Front dynamics in turbulent media

A study of a stable front propagating in a turbulent medium is presented. The front is generated through a reaction-diffusion equation, and the turbulent medium is statistically modeled using a Langevin equation. Numerical simulations indicate the presence of two different dynamical regimes. These regimes appear when the turbulent flow either wrinkles a still rather sharp propagating interfase or broadens it. Specific dependences of the propagating velocities on stirring intensities appropriate to each case are found and fitted when possible according to theoretically predicted laws. Different turbulent spectra are considered.

Three-dimensional aspects of fluid flows in channels. II. Effects of meniscus and thin film regimes on viscous fingers

We perform a three-dimensional study of steady state viscous fingers that develop in linear channels. By means of a three-dimensional lattice-Boltzmann scheme that mimics the full macroscopic equations of motion of the fluid momentum and order parameter, we study the effect of the thickness of the channel in two cases. First, for total displacement of the fluids in the channel thickness direction, we find that the steady state finger is effectively two-dimensional and that previous two-dimensional results can be recovered by taking into account the effect of a curved meniscus across the channel thickness as a contribution to surface stresses. Second, when a thin film develops in the channel thickness direction, the finger narrows with increasing channel aspect ratio in agreement with experimental results. The effect of the thin film renders the problem three-dimensional and results deviate from the two-dimensional prediction.

Diffusion of passive scalars under stochastic convection

The diffusion of passive scalars convected by turbulent flows is addressed here. A practical procedure to obtain stochastic velocity fields with well¿defined energy spectrum functions is also presented. Analytical results are derived, based on the use of stochastic differential equations, where the basic hypothesis involved refers to a rapidly decaying turbulence. These predictions are favorable compared with direct computer simulations of stochastic differential equations containing multiplicative space¿time correlated noise.

Three-dimensional aspects of fluid flows in channels. I. Meniscus and thin film regimes

We study the forced displacement of a fluid-fluid interface in a three-dimensional channel formed by two parallel solid plates. Using a lattice-Boltzmann method, we study situations in which a slip velocity arises from diffusion effects near the contact line. The difference between the slip and channel velocities determines whether the interface advances as a meniscus or a thin film of fluid is left adhered to the plates. We find that this effect is controlled by the capillary and Péclet numbers. We estimate the crossover from a meniscus to a thin film and find good agreement with numerical results. The penetration regime is examined in the steady state. We find that the occupation fraction of the advancing finger relative to the channel thickness is controlled by the capillary number and the viscosity contrast between the fluids. For high viscosity contrast, lattice-Boltzmann results agree with previous results. For zero viscosity contrast, we observe remarkably narrow fingers. The shape of the finger is found to be universal.

Essays on the treatment of cash flows under stochastic interest rates

Abstract This paper shows how to calculate recursively the moments of the accumulated and discounted value of cash flows when the instantaneous rates of return follow a conditional ARMA process with normally distributed innovations. We investigate various moment based approaches to approximate the distribution of the accumulated value of cash flows and we assess their performance through stochastic Monte-Carlo simulations. We discuss the potential use in insurance and especially in the context of Asset-Liability Management of pension funds.

Stochastic resonance in a suspension of magnetic dipoles under shear flow

We show that a magnetic dipole in a shear flow under the action of an oscillating magnetic field displays stochastic resonance in the linear response regime. To this end, we compute the classical quantifiers of stochastic resonance, i.e., the signal to noise ratio, the escape time distribution, and the mean first passage time. We also discuss the limitations and role of the linear response theory in its applications to the theory of stochastic resonance.

Three-dimensional aspects of fluid flows in channels. II. Effects of meniscus and thin film regimes on viscous fingers

We perform a three-dimensional study of steady state viscous fingers that develop in linear channels. By means of a three-dimensional lattice-Boltzmann scheme that mimics the full macroscopic equations of motion of the fluid momentum and order parameter, we study the effect of the thickness of the channel in two cases. First, for total displacement of the fluids in the channel thickness direction, we find that the steady state finger is effectively two-dimensional and that previous two-dimensional results can be recovered by taking into account the effect of a curved meniscus across the channel thickness as a contribution to surface stresses. Second, when a thin film develops in the channel thickness direction, the finger narrows with increasing channel aspect ratio in agreement with experimental results. The effect of the thin film renders the problem three-dimensional and results deviate from the two-dimensional prediction.

