Semilinear functional difference equations with infinite delay

We obtain boundedness and asymptotic behavior of solutions for semilinear functional difference equations with infinite delay. Applications to Volterra difference equations with infinite delay are shown. (C) 2011 Elsevier Ltd. All rights reserved.

Mass-transport deposits on Mediterranean continental margins

Extensive mass transport deposits and multiple slide scars testify widespread and recurrent submarine sediment failures occurring during the late Quaternary on the SW-Adriatic and SE-Sicilian margins. These mass movements and their consequences contributed to shape the continental slopes and fill the basins with characteristic signatures. Geomorphological, seismo-stratigraphic, sedimentological and biostratigraphic data provide clues to: 1) define distinct failure mechanisms investigating on factors that determine dissimilar organization of coeval displaced masses, 2) reconstruct successive phases of failure stressing on the same location where slide scars crosscut and mass-transport deposits overlap, 3) analyze regional setting and indicate the most suitable place where to calculate mass wasting frequency. Discussions on the role of fluid flow, currents activity and tectonic deformation determine a wider view on the construction of the studied continental margins.

Zum Transport von partikelgebundenen Schadstoffen in der ungesättigten Zone

Bei einer Risikoabschätzung bezüglich einer Gefährdung des Schutzgutes Grundwasser müssen alle relevanten Transportpfade, auf denen Schadstoffe durch die Bodenzone bis ins Grundwasser verlagert werden, identifiziert und quantifiziert werden. Die Verlagerung von Schadstoffen gebunden an mobile Partikel im Sickerwasser wird dabei oft vernachlässigt. In dieser Arbeit wurden sowohl experimentelle Untersuchungen zum Partikeltransport in der Bodenzone als auch Szenarienmodellierungen hinsichtlich der Wechselwirkung Partikel/Schadstoff durchgeführt. Die experimentellen ungesättigten Säulenversuche wurden unter naturnahen stationären und instationären hydraulischen und hydrochemischen Bedingungen durchgeführt. Dabei wurde der Einfluss der Parameter Durchmesser Bodenmatrix, Partikelgröße, Beregnungsintensität, Oberflächenspannung und Hydrochemie auf den Transport von natürlichen und synthetischen Partikeln untersucht. Des Weiteren wurden Untersuchungen zur partikelgebundenen Verlagerung von Phenanthren durchgeführt. In einer numerischen Szenarienmodellierung mit dem Modell SMART wurde untersucht, unter welchen Randbedingungen der Transport von Partikeln gleichzeitig zu signifikanten partikelgebundenen Schadstoffkonzentrationen im Grundwasser führt. Dabei wurden die Parameter Lithologie Partikel/Boden, Hydrophobizität Schadstoff, Partikelkonzentration, Partikeldurchmesser sowie Körnung Bodenmatrix variiert. Die Ergebnisse dieser Arbeit zeigen, dass der partikelgebundene Schadstofftransportpfad in der ungesättigten Bodenzone in verschiedenen Szenarien den Anteil mobiler Schadstoffe, die mit dem Sickerwasser ins Grundwasser gelangen, signifikant erhöht. Auf Basis der experimentellen und theoretischen Untersuchungen wurde ein zweistufiges Bewertungsschema entwickelt, das bereits im Vorfeld einer Risikoabschätzung als Entscheidungshilfe hinsichtlich der Relevanz einer Mobilisierung, eines Transports und des Rückhalts von partikelgebundenen Schadstoffen in der ungesättigten Zone dient.

