Finite integration methods for isospectral flows

In this paper we consider the approximate computation of isospectral flows based on finite integration methods( FIM) with radial basis functions( RBF) interpolation,a new algorithm is developed. Our method ensures the symmetry of the solutions. Numerical experiments demonstrate that the solutions have higher accuracy by our algorithm than by the second order Runge- Kutta( RK2) method.

A multi–physics approach applied to masonry structures with non–hydraulic lime mortars

Tese de Doutoramento em Engenharia Civil (área de especialização em Engenharia de Estruturas).

Translation of biomechanical concepts in bone tissue engineering: from animal study to revision knee arthroplasty.

Bone defects in revision knee arthroplasty are often located in load-bearing regions. The goal of this study was to determine whether a physiologic load could be used as an in situ osteogenic signal to the scaffolds filling the bone defects. In order to answer this question, we proposed a novel translation procedure having four steps: (1) determining the mechanical stimulus using finite element method, (2) designing an animal study to measure bone formation spatially and temporally using micro-CT imaging in the scaffold subjected to the estimated mechanical stimulus, (3) identifying bone formation parameters for the loaded and non-loaded cases appearing in a recently developed mathematical model for bone formation in the scaffold and (4) estimating the stiffness and the bone formation in the bone-scaffold construct. With this procedure, we estimated that after 3 years mechanical stimulation increases the bone volume fraction and the stiffness of scaffold by 1.5- and 2.7-fold, respectively, compared to a non-loaded situation.

Stabilized Petrov-Galerkin methods for the convection-diffusion-reaction and the Helmholtz equations

We present two new stabilized high-resolution numerical methods for the convection–diffusion–reaction (CDR) and the Helmholtz equations respectively. The work embarks upon a priori analysis of some consistency recovery procedures for some stabilization methods belonging to the Petrov–Galerkin framework. It was found that the use of some standard practices (e.g. M-Matrices theory) for the design of essentially non-oscillatory numerical methods is not feasible when consistency recovery methods are employed. Hence, with respect to convective stabilization, such recovery methods are not preferred. Next, we present the design of a high-resolution Petrov–Galerkin (HRPG) method for the 1D CDR problem. The problem is studied from a fresh point of view, including practical implications on the formulation of the maximum principle, M-Matrices theory, monotonicity and total variation diminishing (TVD) finite volume schemes. The current method is next in line to earlier methods that may be viewed as an upwinding plus a discontinuity-capturing operator. Finally, some remarks are made on the extension of the HRPG method to multidimensions. Next, we present a new numerical scheme for the Helmholtz equation resulting in quasi-exact solutions. The focus is on the approximation of the solution to the Helmholtz equation in the interior of the domain using compact stencils. Piecewise linear/bilinear polynomial interpolation are considered on a structured mesh/grid. The only a priori requirement is to provide a mesh/grid resolution of at least eight elements per wavelength. No stabilization parameters are involved in the definition of the scheme. The scheme consists of taking the average of the equation stencils obtained by the standard Galerkin finite element method and the classical finite difference method. Dispersion analysis in 1D and 2D illustrate the quasi-exact properties of this scheme. Finally, some remarks are made on the extension of the scheme to unstructured meshes by designing a method within the Petrov–Galerkin framework.

Local-global splitting for spatiotemporal-adaptive multiscale methods

We present a novel spatiotemporal-adaptive Multiscale Finite Volume (MsFV) method, which is based on the natural idea that the global coarse-scale problem has longer characteristic time than the local fine-scale problems. As a consequence, the global problem can be solved with larger time steps than the local problems. In contrast to the pressure-transport splitting usually employed in the standard MsFV approach, we propose to start directly with a local-global splitting that allows to locally retain the original degree of coupling. This is crucial for highly non-linear systems or in the presence of physical instabilities. To obtain an accurate and efficient algorithm, we devise new adaptive criteria for global update that are based on changes of coarse-scale quantities rather than on fine-scale quantities, as it is routinely done before in the adaptive MsFV method. By means of a complexity analysis we show that the adaptive approach gives a noticeable speed-up with respect to the standard MsFV algorithm. In particular, it is efficient in case of large upscaling factors, which is important for multiphysics problems. Based on the observation that local time stepping acts as a smoother, we devise a self-correcting algorithm which incorporates the information from previous times to improve the quality of the multiscale approximation. We present results of multiphase flow simulations both for Darcy-scale and multiphysics (hybrid) problems, in which a local pore-scale description is combined with a global Darcy-like description. The novel spatiotemporal-adaptive multiscale method based on the local-global splitting is not limited to porous media flow problems, but it can be extended to any system described by a set of conservation equations.