Three-dimensional aspects of fluid flows in channels. I. Meniscus and thin film regimes

We study the forced displacement of a fluid-fluid interface in a three-dimensional channel formed by two parallel solid plates. Using a lattice-Boltzmann method, we study situations in which a slip velocity arises from diffusion effects near the contact line. The difference between the slip and channel velocities determines whether the interface advances as a meniscus or a thin film of fluid is left adhered to the plates. We find that this effect is controlled by the capillary and Péclet numbers. We estimate the crossover from a meniscus to a thin film and find good agreement with numerical results. The penetration regime is examined in the steady state. We find that the occupation fraction of the advancing finger relative to the channel thickness is controlled by the capillary number and the viscosity contrast between the fluids. For high viscosity contrast, lattice-Boltzmann results agree with previous results. For zero viscosity contrast, we observe remarkably narrow fingers. The shape of the finger is found to be universal.

Fluid-rock-strain feedbacks in extensional shear zones

La présence de fluide météorique synchrone à l'activité du détachement (Farmin, 2003 ; Mulch et al., 2007 ; Gébelin et al., 2011), implique que les zones de cisaillement sont des systèmes ouverts avec des cellules de convections à l'échelle crustale et un intense gradient géothermique au sein du détachement (Morrison et Anderson, 1998, Gottardi et al., 2011). De plus, les réactions métamorphiques liées à des infiltrations fluides dans les zones de cisaillement extensionnel peuvent influencer les paramètres rhéologiques du système (White and Knipe, 1978), et impliquer la localisation de la déformation dans la croûte. Dans ce manuscrit, deux zones de cisaillement infiltrées par des fluides météoriques sont étudiées, l'une étant largement quartzitique, et l'autre de nature granitique ; les relations entre déformation, fluides, et roches s'appuient sur des approches structurales, microstructurales, chimiques et isotopiques. L'étude du détachement du Columbia river (WA, USA) met en évidence que la déformation mylonitique se développe en un million d'années. La phase de cisaillement principal s'effectue à 365± 30°C d'après les compositions isotopiques en oxygène du quartz et de la muscovite. Ces minéraux atteignent l'équilibre isotopique lors de leur recristallisation dynamique contemporaine à la déformation. La zone de cisaillement enregistre une baisse de température, remplaçant le mécanisme de glissement par dislocation par celui de dissolution- précipitation dans les derniers stades de l'activité du détachement. La dynamique de circulation fluide bascule d'une circulation pervasive à chenalisée, ce qui engendre localement la rupture des équilibres d'échange isotopiques. La zone de cisaillement de Bitterroot (MT, USA) présente une zone mylonitique de 600m d'épaisseur, progressant des protomylonites aux ultramylonites. L'intensité de la localisation de la déformation se reflète directement sur l'hydratation des feldspaths, réaction métamorphique majeure dite de « rock softening ». Une étude sur roche totale indique des transferts de masse latéraux au sein des mylonites, et d'importantes pertes de volume dans les ultramylonites. La composition isotopique en hydrogène des phyllosilicates met en évidence la présence (1) d'une source magmatique/métamorphique originelle, caractérisée par les granodiorites ayant conservé leur foliation magmatique, jusqu'aux protomylonites, et (2) une source météorique qui tamponne les valeurs des phyllosilicates des fabriques mylonitiques jusqu'aux veines de quartz non-déformées. Les compositions isotopiques en oxygène des minéraux illustrent le tamponnement de la composition du fluide météorique par l'encaissant. Ce phénomène cesse lors du processus de chloritisation de la biotite, puisque les valeurs des chlorites sont extrêmement négatives (-10 per mil). La thermométrie isotopique indique une température d'équilibre isotopique de la granodiorite entre 600-500°C, entre 500-300°C dans les mylonites, et entre 300 et 200°C dans les fabriques cassantes (cataclasites et veines de quartz). Basé sur les résultats issus de ce travail, nous proposons un modèle général d'interactions fluide-roches-déformation dans les zones de détachements infiltrées par des fluides météoriques. Les zones de détachements évoluent rapidement (en quelques millions d'années) au travers de la transition fragile-ductile ; celle-ci étant partiellement contrôlée par l'effet thermique des circulations de fluide météoriques. Les systèmes de détachements sont des lieux où la déformation et les circulations fluides sont couplées ; évoluant rapidement vers une localisation de la déformation, et de ce fait, une exhumation efficace. - The presence of meteoric fluids synchronous with the activity of extensional detachment zones (Famin, 2004; Mulch et al., 2007; Gébelin et al., 2011) implies that extensional systems involve fluid convection at a crustal scale, which results in high geothermal gradients within active detachment zones (Morrison and Anderson, 1998, Gottardi et al., 2011). In addition, the metamorphic reactions related to fluid infiltration in extensional shear zones can influence the rheology of the system (White and Knipe, 1978) and ultimately how strain localizes in the crust. In this thesis, two shear zones that were permeated by meteoric fluids are studied, one quartzite-dominated, and the other of granitic composition; the relations between strain, fluid, and evolving rock composition are addressed using structural, microstructural, and chemical/isotopic measurements. The study of the Columbia River detachment that bounds the Kettle core complex (Washington, USA) demonstrates that the mylonitic fabrics in the 100 m thick quartzite- dominated detachment footwall developed within one million years. The main shearing stage occurred at 365 ± 30°C when oxygen isotopes of quartz and muscovite equilibrated owing to coeval deformation and dynamic recrystallization of these minerals. The detachment shear zone records a decrease in temperature, and dislocation creep during detachment shearing gave way to dissolution-precipitation and fracturing in the later stages of detachment activity. Fluid flow switched from pervasive to channelized, leading to isotopic disequilibrium between different minerals. The Bitterroot shear zone detachment (Montana, USA) developed a 600 m thick mylonite zone, with well-developed transitions from protomylonite to ultramylonite. The localization of deformation relates directly to the intensity of feldspar hydration, a major rock- softening metamorphic reaction. Bulk-rock analyses of the mylonitic series indicate lateral mass transfer in the mylonite (no volume change), and significant volume loss in ultramylonite. The hydrogen isotope composition of phyllosilicates shows (1) the presence of an initial magmatic/metamorphic source characterized by the granodiorite in which a magmatic, and gneissic (protomylonite) foliation developed, and (2) a meteoric source that buffers the values of phyllosilicates in mylonite, ultramylonite, cataclasite, and deformed and undeformed quartz veins. The mineral oxygen isotope compositions were buffered by the host-rock compositions until chloritization of biotite started; the chlorite oxygen isotope values are negative (-10 per mil). Isotope thermometry indicates a temperature of isotopic equilibrium of the granodiorite between 600-500°C, between 500-300°C in the mylonite, and between 300 and 200°C for brittle fabrics (cataclasite and quartz veins). Results from this work suggest a general model for fluid-rock-strain feedbacks in detachment systems that are permeated by meteoric fluids. Phyllosilicates have preserved in their hydrogen isotope values evidence for the interaction between rock and meteoric fluids during mylonite development. Fluid flow generates mass transfer along the tectonic anisotropy, and mylonites do not undergo significant volume change, except locally in ultramylonite zones. Hydration of detachment shear zones attends mechanical grain size reduction and enhances strain softening and localization. Self-exhuming detachment shear zones evolve rapidly (a few million years) through the transition from ductile to brittle, which is partly controlled by the thermal effect of circulating surface fluids. Detachment systems are zones in the crust where strain and fluid flow are coupled; these systems. evolve rapidly toward strain localization and therefore efficient exhumation.

