Discrete linear stability and sensitivity analysis of fluid flows

Este trabajo presenta un método discreto para el cálculo de estabilidad hidrodinámica y análisis de sensibilidad a perturbaciones externas para ecuaciones diferenciales y en particular para las ecuaciones de Navier-Stokes compressible. Se utiliza una aproximación con variable compleja para obtener una precisión analítica en la evaluación de la matriz Jacobiana. Además, mapas de sensibilidad para la sensibilidad a las modificaciones del flujo de base y a una fuerza constante permiten identificar las regiones del campo fluido donde una modificacin (ej. fuerza puntual) tiene un efecto estabilizador del flujo. Se presentan cuatro casos de prueba: (1) un caso analítico para comprobar la derivación discreta, (2) una cavidad cerrada a bajo Reynolds para mostrar la mayor precisión en el cálculo de los valores propios con la aproximación de paso complejo, (3) flujo 2D en un cilindro circular para validar la metodología, y (4) flujo en un cavidad abierta, presentado para validar el método en casos de inestabilidades convectivamente inestables. Los tres últimos casos mencionados (2-4) se resolvieron con las ecuaciones de Navier-Stokes compresibles, utilizando un método Discontinuous Galerkin Spectral Element Method. Se obtuvo una buena concordancia para el caso de validación (3), cuando se comparó el nuevo método con resultados de la literatura. Además, este trabajo muestra que para el cálculo de los modos propios directos y adjuntos, así como para los mapas de sensibilidad, el uso de variables complejas es de suprema importancia para obtener una predicción precisa. El método descrito es aplicado al análisis para la estabilización de la estela generada por un disco actuador, que representa un modelo sencillo para hélices, rotores de helicópteros o turbinas eólicas. Se explora la primera bifurcación del flujo para un disco actuador, y se sugiere que está asociada a una inestabilidad de tipo Kelvin-Helmholtz, cuya estabilidad se controla con en el número de Reynolds y en la resistencia del disco actuador (o fuerza resistente). En primer lugar, se verifica que la disminución de la resistencia del disco tiene un efecto estabilizador parecido a una disminución del Reynolds. En segundo lugar, el análisis hidrodinmico discreto identifica dos regiones para la colocación de una fuerza puntual que controle las inestabilidades, una cerca del disco y otra en una zona aguas abajo. En tercer lugar, se muestra que la inclusión de un forzamiento localizado cerca del actuador produce una estabilización más eficiente que al forzar aguas abajo. El análisis de los campos de flujo controlados confirma que modificando el gradiente de velocidad cerca del actuador es más eficiente para estabilizar la estela. Estos resultados podrían proporcionar nuevas directrices para la estabilización de la estela de turbinas de viento o de marea cuando estén instaladas en un parque eólico y minimizar las interacciones no estacionarias entre turbinas. ABSTRACT A discrete framework for computing the global stability and sensitivity analysis to external perturbations for any set of partial differential equations is presented. In particular, a complex-step approximation is used to achieve near analytical accuracy for the evaluation of the Jacobian matrix. Sensitivity maps for the sensitivity to base flow modifications and to a steady force are computed to identify regions of the flow field where an input could have a stabilising effect. Four test cases are presented: (1) an analytical test case to prove the theory of the discrete framework, (2) a lid-driven cavity at low Reynolds case to show the improved accuracy in the calculation of the eigenvalues when using the complex-step approximation, (3) the 2D flow past a circular cylinder at just below the critical Reynolds number is used to validate the methodology, and finally, (4) the flow past an open cavity is presented to give an example of the discrete method applied to a convectively unstable case. The latter three (2–4) of the aforementioned cases were solved with the 2D compressible Navier–Stokes equations using a Discontinuous Galerkin Spectral Element Method. Good agreement was obtained for the validation test case, (3), with appropriate results in the literature. Furthermore, it is shown that for the calculation of the direct and adjoint eigenmodes and their sensitivity maps to external perturbations, the use of complex variables is paramount for obtaining an accurate prediction. An analysis for stabilising the wake past an actuator disc, which represents a simple model for propellers, helicopter rotors or wind turbines is also presented. We explore the first flow bifurcation for an actuator disc and it suggests that it is associated to a Kelvin- Helmholtz type instability whose stability relies on the Reynolds number and the flow resistance applied through the disc (or actuator forcing). First, we report that decreasing the disc resistance has a similar stabilising effect to an decrease in the Reynolds number. Second, a discrete sensitivity analysis identifies two regions for suitable placement of flow control forcing, one close to the disc and one far downstream where the instability originates. Third, we show that adding a localised forcing close to the actuator provides more stabilisation that forcing far downstream. The analysis of the controlled flow fields, confirms that modifying the velocity gradient close to the actuator is more efficient to stabilise the wake than controlling the sheared flow far downstream. An interesting application of these results is to provide guidelines for stabilising the wake of wind or tidal turbines when placed in an energy farm to minimise unsteady interactions.

