Geometric diagnostics of complex patterns: Spiral defect chaos

Motivated by the observation of spiral patterns in a wide range of physical, chemical, and biological systems, we present an automated approach that aims at characterizing quantitatively spiral-like elements in complex stripelike patterns. The approach provides the location of the spiral tip and the size of the spiral arms in terms of their arc length and their winding number. In addition, it yields the number of pattern components (Betti number of order 1), as well as their size and certain aspects of their shape. We apply the method to spiral defect chaos in thermally driven Rayleigh- Bénard convection and find that the arc length of spirals decreases monotonically with decreasing Prandtl number of the fluid and increasing heating. By contrast, the winding number of the spirals is nonmonotonic in the heating. The distribution function for the number of spirals is significantly narrower than a Poisson distribution. The distribution function for the winding number shows approximately an exponential decay. It depends only weakly on the heating, but strongly on the Prandtl number. Large spirals arise only for larger Prandtl numbers. In this regime the joint distribution for the spiral length and the winding number exhibits a three-peak structure, indicating the dominance of Archimedean spirals of opposite sign and relatively straight sections. For small Prandtl numbers the distribution function reveals a large number of small compact pattern components.

Defect chaos and bursts: Hexagonal rotating convection and the complex Ginzburg-Landau equation

We employ numerical computations of the full Navier-Stokes equations to investigate non-Boussinesq convection in a rotating system using water as the working fluid. We identify two regimes. For weak non- Boussinesq effects the Hopf bifurcation from steady to oscillating (whirling) hexagons is supercritical and typical states exhibit defect chaos that is systematically described by the cubic complex Ginzburg-Landau equation. For stronger non-Boussinesq effects the Hopf bifurcation becomes subcritical and the oscil- lations exhibit localized chaotic bursting, which is modeled by a quintic complex Ginzburg-Landau equation.

The influence of axial microgravity on the breakage of axisymmetric slender liquid bridges

The dynamics of inviscid, axisymmetric liquid bridges permits a simplified treatment if the bridge is long enough. Under such condition the evolution of the liquid zone is satisfactorily explained through a non-linear one-dimensional model. In the case of breaking, the one-dimensional model fails when the neck radius of the liquid column is close to zero; however, the model allows the calculation of the time variation of the liquid-bridge interface as well as of the fluid velocity field and, because the last part of the evolution is not needed, the overall results such as the breaking time and the volume of each of the two drops resulting after breakage can be calculated. In this paper numerical results concerning the behavior of clinical liquid bridges subjected to a small axial gravitational field are presented.

Axisymmetric long liquid bridges in a time-dependent microgravity field

This paper deals with the dynamics of liquid bridges when subjected to an oscillatory microgravity field. The analysis has been performed by using a one-dimensional slice model, already used in liquid bridge problems, which allows to calculate not only the resonance frequencies of a wide range of such fluid configurations but also the dependence of the dynamic response of the liquid bridge on the frequency on the imposed perturbations. Theoretical results are compared with experimental ones obtained aboard Spacelab-Dl, the agreement between theoretical and experimental results being satisfactory

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.

Direct visualization of antigen-specific T cells: HTLV-1 Tax11–19- specific CD8+ T cells are activated in peripheral blood and accumulate in cerebrospinal fluid from HAM/TSP patients

Human T lymphotropic virus type 1 (HTLV-1) -associated myelopathy/tropic spastic paraparesis is a demyelinating inflammatory neurologic disease associated with HTLV-1 infection. HTLV-1 Tax11–19-specific cytotoxic T cells have been isolated from HLA-A2-positive patients. We have used a peptide-loaded soluble HLA-A2–Ig complex to directly visualize HTLV-1 Tax11–19-specific T cells from peripheral blood and cerebrospinal fluid without in vitro stimulation. Five of six HTLV-1-associated myelopathy/tropic spastic paraparesis patients carried a significant number (up to 13.87%) of CD8+ lymphocytes specific for the HTLV-1 Tax11–19 peptide in their peripheral blood, which were not found in healthy controls. Simultaneous comparison of peripheral blood and cerebrospinal fluid from one patient revealed 2.5-fold more Tax11–19-specific T cells in the cerebrospinal fluid (23.7% vs. 9.4% in peripheral blood lymphocyte). Tax11–19-specific T cells were seen consistently over a 9-yr time course in one patient as far as 19 yrs after the onset of clinical symptoms. Further analysis of HTLV-1 Tax11–19-specific CD8+ T lymphocytes in HAM/TSP patients showed different expression patterns of activation markers, intracellular TNF-α and γ-interferon depending on the severity of the disease. Thus, visualization of antigen-specific T cells demonstrates that HTLV-1 Tax11–19-specific CD8+ T cells are activated, persist during the chronic phase of the disease, and accumulate in cerebrospinal fluid, showing their pivotal role in the pathogenesis of this neurologic disease.