Effets de la perfusion de facteurs natriurétiques auriculaires synthétiques sur quelques flux régionaux chez le volontaire sain [Effect of synthetic atrial natriuretic factors on various regional blood flows in the healthy subject]

The effects of continuous infusions of 2 synthetic atrial natriuretic peptides Ile12-(3-28) (rANP) and Meth12-(3-28) (hANP) eicosahexapeptides on blood pressure, heart rate, skin blood flow, glomerular filtration rate, renal plasma flow, apparent hepatic blood flow, and carotid blood flow were evaluated in normal volunteers. A rANP infusion at increasing rates (1-40 micrograms/min) induced a decrease in blood pressure, an increase in heart rate and in skin blood flow linearly related to the dose administered. In contrast, hANP infusion at 1 microgram/min for 4 hours induced an initial increase followed by a secondary fall in skin blood flow without blood pressure changes. A 4-hour rANP infusion at 0.5 and 5 mcg/min did not alter glomerular filtration rate but induced a delayed and dose-related fall in renal plasma flow from 531 to 461 (p less than 0.05), and from 554 to 342 ml/min (p less than 0.001) respectively, with a consequential rise in the filtration fraction. The 5 mcg/min dose furthermore significantly reduced blood pressure following a latency period of 2.5 hours. A 2-hours rANP infusion at 0.5 micrograms/min induced a fall in apparent hepatic blood flow from 1,087 to 863 ml/min (p less than 0.01), without simultaneously altering blood pressure. Similarly, a 2-hour hANP infusion at 2 micrograms/min altered neither blood pressure nor carotid blood flow. In conclusion, ANP infusion induced changes in systemic and regional hemodynamics varying in direction, intensity and duration.

