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.

Reciprocal interactions between β1-integrin and epidermal growth factor receptor in three-dimensional basement membrane breast cultures: A different perspective in epithelial biology

Anchorage and growth factor independence are cardinal features of the transformed phenotype. Although it is logical that the two pathways must be coregulated in normal tissues to maintain homeostasis, this has not been demonstrated directly. We showed previously that down-modulation of β1-integrin signaling reverted the malignant behavior of a human breast tumor cell line (T4–2) derived from phenotypically normal cells (HMT-3522) and led to growth arrest in a three-dimensional (3D) basement membrane assay in which the cells formed tissue-like acini (14). Here, we show that there is a bidirectional cross-modulation of β1-integrin and epidermal growth factor receptor (EGFR) signaling via the mitogen-activated protein kinase (MAPK) pathway. The reciprocal modulation does not occur in monolayer (2D) cultures. Antibody-mediated inhibition of either of these receptors in the tumor cells, or inhibition of MAPK kinase, induced a concomitant down-regulation of both receptors, followed by growth-arrest and restoration of normal breast tissue morphogenesis. Cross-modulation and tissue morphogenesis were associated with attenuation of EGF-induced transient MAPK activation. To specifically test EGFR and β1-integrin interdependency, EGFR was overexpressed in nonmalignant cells, leading to disruption of morphogenesis and a compensatory up-regulation of β1-integrin expression, again only in 3D. Our results indicate that when breast cells are spatially organized as a result of contact with basement membrane, the signaling pathways become coupled and bidirectional. They further explain why breast cells fail to differentiate in monolayer cultures in which these events are mostly uncoupled. Moreover, in a subset of tumor cells in which these pathways are misregulated but functional, the cells could be “normalized” by manipulating either pathway.

Structure-based assignment of the biochemical function of a hypothetical protein: A test case of structural genomics

Many small bacterial, archaebacterial, and eukaryotic genomes have been sequenced, and the larger eukaryotic genomes are predicted to be completely sequenced within the next decade. In all genomes sequenced to date, a large portion of these organisms’ predicted protein coding regions encode polypeptides of unknown biochemical, biophysical, and/or cellular functions. Three-dimensional structures of these proteins may suggest biochemical or biophysical functions. Here we report the crystal structure of one such protein, MJ0577, from a hyperthermophile, Methanococcus jannaschii, at 1.7-Å resolution. The structure contains a bound ATP, suggesting MJ0577 is an ATPase or an ATP-mediated molecular switch, which we confirm by biochemical experiments. Furthermore, the structure reveals different ATP binding motifs that are shared among many homologous hypothetical proteins in this family. This result indicates that structure-based assignment of molecular function is a viable approach for the large-scale biochemical assignment of proteins and for discovering new motifs, a basic premise of structural genomics.

Kinetic stability as a mechanism for protease longevity

The folding of the extracellular serine protease, α-lytic protease (αLP; EC 3.4.21.12) reveals a novel mechanism for stability that appears to lead to a longer functional lifetime for the protease. For αLP, stability is based not on thermodynamics, but on kinetics. Whereas this has required the coevolution of a pro region to facilitate folding, the result has been the optimization of native-state properties independent of their consequences on thermodynamic stability. Structural and mutational data lead to a model for catalysis of folding in which the pro region binds to a conserved β-hairpin in the αLP C-terminal domain, stabilizing the folding transition state and the native state. The pro region is then proteolytically degraded, leaving the active αLP trapped in a metastable conformation. This metastability appears to be a consequence of pressure to evolve properties of the native state, including a large, highly cooperative barrier to unfolding, and extreme rigidity, that reduce susceptibility to proteolytic degradation. In a test of survival under highly proteolytic conditions, homologous mammalian proteases that have not evolved kinetic stability are much more rapidly degraded than αLP. Kinetic stability as a means to longevity is likely to be a mechanism conserved among the majority of extracellular bacterial pro-proteases and may emerge as a general strategy for intracellular eukaryotic proteases subject to harsh conditions as well.