Complex gangliosides are essential in spermatogenesis of mice: Possible roles in the transport of testosterone

Mice, homozygous for disrupted ganglioside GM2/GD2 synthase (EC 2.4.1.94) gene and lacking all complex gangliosides, do not display any major neurologic abnormalities. Further examination of these mutant mice, however, revealed that the males were sterile and aspermatogenic. In the seminiferous tubules of the mutant mice, a number of multinuclear giant cells and vacuolated Sertoli cells were observed. The levels of testosterone in the serum of these mice were very low, although testosterone production equaled that produced in wild-type mice. Testosterone was found to be accumulated in interstitial Leydig cells, and intratesticularly injected testosterone was poorly drained in seminiferous fluid in the mutant mice. These results suggested that complex gangliosides are essential in the transport of testosterone to the seminiferous tubules and bloodstream from Leydig cells. Our results provide insights into roles of gangliosides in vivo.

Domains of the Rsp5 Ubiquitin-Protein Ligase Required for Receptor-mediated and Fluid-Phase Endocytosis

Yeast Rsp5p and its mammalian homologue, Nedd4, are hect domain ubiquitin-protein ligases (E3s) required for the ubiquitin-dependent endocytosis of plasma membrane proteins. Because ubiquitination is sufficient to induce internalization, E3-mediated ubiquitination is a key regulatory event in plasma membrane protein endocytosis. Rsp5p is an essential, multidomain protein containing an amino-terminal C2 domain, three WW protein-protein interaction domains, and a carboxy-terminal hect domain that carries E3 activity. In this study, we demonstrate that Rsp5p is peripherally associated with membranes and provide evidence that Rsp5p functions as part of a multimeric protein complex. We define the function of Rsp5p and its domains in the ubiquitin-dependent internalization of the yeast α-factor receptor, Ste2p. Temperature-sensitive rsp5 mutants were unable to ubiquitinate or to internalize Ste2p at the nonpermissive temperature. Deletion of the entire C2 domain had no effect on α-factor internalization; however, point mutations in any of the three WW domains impaired both receptor ubiquitination and internalization. These observations indicate that the WW domains play a role in the important regulatory event of selecting phosphorylated proteins as endocytic cargo. In addition, mutations in the C2 and WW1 domains had more severe defects on transport of fluid-phase markers to the vacuole than on receptor internalization, suggesting that Rsp5p functions at multiple steps in the endocytic pathway.

Order and disorder in fluid motion.

The development of complex states of fluid motion is illustrated by reviewing a series of experiments, emphasizing film flows, surface waves, and thermal convection. In one dimension, cellular patterns bifurcate to states of spatiotemporal chaos. In two dimensions, even ordered patterns can be surprisingly intricate when quasiperiodic patterns are included. Spatiotemporal chaos is best characterized statistically, and methods for doing so are evolving. Transport and mixing phenomena can also lead to spatial complexity, but the degree depends on the significance of molecular or thermal diffusion.

Polymer Fluid Dynamics: Continuum and Molecular Appoaches

To solve problems in polymer fluid dynamics, one needs the equation of continuity, motion, and energy. The last two equations contain the stress tensor and the heat-flux vector for the material. There are two ways to formulate the stress tensor: (1) one can write a continuum expression for the stress tensor in terms of kinematic tensors, or (2) one can select a molecular model that represents the polymer molecule, and then develop an expression for the stress tensor from kinetic theory. The advantage of the kinetic theory approach is that one gets information about the relation between the molecular structure of the polymers and the rheological properties. In this review, we restrict the discussion primarily to the simplest stress tensor expressions or “constitutive equations” containing from two to four adjustable parameters, although we do indicate how these formulations may be extended to give more complicated expressions. We also explore how these simplest expressions are recovered as special cases of a more general framework, the Oldroyd 8-constant model. The virtue of studying the simplest models is that we can discover some general notions as to which types of empiricisms or which types of molecular models seem to be worth investigating further. We also explore equivalences between continuum and molecular approaches. We restrict the discussion to several types of simple flows, such as shearing flows and extensional flows. These are the flows that are of greatest importance in industrial operations. Furthermore, if these simple flows cannot be well described by continuum or molecular models, then it is not necessary to lavish time and energy to apply them to more complex flow problems.