Static and dynamic lengths of neutrophil microvilli

Containing most of the L-selectin and P-selectin glycoprotein ligand-1 (PSGL-1) on their tips, microvilli are believed to promote the initial arrest of neutrophils on endothelium. At the rolling stage following arrest, the lifetimes of the involved molecular bonds depend on the pulling force imposed by the shear stress of blood flow. With two different methods, electron microscopy and micropipette manipulation, we have obtained two comparable neutrophil microvillus lengths, both ≈0.3 μm in average. We have found also that, under a pulling force, a microvillus can be extended (microvillus extension) or a long thin membrane cylinder (a tether) can be formed from it (tether formation). If the force is ≤34 pN (± 3 pN), the length of the microvillus will be extended; if the force is >61 pN (± 5 pN), a tether will be formed from the microvillus at a constant velocity, which depends linearly on the force. When the force is between 34 pN and 61 pN (transition zone), the degree of association between membrane and cytoskeleton in individual microvilli will dictate whether microvillus extension or tether formation occurs. When a microvillus is extended, it acts like a spring with a spring constant of ≈43 pN/μm. In contrast to a rigid or nonextendible microvillus, both microvillus extension and tether formation can decrease the pulling force imposed on the adhesive bonds, and thus prolonging the persistence of the bonds at high physiological shear stresses.

Regulation of sulfur assimilation in higher plants: A sulfate transporter induced in sulfate-starved roots plays a central role in Arabidopsis thaliana

Proton/sulfate cotransporters in the plasma membranes are responsible for uptake of the environmental sulfate used in the sulfate assimilation pathway in plants. Here we report the cloning and characterization of an Arabidopsis thaliana gene, AST68, a new member of the sulfate transporter gene family in higher plants. Sequence analysis of cDNA and genomic clones of AST68 revealed that the AST68 gene is composed of 10 exons encoding a 677-aa polypeptide (74.1 kDa) that is able to functionally complement a Saccharomyces cerevisiae mutant lacking a sulfate transporter gene. Southern hybridization and restriction fragment length polymorphism mapping confirmed that AST68 is a single-copy gene that maps to the top arm of chromosome 5. Northern hybridization analysis of sulfate-starved plants indicated that the steady-state mRNA abundance of AST68 increased specifically in roots up to 9-fold by sulfate starvation. In situ hybridization experiments revealed that AST68 transcripts were accumulated in the central cylinder of sulfate-starved roots, but not in the xylem, endodermis, cortex, and epidermis. Among all the structural genes for sulfate assimilation, sulfate transporter (AST68), APS reductase (APR1), and serine acetyltransferase (SAT1) were inducible by sulfate starvation in A. thaliana. The sulfate transporter (AST68) exhibited the most intensive and specific response in roots, indicating that AST68 plays a central role in the regulation of sulfate assimilation in plants.

Development of pilus organelle subassemblies in vitro depends on chaperone uncapping of a beta zipper