Symmetry, stability, and dynamics of multidomain and multicomponent protein systems

Symmetry is commonly observed in many biological systems. Here we discuss representative examples of the role of symmetry in structural molecular biology. Point group symmetries are observed in many protein oligomers whose three-dimensional atomic structures have been elucidated by x-ray crystallography. Approximate symmetry also occurs in multidomain proteins. Symmetry often confers stability on the molecular system and results in economical usage of basic components to build the macromolecular structure. Symmetry is also associated with cooperativity. Mild perturbation from perfect symmetry may be essential in some systems for dynamic functions.

A test of the "jigsaw puzzle" model for protein folding by multiple methionine substitutions within the core of T4 lysozyme.

To test whether the structure of a protein is determined in a manner akin to the assembly of a jigsaw puzzle, up to 10 adjacent residues within the core of T4 lysozyme were replaced by methionine. Such variants are active and fold cooperatively with progressively reduced stability. The structure of a seven-methionine variant has been shown, crystallographically, to be similar to wild type and to maintain a well ordered core. The interaction between the core residues is, therefore, not strictly comparable with the precise spatial complementarity of the pieces of a jigsaw puzzle. Rather, a certain amount of give and take in forming the core structure is permitted. A simplified hydrophobic core sequence, imposed without genetic selection or computer-based design, is sufficient to retain native properties in a globular protein.

Role of aromatic residues in stabilization of the [Fe4S4] cluster in high-potential iron proteins (HiPIPs): physical characterization and stability studies of Tyr-19 mutants of Chromatium vinosum HiPIP.

The functional role of residue Tyr-19 of Chromatium vinosum HiPIP has been evaluated by site-directed mutagenesis experiments. The stability of the [Fe4S4] cluster prosthetic center is sensitive to side-chain replacements. Polar residues result in significant instability, while nonpolar residues (especially with aromatic side chains) maintain cluster stability. Two-dimensional NMR data of native and mutant HiPIPs are consistent with a model where Tyr-19 serves to preserve the structural rigidity of the polypeptide backbone, thereby maintaining a hydrophobic barrier for exclusion of water from the cluster cavity. Solvent accessibility results in more facile oxidation of the cluster by atmospheric oxygen, with subsequent rapid hydrolysis of the [Fe4S4]3+ core.

Structure and stability of a second molten globule intermediate in the apomyoglobin folding pathway.

Apomyoglobin folding proceeds through a molten globule intermediate (low-salt form; I1) that has been characterized by equilibrium (pH 4) and kinetic (pH 6) folding experiments. Of the eight alpha-helices in myoglobin, three (A, G, and H) are structured in I1, while the rest appear to be unfolded. Here we report on the structure and stability of a second intermediate, the trichloroacetate form of the molten globule intermediate (I2), which is induced either from the acid-unfolded protein or from I1 by > or = 5 mM sodium trichloroacetate. Circular dichroism measurements monitoring urea- and acid-induced unfolding indicate that I2 is more highly structured and more stable than I1. Although I2 exhibits properties closer to those of the native protein, one-dimensional NMR spectra show that it maintains the lack of fixed side-chain structure that is the hallmark of a molten globule. Amide proton exchange and 1H-15N two-dimensional NMR experiments are used to identify the source of the extra helicity observed in I2. The results reveal that the existing A, G, and H helices present in I1 have become more stable in I2 and that a fourth helix--the B helix--has been incorporated into the molten globule. Available evidence is consistent with I2 being an on-pathway intermediate. The data support the view that apomyoglobin folds in a sequential fashion through a single pathway populated by intermediates of increasing structure and stability.

Three-dimensional inverse modelling of magnetic anomaly sources based on a genetic algorithm.