Oscillation modes of microtubules.

Microtubules are long, filamentous protein complexes which play a central role in several cellular physiological processes, such as cell division transport and locomotion. Their mechanical properties are extremely important since they determine the biological function. In a recently published experiment [Phys. Rev. Lett. 89 (2002) 248101], microtubule's Young's and shear moduli were simultaneously measured, proving that they are highly anisotropic. Together with the known structure, this finding opens the way to better understand and predict their mechanical behavior under a particular set of conditions. In the present study, we modeled microtubules by using the finite elements method and analyzed their oscillation modes. The analysis revealed that oscillation modes involving a change in the diameter of the microtubules strongly depend on the shear modulus. In these modes, the correlation times of the movements are just slightly shorter than diffusion times of free molecules surrounding the microtubule. It could be therefore speculated that the matching of the two timescales could play a role in facilitating the interactions between microtubules and MT associated proteins, and between microtubules and tubulins themselves.

The Role of AtPHO1 in the Guard Cell Movements of Arabidopsis thaliana

In plants, stomatal opening and closing are driven by ion fluxes that cause changes in guard cell turgor and volume, a process that is in turn regulated by complex environ¬mental and hormonal signals such as light and the phytohormone abscisic acid (ABA). With this study, we present genetic evidence that stomatal movements in response to ABA are influenced by PHOl expression in guard cells of Arabidopsis thaliana. PHOl is a phosphate exporter involved in phosphate loading into the root xylem ves¬sels and, as a result, the phol mutant is characterized by low shoot phosphate lev¬els. In leaves, PHOl was found expressed at higher level in guard cells, and was quickly up-regulated following treatment with ABA. The phol mutant was unaffected in ROS production following ABA treatment, and in stomatal movements in response to different light cues, high extracellular calcium, auxin, and fusicoccin. However, stomatal movements in response to ABA treatment were severely impaired, both in terms of induction of closure and inhibition of opening. Stomatal movements in re¬sponse to hydrogen peroxide and reduced CO2 was altered as well. Micro-grafting a phol shoot scion onto wild-type root stock resulted in plants with normal shoot growth and Pi content, but failed to restore normal stomatal response to ABA treat-ment, showing that the impairment was not a simple pleiotropic consequence of phos¬phate deficiency. PHOl knockdown using RNAi specifically in guard cells of wild-type plants caused a reduced stomatal response to ABA. In agreement, specific expression of PHOl in guard cells of phol plants complemented the mutant guard cell phenotype and re-established ABA sensitivity, although full functional complementation was co- dependent on shoot Pi sufficiency. Down-regulation of PHOl in guard cells did not alter the expression of ABA marker genes, indicating that PHOl does not affect the ABA signal transduction cascade at the transcriptional level. Together, these data reveal an important role for phosphate and PHOl action in the stomatal response to ABA. Résumé L'ouverture et la fermeture des stomates des plantes sont des mouvements contrôlés par des flux d'ions causant des fluctuations de la turgescence des cellules de garde. Ce procédé est en retour régulé par des signaux environnementaux et hormonaux complexes, comme la lumière et l'hormone végétale acide abscissique (ABA). Nous présentons ici des preuves génétiques montrant que les mouvements stomatiques en réponse à l'ABA sont influencés par l'expression de PHOl dans les cellules de garde d'Arabidopsis thaliana. PHOl est un exporteur de phosphate, impliqué dans l'efflux de phosphate des cellules corticales racinaires vers les vaisseaux de xylème. En con¬séquence, le mutant phol est caractérisé par de faibles niveaux de phosphate dans les parties aériennes. Dans les feuilles, PHOl est exprimé préférentiellement dans les cellules de garde, comparé au mésophylle, et est rapidement induit par le traitement à l'ABA. Le mutant phol n'est pas affecté dans la perception de l'ABA, dans la pro¬duction de ROS en réponse à l'ABA, et dans la réponse des stomates aux traitements de lumière, à l'auxine, à la fusiccocine, et la forte concentration extracellulaire de cal¬cium. En revanche, les mouvements de stomates en réponse aux traitements à l'ABA sont fortement affectés, dans l'induction de la fermeture des stomates comme dans l'inhibition de leur ouverture. De plus, les mouvements de stomates en réponse au péroxyde d'hydrogène et à la diminution du CO2 sont aussi compromis. La création de micro-greffes composées d'une partie aérienne phol greffés sur un système racinaire sauvage génère des plantes avec une croissance et une teneur en phosphate normale, mais ne permet pas de restaurer la réponse des stomates à l'ABA, ce qui démontre que le défaut de réponse à l'ABA n'est pas une simple conséquence pléiotropique de la carence en phosphate. La répression par RNAi de l'expression de PHOl dans les stomates de plantes sauvages provoque une réduction de la réponse des stomates à l'ABA, mais n'affecte pas la réponse de gènes marqueurs à l'ABA, ce qui suggère que PHOl n'agit pas au niveau transcriptionnel. Parallèlement, l'expression de PHOl dans les cellules de gardes de mutants phol complémente le phénotype stomatique mutant et rétablit la réponse à l'ABA, bien que la totale complémentation nécessite l'apport normal de phosphate aux parties aériennes. Ensemble, ces résultats révè¬lent l'influence importante de PHOl et du phosphate dans la réponse des stomates à l'ABA.