The major subassemblies of virulence-associated P pili, the pilus rod (comprised of PapA) and tip fibrillum (comprised of PapE), were reconstituted from purified chaperone-subunit complexes in vitro. Subunits are held in assembly-competent conformations in chaperone-subunit complexes prior to their assembly into mature pili. The PapD chaperone binds, in part, to a conserved motif present at the C terminus of the subunits via a beta zippering interaction. Amino acid residues in this conserved motif were also found to be essential for subunit–subunit interactions necessary for the formation of pili, thus revealing a molecular mechanism whereby the PapD chaperone may prevent premature subunit–subunit interactions in the periplasm. Uncapping of the chaperone-protected C terminus of PapA and PapE was mimicked in vitro by freeze–thaw techniques and resulted in the formation of pilus rods and tip fibrillae, respectively. A mutation in the leading edge of the beta zipper of PapA produces pilus rods with an altered helical symmetry and azimuthal disorder. This change in the number of subunits per turn of the helix most likely reflects involvement of the leading edge of the beta zipper in forming a right-handed helical cylinder. Organelle development is a fundamental process in all living cells, and these studies shed new light on how immunoglobulin-like chaperones govern the formation of virulence-associated organelles in pathogenic bacteria.

Borrelia burgdorferi periplasmic flagella have both skeletal and motility functions

Bacterial shape usually is dictated by the peptidoglycan layer of the cell wall. In this paper, we show that the morphology of the Lyme disease spirochete Borrelia burgdorferi is the result of a complex interaction between the cell cylinder and the internal periplasmic flagella. B. burgdorferi has a bundle of 7–11 helically shaped periplasmic flagella attached at each end of the cell cylinder and has a flat-wave cell morphology. Backward moving, propagating waves enable these bacteria to swim in both low viscosity media and highly viscous gel-like media. Using targeted mutagenesis, we inactivated the gene encoding the major periplasmic flagellar filament protein FlaB. The resulting flaB mutants not only were nonmotile, but were rod-shaped. Western blot analysis indicated that FlaB was no longer synthesized, and electron microscopy revealed that the mutants were completely deficient in periplasmic flagella. Wild-type cells poisoned with the protonophore carbonyl cyanide-m-chlorophenylhydrazone retained their flat-wave morphology, indicating that the periplasmic flagella do not need to be energized for the cell to maintain this shape. Our results indicate that the periplasmic flagella of B. burgdorferi have a skeletal function. These organelles dynamically interact with the rod-shaped cell cylinder to enable the cell to swim, and to confer in part its flat-wave morphology.

ClpA mediates directional translocation of substrate proteins into the ClpP protease

The intracellular degradation of many proteins is mediated in an ATP-dependent manner by large assemblies comprising a chaperone ring complex associated coaxially with a proteolytic cylinder, e.g., ClpAP, ClpXP, and HslUV in prokaryotes, and the 26S proteasome in eukaryotes. Recent studies of the chaperone ClpA indicate that it mediates ATP-dependent unfolding of substrate proteins and directs their ATP-dependent translocation into the ClpP protease. Because the axial passageway into the proteolytic chamber is narrow, it seems likely that unfolded substrate proteins are threaded from the chaperone into the protease, suggesting that translocation could be directional. We have investigated directionality in the ClpA/ClpP-mediated reaction by using two substrate proteins bearing the COOH-terminal ssrA recognition element, each labeled near the NH2 or COOH terminus with fluorescent probes. Time-dependent changes in both fluorescence anisotropy and fluorescence resonance energy transfer between donor fluorophores in the ClpP cavity and the substrate probes as acceptors were measured to monitor translocation of the substrates from ClpA into ClpP. We observed for both substrates that energy transfer occurs 2–4 s sooner with the COOH-terminally labeled molecules than with the NH2-terminally labeled ones, indicating that translocation is indeed directional, with the COOH terminus of the substrate protein entering ClpP first.

Differential Expression of Genes for Cyclin-Dependent Protein Kinases in Rice Plants1

Cyclin-dependent protein kinases (CDKs) play key roles in regulating the eukaryotic cell cycle. We have analyzed the expression of four rice (Oryza sativa) CDK genes, cdc2Os1, cdc2Os2, cdc2Os3, and R2, by in situ hybridization of sections of root apices. Transcripts of cdc2Os1, cdc2Os2, and R2 were detected uniformly in the dividing region of the root apex. cdc2Os1 and cdc2Os2 were also expressed in differentiated cells such as those in the sclerenchyma, pericycle, and parenchyma of the central cylinder. By contrast, signals corresponding to transcripts of cdc2Os3 were distributed only in patches in the dividing region. Counterstaining of sections with 4′,6-diamidino-2-phenylindole and double-target in situ hybridization with a probe for histone H4 transcripts revealed that cdc2Os3 transcripts were abundant from the G2 to the M phase, but were less abundant or absent during the S phase. The levels of the Cdc2Os3 protein and its associated histone H1-kinase activity were reduced by treatment of cultured cells with hydroxyurea, which blocks cycling cells at the onset of the S phase. Our results suggest that domains other than the conserved amino acid sequence (the PSTAIRE motif) have important roles in the function of non-PSTAIRE CDKs in distinct cell-cycle phases.