We present a modelling method to estimate the 3-D geometry and location of homogeneously magnetized sources from magnetic anomaly data. As input information, the procedure needs the parameters defining the magnetization vector (intensity, inclination and declination) and the Earth's magnetic field direction. When these two vectors are expected to be different in direction, we propose to estimate the magnetization direction from the magnetic map. Then, using this information, we apply an inversion approach based on a genetic algorithm which finds the geometry of the sources by seeking the optimum solution from an initial population of models in successive iterations through an evolutionary process. The evolution consists of three genetic operators (selection, crossover and mutation), which act on each generation, and a smoothing operator, which looks for the best fit to the observed data and a solution consisting of plausible compact sources. The method allows the use of non-gridded, non-planar and inaccurate anomaly data and non-regular subsurface partitions. In addition, neither constraints for the depth to the top of the sources nor an initial model are necessary, although previous models can be incorporated into the process. We show the results of a test using two complex synthetic anomalies to demonstrate the efficiency of our inversion method. The application to real data is illustrated with aeromagnetic data of the volcanic island of Gran Canaria (Canary Islands).

Sample-to-sample fluctuations of the overlap distributions in the three-dimensional Edwards-Anderson spin glass

We study the sample-to-sample fluctuations of the overlap probability densities from large-scale equilibrium simulations of the three-dimensional Edwards-Anderson spin glass below the critical temperature. Ultrametricity, stochastic stability, and overlap equivalence impose constraints on the moments of the overlap probability densities that can be tested against numerical data. We found small deviations from the Ghirlanda Guerra predictions, which get smaller as system size increases. We also focus on the shape of the overlap distribution, comparing the numerical data to a mean-field-like prediction in which finite-size effects are taken into account by substituting delta functions with broad peaks.

Kink stability, propagation, and length-scale competition in the periodically modulated sine-gordon equation

We have examined the dynamical behavior of the kink solutions of the one-dimensional sine-Gordon equation in the presence of a spatially periodic parametric perturbation. Our study clarifies and extends the currently available knowledge on this and related nonlinear problems in four directions. First, we present the results of a numerical simulation program that are not compatible with the existence of a radiative threshold predicted by earlier calculations. Second, we carry out a perturbative calculation that helps interpret those previous predictions, enabling us to understand in depth our numerical results. Third, we apply the collective coordinate formalism to this system and demonstrate numerically that it reproduces accurately the observed kink dynamics. Fourth, we report on the occurrence of length-scale competition in this system and show how it can be understood by means of linear stability analysis. Finally, we conclude by summarizing the general physical framework that arises from our study.

Stability of a Novel Intraocular Lens Design: Comparison of Two Trifocal Lenses

PURPOSE: To compare visual outcomes, rotational stability, and centration in a randomized controlled trial in patients undergoing cataract surgery who were bilaterally implanted with two different trifocal intraocular lenses (IOLs) with a similar optical zone but different haptic shape. METHODS: Twenty-one patients (42 eyes) with cataract and less than 1.50 D of corneal astigmatism underwent implantation of one FineVision/MicoF IOL in one eye and one POD FineVision IOL in the contralateral eye (PhysIOL, Liège, Belgium) at IOA Madrid Innova Ocular, Madrid, Spain. IOL allocation was random. Outcome measures, all evaluated 3 months postoperatively, included monocular and binocular uncorrected distance (UDVA), corrected distance (CDVA), distance-corrected intermediate (DCIVA), and near (DCNVA) visual acuity (at 80, 40, and 25 cm) under photopic conditions, refraction, IOL centration, haptic rotation, dysphotopsia, objective quality of vision and aberration quantification, patient satisfaction, and spectacle independence. RESULTS: Three months postoperatively, mean monocular UDVA, CDVA, DCIVA, and DCNVA (40 cm) under photopic conditions were 0.04 ± 0.07, 0.01 ± 0.04, 0.15 ± 0.11, and 0.16 ± 0.08 logMAR for the eyes implanted with the POD FineVision IOL and 0.03 ± 0.05, 0.01 ± 0.02, 0.17 ± 0.12, and 0.14 ± 0.08 logMAR for those receiving the FineVision/MicroF IOL. Moreover, the POD FineVision IOL showed similar centration (P > .05) and better rotational stability (P < .05) than the FineVision/MicroF IOL. Regarding halos, there was a minimal but statistically significant difference, obtaining better results with FineVision/MicroF. Full spectacle independence was reported by all patients. CONCLUSIONS: This study revealed similar visual outcomes for both trifocal IOLs under test (POD FineVision and FineVision/MicroF). However, the POD FineVision IOL showed better rotational stability, as afforded by its design.

