibrated against experimental data for an in-line fiber bundle. The results are: (i) the calibration process allows the precise determination of the mass transfer conductance for both oxygen and carbon dioxide; (ii) very alkaline pH values occur in the blood path at the gas inlet side of the fiber bundle; (iii) the parametric analysis of the effect of the blood base excess (BE) shows that V(CO2) is similar in the case of blood metabolic alkalosis, metabolic acidosis, or normal BE, for a similar blood inlet P(CO2), although the condition of metabolic alkalosis is the worst case, as the pH in the vicinity of the gas inlet is the most alkaline; (iv) the parametric analysis of the effect of the gas flow to blood flow ratio (Q(G)/Q(B)) shows that V(CO2) variation with the gas flow is almost linear up to Q(G)/Q(B) = 2.0. V(O2) is not affected by the gas flow as it was observed that by increasing the gas flow up to eight times, the V(O2) grows only 1%. The mass exchange of carbon dioxide uses the full length of the hollow-fiber only if Q(G)/Q(B) > 2.0, as it was observed that only in this condition does the local variation of pH and blood P(CO2) comprise the whole fiber bundle.

Experimental and Numerical Analysis of Different Volutes in a Centrifugal Compressor

In a centrifugal compressor the flow around the diffuser is collected and led to the pipe system by a spiral-shaped volute. In this study a single-stage centrifugal compressor with three different volutes is investigated. The compressorwas first equipped with the original volute, the cross-section of which was a combination of a rectangle and semi-circle. Next a new volute with a fully circular cross-section was designed and manufactured. Finally, the circular volute wasmodified by rounding the tongue and smoothing the tongue area. The overall performance of the compressor as well as the static pressure distribution after the impeller and on the volute surface were measured. The flow entering the volute was measured using a three-hole Cobra-probe, and flow visualisations were carriedout in the exit cone of the volute. In addition, the radial force acting on theimpeller was measured using magnetic bearings. The complete compressor with thecircular volute (inlet pipe, full impeller, diffuser, volute and outlet pipe) was also modelled using computational fluid dynamics (CFD). A fully 3-D viscous flow was solved using a Navier-Stokes solver, Finflo, developed at Helsinki University of Technology. Chien's k-e model was used to take account of the turbulence. The differences observed in the performance of the different volutes were quite small. The biggest differences were at low speeds and high volume flows,i.e. when the flow entered the volute most radially. In this operating regime the efficiency of the compressor with the modified circular volute was about two percentage points higher than with the other volutes. Also, according to the Cobra-probe measurements and flow visualisations, the modified circular volute performed better than the other volutes in this operating area. The circumferential static pressure distribution in the volute showed increases at low flow, constant distribution at the design flow and decrease at high flow. The non-uniform static pressure distribution of the volute was transmitted backwards across the vaneless diffuser and observed at the impeller exit. At low volume flow a strong two-wave pattern developed into the static pressure distribution at the impeller exit due to the response of the impeller to the non-uniformity of pressure. The radial force of the impeller was the greatest at the choke limit, the smallest atthe design flow, and moderate at low flow. At low flow the force increase was quite mild, whereas the increase at high flow was rapid. Thus, the non-uniformityof pressure and the force related to it are strong especially at high flow. Theforce caused by the modified circular volute was weaker at choke and more symmetric as a function of the volume flow than the force caused by the other volutes.

Weighted geometric mean of large-scale matrices: numerical analysis and algorithms

Computing the weighted geometric mean of large sparse matrices is an operation that tends to become rapidly intractable, when the size of the matrices involved grows. However, if we are not interested in the computation of the matrix function itself, but just in that of its product times a vector, the problem turns simpler and there is a chance to solve it even when the matrix mean would actually be impossible to compute. Our interest is motivated by the fact that this calculation has some practical applications, related to the preconditioning of some operators arising in domain decomposition of elliptic problems. In this thesis, we explore how such a computation can be efficiently performed. First, we exploit the properties of the weighted geometric mean and find several equivalent ways to express it through real powers of a matrix. Hence, we focus our attention on matrix powers and examine how well-known techniques can be adapted to the solution of the problem at hand. In particular, we consider two broad families of approaches for the computation of f(A) v, namely quadrature formulae and Krylov subspace methods, and generalize them to the pencil case f(A\B) v. Finally, we provide an extensive experimental evaluation of the proposed algorithms and also try to assess how convergence speed and execution time are influenced by some characteristics of the input matrices. Our results suggest that a few elements have some bearing on the performance and that, although there is no best choice in general, knowing the conditioning and the sparsity of the arguments beforehand can considerably help in choosing the best strategy to tackle the problem.

Optimal Piecewise Linear Function Approximation for GPU-based Applications

Many computer vision and human-computer interaction applications developed in recent years need evaluating complex and continuous mathematical functions as an essential step toward proper operation. However, rigorous evaluation of this kind of functions often implies a very high computational cost, unacceptable in real-time applications. To alleviate this problem, functions are commonly approximated by simpler piecewise-polynomial representations. Following this idea, we propose a novel, efficient, and practical technique to evaluate complex and continuous functions using a nearly optimal design of two types of piecewise linear approximations in the case of a large budget of evaluation subintervals. To this end, we develop a thorough error analysis that yields asymptotically tight bounds to accurately quantify the approximation performance of both representations. It provides an improvement upon previous error estimates and allows the user to control the trade-off between the approximation error and the number of evaluation subintervals. To guarantee real-time operation, the method is suitable for, but not limited to, an efficient implementation in modern Graphics Processing Units (GPUs), where it outperforms previous alternative approaches by exploiting the fixed-function interpolation routines present in their texture units. The proposed technique is a perfect match for any application requiring the evaluation of continuous functions, we have measured in detail its quality and efficiency on several functions, and, in particular, the Gaussian function because it is extensively used in many areas of computer vision and cybernetics, and it is expensive to evaluate.