Radial and longitudinal diffusion of myoglobin in single living heart and skeletal muscle cells

We have used a fluorescence recovery after photobleaching (FRAP) technique to measure radial diffusion of myoglobin and other proteins in single skeletal and cardiac muscle cells. We compare the radial diffusivities, Dr (i.e., diffusion perpendicular to the long fiber axis), with longitudinal ones, Dl (i.e., parallel to the long fiber axis), both measured by the same technique, for myoglobin (17 kDa), lactalbumin (14 kDa), and ovalbumin (45 kDa). At 22°C, Dl for myoglobin is 1.2 × 10−7 cm2/s in soleus fibers and 1.1 × 10−7 cm2/s in cardiomyocytes. Dl for lactalbumin is similar in both cell types. Dr for myoglobin is 1.2 × 10−7 cm2/s in soleus fibers and 1.1 × 10−7 cm2/s in cardiomyocytes and, again, similar for lactalbumin. Dl and Dr for ovalbumin are 0.5 × 10−7 cm2/s. In the case of myoglobin, both Dl and Dr at 37°C are about 80% higher than at 22°C. We conclude that intracellular diffusivity of myoglobin and other proteins (i) is very low in striated muscle cells, ≈1/10 of the value in dilute protein solution, (ii) is not markedly different in longitudinal and radial direction, and (iii) is identical in heart and skeletal muscle. A Krogh cylinder model calculation holding for steady-state tissue oxygenation predicts that, based on these myoglobin diffusivities, myoglobin-facilitated oxygen diffusion contributes 4% to the overall intracellular oxygen transport of maximally exercising skeletal muscle and less than 2% to that of heart under conditions of high work load.

The Three-Dimensional Structure of Aspergillus niger Pectin Lyase B at 1.7-Å Resolution1

The three-dimensional structure of Aspergillus niger pectin lyase B (PLB) has been determined by crystallographic techniques at a resolution of 1.7 Å. The model, with all 359 amino acids and 339 water molecules, refines to a final crystallographic R factor of 16.5%. The polypeptide backbone folds into a large right-handed cylinder, termed a parallel β helix. Loops of various sizes and conformations protrude from the central helix and probably confer function. The largest loop of 53 residues folds into a small domain consisting of three antiparallel β strands, one turn of an α helix, and one turn of a 310 helix. By comparison with the structure of Erwinia chrysanthemi pectate lyase C (PelC), the primary sequence alignment between the pectate and pectin lyase subfamilies has been corrected and the active site region for the pectin lyases deduced. The substrate-binding site in PLB is considerably less hydrophilic than the comparable PelC region and consists of an extensive network of highly conserved Trp and His residues. The PLB structure provides an atomic explanation for the lack of a catalytic requirement for Ca2+ in the pectin lyase family, in contrast to that found in the pectate lyase enzymes. Surprisingly, however, the PLB site analogous to the Ca2+ site in PelC is filled with a positive charge provided by a conserved Arg in the pectin lyases. The significance of the finding with regard to the enzymatic mechanism is discussed.

Polarity of microtubule assemblies during neuronal cell migration.

The active migration of neurons from their sites of origin to their final destinations requires the unidirectional translocation of the nuclei and somatic cytoplasm within the growing leading processes. To explore the cellular machinery underlying this translocation, we determined the polarity of microtubules situated within the leading and trailing processes of migrating cerebellar granule cells in situ. Our analysis reveals that the newly assembled positive ends of the microtubules in the leading process uniformly face the growing tip, while their disintegrating negative ends face the nucleus. In the trailing process, by contrast, microtubule arrays are of mixed polarity. We suggest that the dynamics of slow polymerization in combination with fast disintegration of oriented microtubules create "push" and "pull" forces that contribute to the piston-like saltatory displacement of the nucleus and cytoplasm within the membrane cylinder of the leading process of the migrating neuron.