Quantitative stability of linear infinite inequality systems under block perturbations with applications to convex systems

The original motivation for this paper was to provide an efficient quantitative analysis of convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional (resp. finite-dimensional) Banach spaces and that are indexed by an arbitrary fixed set J. Parameter perturbations on the right-hand side of the inequalities are required to be merely bounded, and thus the natural parameter space is l ∞(J). Our basic strategy consists of linearizing the parameterized convex system via splitting convex inequalities into linear ones by using the Fenchel–Legendre conjugate. This approach yields that arbitrary bounded right-hand side perturbations of the convex system turn on constant-by-blocks perturbations in the linearized system. Based on advanced variational analysis, we derive a precise formula for computing the exact Lipschitzian bound of the feasible solution map of block-perturbed linear systems, which involves only the system’s data, and then show that this exact bound agrees with the coderivative norm of the aforementioned mapping. In this way we extend to the convex setting the results of Cánovas et al. (SIAM J. Optim. 20, 1504–1526, 2009) developed for arbitrary perturbations with no block structure in the linear framework under the boundedness assumption on the system’s coefficients. The latter boundedness assumption is removed in this paper when the decision space is reflexive. The last section provides the aimed application to the convex case.

Steam reforming of ethanol over bimetallic RhPt/La2O3: Long-term stability under favorable reaction conditions

Recently, the steam reforming of biofuels has been presented as a potential hydrogen source for fuel cells. Because this scenario represents an interesting opportunity for Colombia (South America), which produces large amounts of bioethanol, the steam reforming of ethanol was studied over a bimetallic RhPt/La2O3 catalyst under bulk mass transfer conditions. The effect of temperature and the initial concentrations of ethanol and water were evaluated at space velocities above 55,000 h−1 to determine the conditions that maximize the H2/CO ratio and reduce CH4 production while maintaining 100% conversion of ethanol. These requirements were accomplished when 21 mol% H2O and 3 mol% C2H5OH (steam/ethanol molar ratio = 7) were reacted at 600 °C. The catalyst stability was assessed under these reaction conditions during 120 h on stream, obtaining ethanol conversions above 99% during the entire test. The effect of both H2 and air flows as catalyst regeneration treatments were evaluated after 44 and 67 h on stream, respectively. The results showed that H2 treatment accelerated catalyst deactivation, and air regeneration increased both the catalyst stability and the H2 selectivity while decreasing CH4 generation. Fresh and spent catalyst samples were characterized by TEM/EDX, XPS, TPR, and TGA. Although the Rh and Pt in the fresh catalyst were completely reduced, the spent samples showed a partial oxidation of Rh and small amounts of carbonaceous residue. A possible Rh–Pt–Rh2O3 structure was proposed as the active site on the catalyst, which was regenerated by air treatment.

Boston, Massachusetts, 2-Dimensional Building Footprints with Height Data (from LIDAR data), 2002

This dataset consists of 2D footprints of the buildings in the metropolitan Boston area, based on tiles in the orthoimage index (orthophoto quad ID: 229890, 229894, 229898, 229902, 233886, 233890, 233894, 233898, 233902, 237890, 237894, 237898, 237902, 241890, 241894, 241898, 241902, 245898, 245902). This data set was collected using 3Di's Digital Airborne Topographic Imaging System II (DATIS II). Roof height and footprint elevation attributes (derived from 1-meter resolution LIDAR (LIght Detection And Ranging) data) are included as part of each building feature. This data can be combined with other datasets to create 3D representations of buildings and the surrounding environment.