Viscoelasticity in Achilles Tendonopathy: Quantitative Assessment by Using Real-time Shear-Wave Elastography.

Purpose To investigate the differences in viscoelastic properties between normal and pathologic Achilles tendons ( AT Achilles tendon s) by using real-time shear-wave elastography ( SWE shear-wave elastography ). Materials and Methods The institutional review board approved this study, and written informed consent was obtained from 25 symptomatic patients and 80 volunteers. One hundred eighty ultrasonographic (US) and SWE shear-wave elastography studies of AT Achilles tendon s without tendonopathy and 30 studies of the middle portion of the AT Achilles tendon in patients with tendonopathy were assessed prospectively. Each study included data sets acquired at B-mode US (tendon morphology and cross-sectional area) and SWE shear-wave elastography (axial and sagittal mean velocity and relative anisotropic coefficient) for two passively mobilized ankle positions. The presence of AT Achilles tendon tears at B-mode US and signal-void areas at SWE shear-wave elastography were noted. Results Significantly lower mean velocity was shown in tendons with tendonopathy than in normal tendons in the relaxed position at axial SWE shear-wave elastography (P < .001) and in the stretched position at sagittal (P < .001) and axial (P = .0026) SWE shear-wave elastography . Tendon softening was a sign of tendonopathy in relaxed AT Achilles tendon s when the mean velocity was less than or equal to 4.06 m · sec(-1) at axial SWE shear-wave elastography (sensitivity, 54.2%; 95% confidence interval [ CI confidence interval ]: 32.8, 74.4; specificity, 91.5%; 95% CI confidence interval : 86.3, 95.1) and less than or equal to 5.70 m · sec(-1) at sagittal SWE shear-wave elastography (sensitivity, 41.7%; 95% CI confidence interval : 22.1, 63.3; specificity, 81.8%; 95% CI confidence interval : 75.3, 87.2) and in stretched AT Achilles tendon s, when the mean velocity was less than or equal to 4.86 m · sec(-1) at axial SWE shear-wave elastography (sensitivity, 66.7%; 95% CI confidence interval : 44.7, 84.3; specificity, 75.6%; 95% CI confidence interval : 68.5, 81.7) and less than or equal to 14.58 m · sec(-1) at sagittal SWE shear-wave elastography (sensitivity, 58.3%; 95% CI confidence interval : 36.7, 77.9; specificity, 83.5%; 95% CI confidence interval : 77.2, 88.7). Anisotropic results were not significantly different between normal and pathologic AT Achilles tendon s. Six of six (100%) partial-thickness tears appeared as signal-void areas at SWE shear-wave elastography . Conclusion Whether the AT Achilles tendon was relaxed or stretched, SWE shear-wave elastography helped to confirm and quantify pathologic tendon softening in patients with tendonopathy in the midportion of the AT Achilles tendon and did not reveal modifications of viscoelastic anisotropy in the tendon. Tendon softening assessed by using SWE shear-wave elastography appeared to be highly specific, but sensitivity was relatively low. © RSNA, 2014.

Diffusion in spatially and temporarily inhomogeneous media: Effects of turbulent mixing

We consider diffusion of a passive substance C in a phase-separating nonmiscible binary alloy under turbulent mixing. The substance is assumed to have different diffusion coefficients in the pure phases A and B, leading to a spatially and temporarily dependent diffusion ¿coefficient¿ in the diffusion equation plus convective term. In this paper we consider especially the effects of a turbulent flow field coupled to both the Cahn-Hilliard type evolution equation of the medium and the diffusion equation (both, therefore, supplemented by a convective term). It is shown that the formerly observed prolonged anomalous diffusion [H. Lehr, F. Sagués, and J.M. Sancho, Phys. Rev. E 54, 5028 (1996)] is no longer seen if a flow of sufficient intensity is supplied.

Stochastic generation of homogeneous isotropic turbulence with well-defined-spectra

A precise and simple computational model to generate well-behaved two-dimensional turbulent flows is presented. The whole approach rests on the use of stochastic differential equations and is general enough to reproduce a variety of energy spectra and spatiotemporal correlation functions. Analytical expressions for both the continuous and the discrete versions, together with simulation algorithms, are derived. Results for two relevant spectra, covering distinct ranges of wave numbers, are given.