Immunolocalization of estrogen receptor protein in the mouse blastocyst during normal and delayed implantation.

We previously showed that estrogen receptor (ER) mRNA is present in preimplantation mouse embryos. The apparent synthesis of ER mRNA by the blastocyst at the time of implantation when estrogen is required was of special interest. A demonstration of the presence of ER protein would support the idea that estrogen can act directly on the embryo. The mouse embryo at the blastocyst stage is differentiated into two cell types, the trophectoderm and the inner cell mass. To determine whether ER mRNA is translated into ER protein and its cell-specific distribution, immunocytochemical analyses were performed in mouse blastocysts. ER protein was detected in all cell types of the normal, dormant, or activated blastocyst. To trace the fate of ER in these cell types, immunocytochemistry was performed in implanting blastocysts and early egg cylinder stage embryos developed in culture. Again, ER was detected in all cells of the implanting blastocyst. At the early egg cylinder stage, continued expression of ER was observed in cells derived from the inner cell mass or the trophoblast. In trophoblast giant cells, ER was concentrated in small regions of the nucleus, possibly the nucleoli, which was similar to that observed in dormant and activated blastocysts. The embryonic expression of ER at such early stages in a broad array of cells suggests that ER may have a general role during early development.

Modelagem e controle de posição e orientação de uma Plataforma de Stewart

Este trabalho apresenta o controle de posição e orientação de um modelo não linear de Plataforma de Stewart com seis graus de liberdade construído no ambiente de sistemas multicorpos ADAMS® desenvolvido pela Mechanical Dynamics, Inc. O modelo não linear é exportado para o ambiente SIMULINK® desenvolvido pela MathWorks, Inc., onde o controle de posição e orientação é realizado a partir da linearização do modelo e a aplicação de um sistema seguidor com realimentação de estados. Utililiza-se, também o SIMULINK® para implementar a dinâmica de um sistema servoválvula e cilindro hidráulico com um servocontrole de pressão e assim simular o comportamento dinâmico de um simulador de vôo com acionamento hidráulico. A utilização destes pacotes comerciais visa obter uma economia de tempo e esforço na modelagem de sistemas mecânicos complexos e na programação para obtenção da resposta do sistema no tempo, além de facilitar a análise de várias configurações de Plataformas de Stewart

Estudo dos solos da região metropolitana de Fortaleza para aplicação na engenharia rodoviária

O trabalho aqui apresentado é resultado de uma pesquisa onde se procurou caracterizar os solos da Região Metropolitana de Fortaleza (RMF). Inicialmente, o objetivo deixou de ser principal devido às limitações desse método quando aplicado aos solos da RMF. O objetivo principal do trabalho passou a ser estudar mais detalhadamente os solos que ocorrem na Região Metropolitana de Fortaleza à luz de métodos convencionais e não convencionais, para aplicação na engenharia rodoviária. Para tanto, foram estudados sessenta solos pertencentes às classes pedológicas que ocorrem na RMF. Esses solos foram submetidos a um programa experimental que envolveu a execução de ensaios \"convencionais\" e \"não convencionais\". A partir dos resultados experimentais foram estabelecidas correlações entre os valores de algumas propriedades de interesse à pavimentação realizadas em cilindro convencional e miniatura. Tentou-se determinar o valor de CBR de um solo, dispondo das cargas calculadas no ensaio mini-CBR, mas essa tarefa não logrou êxito. As amostras foram classificadas pelas classificações HBR e MCT para verificação da qualidade da previsão das propriedades dos solos obtidas por esses métodos e aqueles resultantes da execução dos ensaios de laboratório. Foi proposto, a partir da execução de ensaio de adsorção de azul de metileno, a inclusão no ábaco de três zonas para se caracterizar o comportamento dos solos da RMF. Os resultados experimentais permitiram, também, concluir que pode-se identificar os materiais com potencial de uso na pavimentação de sua classe pedológica.

Estudo experimental do fenômeno de vibração induzida por vórtices em cilindro rígido livre para oscilar com dois graus de liberdade.