A time-domain method for the analysis of thermal impedance response preserving the convolution form

The study of the thermal behavior of complex packages as multichip modules (MCM¿s) is usually carried out by measuring the so-called thermal impedance response, that is: the transient temperature after a power step. From the analysis of this signal, the thermal frequency response can be estimated, and consequently, compact thermal models may be extracted. We present a method to obtain an estimate of the time constant distribution underlying the observed transient. The method is based on an iterative deconvolution that produces an approximation to the time constant spectrum while preserving a convenient convolution form. This method is applied to the obtained thermal response of a microstructure as analyzed by finite element method as well as to the measured thermal response of a transistor array integrated circuit (IC) in a SMD package.

Dynamics of the two-dimensional gonihedric spin model

In this paper, we study dynamical aspects of the two-dimensional (2D) gonihedric spin model using both numerical and analytical methods. This spin model has vanishing microscopic surface tension and it actually describes an ensemble of loops living on a 2D surface. The self-avoidance of loops is parametrized by a parameter ¿. The ¿=0 model can be mapped to one of the six-vertex models discussed by Baxter, and it does not have critical behavior. We have found that allowing for ¿¿0 does not lead to critical behavior either. Finite-size effects are rather severe, and in order to understand these effects, a finite-volume calculation for non-self-avoiding loops is presented. This model, like his 3D counterpart, exhibits very slow dynamics, but a careful analysis of dynamical observables reveals nonglassy evolution (unlike its 3D counterpart). We find, also in this ¿=0 case, the law that governs the long-time, low-temperature evolution of the system, through a dual description in terms of defects. A power, rather than logarithmic, law for the approach to equilibrium has been found.

Fourier transform convolution integrals applied to generalized Born molecular volume.

Generalized Born methods are currently among the solvation models most commonly used for biological applications. We reformulate the generalized Born molecular volume method initially described by (Lee et al, 2003, J Phys Chem, 116, 10606; Lee et al, 2003, J Comp Chem, 24, 1348) using fast Fourier transform convolution integrals. Changes in the initial method are discussed and analyzed. Finally, the method is extensively checked with snapshots from common molecular modeling applications: binding free energy computations and docking. Biologically relevant test systems are chosen, including 855-36091 atoms. It is clearly demonstrated that, precision-wise, the proposed method performs as good as the original, and could better benefit from hardware accelerated boards.

Effective notch method assessment of misalignment for fatigue loaded welds

 The objective of this thesis work was to assess axial misalignment in fatigue loaded welds using the effective notch method. As a result, the fatigue behaviour of non-load carrying cruciform fillet welded joint under cyclic tensile loading has been studied. Various degrees of axial misalignment have been found in one series of non-load carrying cruciform fillet welded joints used in a laboratory investigation. As a result, it was important to carry out a comprehensive investigation since axial misalignment forms part of thequality of fatigue loaded structure and can reduce the fatigue strength. To extend the study, the correlation between fatigue strength and stress ratio, as well as stress concentration factor, were also studied. Moreover, a closer investigation of place of crack initiation and its dependence on weld sequence and imperfections of test specimen (angular distortion) was studied. For the fatigue class calculations, FEM (finite element method) and the effectivenotch approach are used. The addressed variable is the axial misalignment whichis introduce by modeling the entire joint. Fracture mechanics based calculations are also used and quantitatively compared with effective notch and experimental results.