Chemistry and fluid inclusions of the sheeted dike comples of ODP Holes 137-504B and 140-504B

Fluid inclusions in variably altered diabase recovered from Ocean Drilling Program Legs 137 and 140 at Hole 504B, Costa Rica Rift, exhibit fluid salinities up to 3.7 times that of seawater values (11.7 wt% NaCl equivalent) and exhibit uncorrected homogenization temperatures of 125°C to 202°C. The liquid-dominated inclusions commonly are entrapped in zones of secondary plagioclase and may be primary in origin. Fluid salinities are similar to compositions of fluids venting on the seafloor (0.4-7.0 wt% NaCl) and overlap with those measured in metabasalt samples recovered from near the Kane Fracture Zone on the Mid-Atlantic Ridge and from the Troodos ophiolite, Cyprus. The salinity variations may reflect hydration reactions involving formation of secondary mineral assemblages under rock-dominated conditions, which modify the ionic strength of hydrothermal fluids by consuming or liberating water and chloride ion. Rare CO2-CH4-bearing inclusions, subjacent to zones where talc after olivine becomes an important secondary mineral phase (1700 mbsf), may have formed due to local interaction of seawater and olivine at low water to rock ratios. Corrected average fluid inclusion homogenization temperatures exhibit a gradient from 159°C at a depth of 1370 mbsf to 183°C at a depth of 1992 mbsf and are in apparent equilibrium with the present conductive downhole temperatures. These data indicate that fluid inclusions may be used to estimate downhole temperatures if logging data are unavailable. The compositional and thermal evolution of the diabase-hosted fluids may reflect late-stage, off-axis circulation and conductive heating of compositionally modified seawater in the sheeted dike complex at Hole 504B.

Phosphate forms an unusual tripodal complex with the Fe-Mn center of sweet potato purple acid phosphatase

Purple acid phosphatases (PAPs) are a family of binuclear metalloenzymes that catalyze the hydrolysis of phosphoric acid esters and anhydrides. A PAP in sweet potato has a unique, strongly antiferromagnetically coupled Fe(III)-Mn(II) center and is distinguished from other PAPs by its increased catalytic efficiency for a range of activated and unactivated phosphate esters, its strict requirement for Mn(II), and the presence of a mu-oxo bridge at pH 4.90. This enzyme displays maximum catalytic efficiency (k(cat)/K-m) at pH 4.5, whereas its catalytic rate constant (k(cat)) is maximal at near-neutral pH, and, in contrast to other PAPs, its catalytic parameters are not dependent on the pK(a) of the leaving group. The crystal structure of the phosphate-bound Fe(III)-Mn(II) PAP has been determined to 2.5-Angstrom resolution (final R-free value of 0.256). Structural comparisons of the active site of sweet potato, red kidney bean, and mammalian PAPs show several amino acid substitutions in the sweet potato enzyme that can account for its increased catalytic efficiency. The phosphate molecule binds in an unusual tripodal mode to the two metal ions, with two of the phosphate oxygen atoms binding to Fe(III) and Mn(II), a third oxygen atom bridging the two metal ions, and the fourth oxygen pointing toward the substrate binding pocket. This binding mode is unique among the known structures in this family but is reminiscent of phosphate binding to urease and of sulfate binding to A protein phosphatase. The structure and kinetics support the hypothesis that the bridging oxygen atom initiates hydrolysis.