O fenômeno de vibração induzida por vórtices (VIV) é um problema fundamental dentro da Mecânica dos Fluidos e um exemplo importante de interação fluido-estrutura. Esta tese investiga fenômeno de VIV quando um cilindro rígido, submetido a escoamento uniforme, está livre para oscilar na direção transversal e alinhada com a corrente incidente. A tese foi estruturada ao redor de sete perguntas relacionadas ao fenômeno de VIV: 1) O fenômeno e os resultados experimentais são repetitivos? 2) Como ocorre a transição entre ramos de resposta? 3) Qual é o papel da inércia da estrutura oscilante? 4) Qual é o papel de sua rigidez? 5) Quais são as frequências naturais mais importantes da estrutura? 6) Quais padrões de esteira se desenvolvem para VIV com dois graus de liberdade? 7) Quais são os efeitos do movimento na direção alinhada com a corrente no processo de formação e desprendimento de vórtices? O fenômeno de VIV é estudado de maneira experimental em uma base elástica pendular capaz de oscilar com o mesmo momento de inércia e frequência natural nas duas direções. Os experimentos de VIV foram realizados em canal de água recirculante e com diferentes condições de inércia e rigidez. A técnica de velocimetria por imagem de partículas foi usada e permitiu identificar diferentes padrões de esteira de vórtices. Verificou-se que o VIV é repetitivo a nível de amplitudes médias e frequências dominantes. A transição dos ramos pode ocorrer de maneira intermitente ou com histerese. Os parâmetros de inércia e rigidez da estrutura são capazes de mudar o regime de oscilação e, para algumas condições, suprimir as vibrações alinhadas com a corrente. Dentre os padrões de esteira observados, um deles não havia sido relatado na literatura e é definido nesta tese. O novo modo de emissão apresenta dois vórtices com circulação oposta e elevada intensidade emitidos por ciclo. A influência da direção alinhada com o escoamento está relacionada a dois efeitos: a velocidade relativa entre o cilindro e o fluido, responsável pelo aumento da circulação dos vórtices na esteira, e o ângulo de fase do movimento nas direções alinhada e transversal, capaz de mudar o processo de formação dos vórtices.

Desenvolvimento da modelagem de turbulência e interação fluido-estrutura para as vibrações induzidas por vórtices de cilindro rígido.

Esta tese apresenta o desenvolvimento e aplicação de modelos de turbulência, transição laminar-turbulenta e de interações fluido-estrutura ao escoamento externo em cilindro rígido estacionário e em vibrações induzidas por vórtices. Tais desenvolvimentos foram realizados no código ReFRESCO, baseado em técnicas de dinâmica de fluidos computacional (CFD). Realizou-se um estudo quanto ao desempenho do modelo k- SST em extensa faixa de números de Reynolds, segundo o qual se identificaram as deficiências de modelagem para este escoamento. A modelagem adaptativa das escalas (SAS) e o modelo de transição por correlações locais (LCTM), ambos combinados ao SST, melhoraram a aderência aos resultados experimentais para este escoamento, em uma contribuição original deste trabalho. A aplicação de técnicas de verificação e validação possibilitou a estimação de incertezas e erros para os modelos e números de Reynolds e também de identificada como outra contribuição deste trabalho. A combinação da modelagem em SST, SAS e LCTM com movimentos impostos de realizada para números de Reynolds moderados, diferentes frequências e amplitudes de vibração, algo que poucas publicações abordam em detalhes. Com relação aos movimentos livres, este trabalho traz contribuições com a aplicação dos modelos SST e SAS ao estudo de vibrações induzidas por vórtices em dois graus de liberdade, baixa razão de massa e números de Reynolds moderados, mais altos do que normalmente observados na literatura. Por fim, a investigação da importância relativa de efeitos da turbulência aos casos de movimentos livres e impostos, com relação ao caso de cilindro estacionário, comprovou a conjetura formulada na parte inicial deste trabalho, no que tange à escolha do modelo de turbulência em determinadas aplicações. Tal escolha mostrou-se menos decisiva no caso do cilindro em movimento imposto e ainda menos nos movimentos livres, em comparação ao caso estacionário, uma vez que a resposta em movimentos do corpo filtra grande parte dos efeitos turbulentos de ordem superior. Esta observação mostra-se relevante, uma vez que pode permitir simplificações na modelagem e aplicação de ferramentas de CFD em uma classe importante de projetos de engenharia.