Miehistönkuljetusajoneuvon rungon suunnittelu

Tämän diplomityön tavoitteena oli suunnitella miehistönkuljetusajoneuvon runko. Rungosta suunniteltiin mahdollisimman hyvin energiaa absorboiva. Rakenne toteutettiin kennora-kenteena. Suunnittelussa sovellettiin koneensuunnittelun periaatteiden lisäksi energiaa ab-sorboivien rakenteiden suunnittelun periaatteita. Myös valmistustekniset näkökohdat otet-tiin huomioon. Rakenteessa hyödynnettiin Ruukki Oy:n Ramor 500 suojausterästä sekä OPTIM 500 MC terästä. Lisäksi erilaisten täyteaineiden käyttöä tutkittiin. Suunnittelun työkaluna käytettiin epälineaarista elementtimenetelmää, koska energiaa ab-sorboivien rakenteiden suunnittelussa on otettava huomioon materiaalien epälineaarinen käyttäytyminen. Rakenteen suunnittelu jakaantui viiteen vaiheeseen. Aluksi rakenteeseen kohdistuvat kuormitukset laskettiin elementtimenetelmän avulla. Esisuunnittelussa lasket-tiin plastisuusteorian avulla alustavasti tarvittavat materiaalipaksuudet. Tämän jälkeen ra-kenteen ydingeometria optimoitiin mahdollisimman hyvin energiaa absorboivaksi. Opti-moinnissa hyödynnettiin elementtimenetelmää. Seuraavassa vaiheessa varmistettiin raken-teen globaalit ominaisuudet. Lopuksi rakenteen kestävyyttä tarkasteltiin elementtimene-telmällä. Runko ei mallien mukaan kestänyt siltä vaadittuja kuormitustapauksia. Mallin kaikki ole-tukset pidettiin varmalla puolella. Reunaehdot oletettiin todellisuutta jäykemmiksi. Myös-kään materiaalin venymänopeudesta johtuvaa lujittumista ei otettu huomioon. Koska mii-naräjähdys on monimutkainen tapahtuma, rungon todellinen kestävyys joudutaan ar-viomaan räjähdystesteillä. Elementtimallien perusteella voidaan kuitenkin sanoa, että ener-giaa absorboiva ajoneuvon runko on mahdollista toteuttaa kennorakenteena. Lisäksi voi-daan todeta, että elementtimenetelmää sopii työvälineeksi tämän tyyppisten rakenteiden suunnitteluun.

Non-linear analysis of laminated metal matrix composites by an integrated micro/macro-mechanical model

The present paper describes an integrated micro/macro mechanical study of the elastic-viscoplastic behavior of unidirectional metal matrix composites (MMC). The micromechanical analysis of the elastic moduli is based on the Composites Cylinder Assemblage model (CCA) with comparisons also draw with a Representative Unit Cell (RUC) technique. These "homogenization" techniques are later incorporated into the Vanishing Fiber Diameter (VFD) model and a new formulation is proposed. The concept of a smeared element procedure is employed in conjunction with two different versions of the Bodner and Partom elastic-viscoplastic constitutive model for the associated macroscopic analysis. The formulations developed are also compared against experimental and analytical results available in the literature.

Be-Fe coupled method for the analysis of 3D elastodynamic problems in the time domain

By coupling the Boundary Element Method (BEM) and the Finite Element Method (FEM) an algorithm that combines the advantages of both numerical processes is developed. The main aim of the work concerns the time domain analysis of general three-dimensional wave propagation problems in elastic media. In addition, mathematical and numerical aspects of the related BE-, FE- and BE/FE-formulations are discussed. The coupling algorithm allows investigations of elastodynamic problems with a BE- and a FE-subdomain. In order to observe the performance of the coupling algorithm two problems are solved and their results compared to other numerical solutions.