Prediction of slurry transport in SAG mills using SPH fluid flow in a dynamic DEM based porous media

DEM modelling of the motion of coarse fractions of the charge inside SAG mills has now been well established for more than a decade. In these models the effect of slurry has broadly been ignored due to its complexity. Smoothed particle hydrodynamics (SPH) provides a particle based method for modelling complex free surface fluid flows and is well suited to modelling fluid flow in mills. Previous modelling has demonstrated the powerful ability of SPH to capture dynamic fluid flow effects such as lifters crashing into slurry pools, fluid draining from lifters, flow through grates and pulp lifter discharge. However, all these examples were limited by the ability to model only the slurry in the mill without the charge. In this paper, we represent the charge as a dynamic porous media through which the SPH fluid is then able to flow. The porous media properties (specifically the spatial distribution of porosity and velocity) are predicted by time averaging the mill charge predicted using a large scale DEM model. This allows prediction of transient and steady state slurry distributions in the mill and allows its variation with operating parameters, slurry viscosity and slurry volume, to be explored. (C) 2006 Published by Elsevier Ltd.

Using computational fluid dynamics in combating erosion-corrosion

Computational fluid dynamics was used to search for the links between the observed pattern of attack seen in a bauxite refinery's heat exchanger headers and the hydrodynamics inside the header. Validation of the computational fluid dynamics results was done by comparing then with flow parameters measured in a 1:5 scale model of the first pass header in the laboratory. Computational fluid dynamics simulations were used to establish hydrodynamic similarity between the 1:5 scale and full scale models of the first pass header. It was found that the erosion-corrosion damage seen at the tubesheet of the first pass header was a consequence of increased levels of turbulence at the tubesheet caused by a rapidly turning flow. A prismatic flow corrections device introduced in the past helped in rectifying the problem at the tubesheet but exaggerated the erosion-corrosion problem at the first pass header shell. A number of alternative flow correction devices were tested using computational fluid dynamics. Axial ribbing in the first pass header and an inlet flow diffuser have shown the best performance and were recommended for implementation. Computational fluid dynamics simulations have revealed a smooth orderly low turbulence flow pattern in the second, third and fourth pass as well as the exit headers where no erosion-corrosion was seen in practice. This study has confirmed that near-wall turbulence intensity, which can be successfully predicted by using computational fluid dynamics, is a good hydrodynamic predictor of erosion-corrosion damage in complex geometries. (c) 2006 Published by Elsevier Ltd.

Use of computational fluid dynamics in the design of bubble column reactors

Investigations into the modelling techniques that depict the transport of discrete phases (gas bubbles or solid particles) and model biochemical reactions in a bubble column reactor are discussed here. The mixture model was used to calculate gas-liquid, solid-liquid and gasliquid-solid interactions. Multiphase flow is a difficult phenomenon to capture, particularly in bubble columns where the major driving force is caused by the injection of gas bubbles. The gas bubbles cause a large density difference to occur that results in transient multi-dimensional fluid motion. Standard design procedures do not account for the transient motion, due to the simplifying assumptions of steady plug flow. Computational fluid dynamics (CFD) can assist in expanding the understanding of complex flows in bubble columns by characterising the flow phenomena for many geometrical configurations. Therefore, CFD has a role in the education of chemical and biochemical engineers, providing the examples of flow phenomena that many engineers may not experience, even through experimentation. The performance of the mixture model was investigated for three domains (plane, rectangular and cylindrical) and three flow models (laminar, k-e turbulence and the Reynolds stresses). mThis investigation raised many questions about how gas-liquid interactions are captured numerically. To answer some of these questions the analogy between thermal convection in a cavity and gas-liquid flow in bubble columns was invoked. This involved modelling the buoyant motion of air in a narrow cavity for a number of turbulence schemes. The difference in density was caused by a temperature gradient that acted across the width of the cavity. Multiple vortices were obtained when the Reynolds stresses were utilised with the addition of a basic flow profile after each time step. To implement the three-phase models an alternative mixture model was developed and compared against a commercially available mixture model for three turbulence schemes. The scheme where just the Reynolds stresses model was employed, predicted the transient motion of the fluids quite well for both mixture models. Solid-liquid and then alternative formulations of gas-liquid-solid model were compared against one another. The alternative form of the mixture model was found to perform particularly well for both gas and solid phase transport when calculating two and three-phase flow. The improvement in the solutions obtained was a result of the inclusion of the Reynolds stresses model and differences in the mixture models employed. The differences between the alternative mixture models were found in the volume fraction equation (flux and deviatoric stress tensor terms) and the viscosity formulation for the mixture phase.