Numerical analysis of artificial neural network and volterra-based nonlinear equalizers for coherent optical OFDM

One major drawback of coherent optical orthogonal frequency-division multiplexing (CO-OFDM) that hitherto remains unsolved is its vulnerability to nonlinear fiber effects due to its high peak-to-average power ratio. Several digital signal processing techniques have been investigated for the compensation of fiber nonlinearities, e.g., digital back-propagation, nonlinear pre- and post-compensation and nonlinear equalizers (NLEs) based on the inverse Volterra-series transfer function (IVSTF). Alternatively, nonlinearities can be mitigated using nonlinear decision classifiers such as artificial neural networks (ANNs) based on a multilayer perceptron. In this paper, ANN-NLE is presented for a 16QAM CO-OFDM system. The capability of the proposed approach to compensate the fiber nonlinearities is numerically demonstrated for up to 100-Gb/s and over 1000km and compared to the benchmark IVSTF-NLE. Results show that in terms of Q-factor, for 100-Gb/s at 1000km of transmission, ANN-NLE outperforms linear equalization and IVSTF-NLE by 3.2dB and 1dB, respectively.

Analysis of the microbial community structure and function of a laboratory scale enhanced biological phosphorus removal reactor

A laboratory scale sequencing batch reactor (SBR) operating for enhanced biological phosphorus removal (EBPR) and fed with a mixture of volatile fatty acids (VFAs) showed stable and efficient EBPR capacity over a four-year-period. Phosphorus (P), poly-beta-hydroxyalkanoate (PHA) and glycogen cycling consistent with classical anaerobic/aerobic EBPR were demonstrated with the order of anaerobic VFA uptake being propionate, acetate then butyrate. The SBR was operated without pH control and 63.67+/-13.86 mg P l(-1) was released anaerobically. The P% of the sludge fluctuated between 6% and 10% over the operating period (average of 8.04+/-1.31%). Four main morphological types of floc-forming bacteria were observed in the sludge during one year of in-tensive microscopic observation. Two of them were mainly responsible for anaerobic/aerobic P and PHA transformations. Fluorescence in situ hybridization (FISH) and post-FISH chemical staining for intracellular polyphosphate and PHA were used to determine that 'Candidatus Accumulibacter phosphatis' was the most abundant polyphosphate accumulating organism (PAO), forming large clusters of coccobacilli (1.0-1.5 mum) and comprising 53% of the sludge bacteria. Also by these methods, large coccobacillus-shaped gammaproteobacteria (2.5-3.5 mum) from a recently described novel cluster were glycogen-accumulating organisms (GAOs) comprising 13% of the bacteria. Tetrad-forming organisms (TFOs) consistent with the 'G bacterium' morphotype were alphaproteobacteria , but not Amaricoccus spp., and comprised 25% of all bacteria. According to chemical staining, TFOs were occasionally able to store PHA anaerobically and utilize it aerobically.

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.

Strap repairs using embedded patches: numerical analysis and experimental results

Adhesively bonded repairs offer an attractive option for repair of aluminium structures, compared to more traditional methods such as fastening or welding. The single-strap (SS) and double-strap (DS) repairs are very straightforward to execute but stresses in the adhesive layer peak at the overlap ends. The DS repair requires both sides of the damaged structures to be reachable for repair, which is often not possible. In strap repairs, with the patches bonded at the outer surfaces, some limitations emerge such as the weight, aerodynamics and aesthetics. To minimize these effects, SS and DS repairs with embedded patches were evaluated in this work, such that the patches are flush with the adherends. For this purpose, in this work standard SS and DS repairs, and also with the patches embedded in the adherends, were tested under tension to allow the optimization of some repair variables such as the overlap length (LO) and type of adhesive, thus allowing the maximization of the repair strength. The effect of embedding the patch/patches on the fracture modes and failure loads was compared with finite elements (FE) analysis. The FE analysis was performed in ABAQUS® and cohesive zone modelling was used for the simulation of damage onset and growth in the adhesive layer. The comparison with the test data revealed an accurate prediction for all kinds of joints and provided some principles regarding this technique.

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.

Trust, alliance management capability and the alliance management function: A comparative analysis of Portuguese SMEs

Strategic alliances represent a key driver for internationalization and growth, being the purpose of this work project to better understand the intertwined relationship between trust and the existence of an alliance management position. Previous research supports the positive impact of such position in stock market returns. However, little attention has been given to the impact of such position on the level of trust in the collaborative arrangement, which is deemed to be a key driver for alliance success. A qualitative comparative case-study of three Portuguese SMEs is used to draw conclusions from the literature to real life business cases and it demonstrates the positive impact of an alliance management position on trust.

Electrokinetic flow and transport in porous media : experimental methods, numerical analysis, and applications

Electrokinetic transport, electrochromatography, electroosmotic flow, electrophoresis, concentration polarization, fixed beds, monoliths, dynamic NMR microscopy, quantitative confocal laser scanning microscopy, mathematical modelling, numerical analysis