Dynamic development of hydrofractures

Natürliche hydraulische Bruchbildung ist in allen Bereichen der Erdkruste ein wichtiger und stark verbreiteter Prozess. Sie beeinflusst die effektive Permeabilität und Fluidtransport auf mehreren Größenordnungen, indem sie hydraulische Konnektivität bewirkt. Der Prozess der Bruchbildung ist sowohl sehr dynamisch als auch hoch komplex. Die Dynamik stammt von der starken Wechselwirkung tektonischer und hydraulischer Prozesse, während sich die Komplexität aus der potentiellen Abhängigkeit der poroelastischen Eigenschaften von Fluiddruck und Bruchbildung ergibt. Die Bildung hydraulischer Brüche besteht aus drei Phasen: 1) Nukleation, 2) zeitabhängiges quasi-statisches Wachstum so lange der Fluiddruck die Zugfestigkeit des Gesteins übersteigt, und 3) in heterogenen Gesteinen der Einfluss von Lagen unterschiedlicher mechanischer oder sedimentärer Eigenschaften auf die Bruchausbreitung. Auch die mechanische Heterogenität, die durch präexistierende Brüche und Gesteinsdeformation erzeugt wird, hat großen Einfluß auf den Wachstumsverlauf. Die Richtung der Bruchausbreitung wird entweder durch die Verbindung von Diskontinuitäten mit geringer Zugfestigkeit im Bereich vor der Bruchfront bestimmt, oder die Bruchausbreitung kann enden, wenn der Bruch auf Diskontinuitäten mit hoher Festigkeit trifft. Durch diese Wechselwirkungen entsteht ein Kluftnetzwerk mit komplexer Geometrie, das die lokale Deformationsgeschichte und die Dynamik der unterliegenden physikalischen Prozesse reflektiert. rnrnNatürliche hydraulische Bruchbildung hat wesentliche Implikationen für akademische und kommerzielle Fragestellungen in verschiedenen Feldern der Geowissenschaften. Seit den 50er Jahren wird hydraulisches Fracturing eingesetzt, um die Permeabilität von Gas und Öllagerstätten zu erhöhen. Geländebeobachtungen, Isotopenstudien, Laborexperimente und numerische Analysen bestätigen die entscheidende Rolle des Fluiddruckgefälles in Verbindung mit poroelastischen Effekten für den lokalen Spannungszustand und für die Bedingungen, unter denen sich hydraulische Brüche bilden und ausbreiten. Die meisten numerischen hydromechanischen Modelle nehmen für die Kopplung zwischen Fluid und propagierenden Brüchen vordefinierte Bruchgeometrien mit konstantem Fluiddruck an, um das Problem rechnerisch eingrenzen zu können. Da natürliche Gesteine kaum so einfach strukturiert sind, sind diese Modelle generell nicht sonderlich effektiv in der Analyse dieses komplexen Prozesses. Insbesondere unterschätzen sie die Rückkopplung von poroelastischen Effekten und gekoppelte Fluid-Festgestein Prozesse, d.h. die Entwicklung des Porendrucks in Abhängigkeit vom Gesteinsversagen und umgekehrt.rnrnIn dieser Arbeit wird ein zweidimensionales gekoppeltes poro-elasto-plastisches Computer-Model für die qualitative und zum Teil auch quantitativ Analyse der Rolle lokalisierter oder homogen verteilter Fluiddrücke auf die dynamische Ausbreitung von hydraulischen Brüchen und die zeitgleiche Evolution der effektiven Permeabilität entwickelt. Das Programm ist rechnerisch effizient, indem es die Fluiddynamik mittels einer Druckdiffusions-Gleichung nach Darcy ohne redundante Komponenten beschreibt. Es berücksichtigt auch die Biot-Kompressibilität poröser Gesteine, die implementiert wurde um die Kontrollparameter in der Mechanik hydraulischer Bruchbildung in verschiedenen geologischen Szenarien mit homogenen und heterogenen Sedimentären Abfolgen zu bestimmen. Als Resultat ergibt sich, dass der Fluiddruck-Gradient in geschlossenen Systemen lokal zu Störungen des homogenen Spannungsfeldes führen. Abhängig von den Randbedingungen können sich diese Störungen eine Neuausrichtung der Bruchausbreitung zur Folge haben kann. Durch den Effekt auf den lokalen Spannungszustand können hohe Druckgradienten auch schichtparallele Bruchbildung oder Schlupf in nicht-entwässerten heterogenen Medien erzeugen. Ein Beispiel von besonderer Bedeutung ist die Evolution von Akkretionskeilen, wo die große Dynamik der tektonischen Aktivität zusammen mit extremen Porendrücken lokal starke Störungen des Spannungsfeldes erzeugt, die eine hoch-komplexe strukturelle Entwicklung inklusive vertikaler und horizontaler hydraulischer Bruch-Netzwerke bewirkt. Die Transport-Eigenschaften der Gesteine werden stark durch die Dynamik in der Entwicklung lokaler Permeabilitäten durch Dehnungsbrüche und Störungen bestimmt. Möglicherweise besteht ein enger Zusammenhang zwischen der Bildung von Grabenstrukturen und großmaßstäblicher Fluid-Migration. rnrnDie Konsistenz zwischen den Resultaten der Simulationen und vorhergehender experimenteller Untersuchungen deutet darauf hin, dass das beschriebene numerische Verfahren zur qualitativen Analyse hydraulischer Brüche gut geeignet ist. Das Schema hat auch Nachteile wenn es um die quantitative Analyse des Fluidflusses durch induzierte Bruchflächen in deformierten Gesteinen geht. Es empfiehlt sich zudem, das vorgestellte numerische Schema um die Kopplung mit thermo-chemischen Prozessen zu erweitern, um dynamische Probleme im Zusammenhang mit dem Wachstum von Kluftfüllungen in hydraulischen Brüchen zu untersuchen.

Functional and structural characterization of a prokaryotic peptide transporter with features similar to mammalian PEPT1

The ydgR gene of Escherichia coli encodes a protein of the proton-dependent oligopeptide transporter (POT) family. We cloned YdgR and overexpressed the His-tagged fusion protein in E. coli BL21 cells. Bacterial growth inhibition in the presence of the toxic phosphonopeptide alafosfalin established YgdR functionality. Transport was abolished in the presence of the proton ionophore carbonyl cyanide p-chlorophenylhydrazone, suggesting a proton-coupled transport mechanism. YdgR transports selectively only di- and tripeptides and structurally related peptidomimetics (such as aminocephalosporins) with a substrate recognition pattern almost identical to the mammalian peptide transporter PEPT1. The YdgR protein was purified to homogeneity from E. coli membranes. Blue native-polyacrylamide gel electrophoresis and transmission electron microscopy of detergent-solubilized YdgR suggest that it exists in monomeric form. Transmission electron microscopy revealed a crown-like structure with a diameter of approximately 8 nm and a central density. These are the first structural data obtained from a proton-dependent peptide transporter, and the YgdR protein seems an excellent model for studies on substrate and inhibitor interactions as well as on the molecular architecture of cell membrane peptide transporters.

Bislug flow in circular and noncircular channels and the role of interface stretching on energy dissipation

The area of microfluidics has increased in popularity with such fields as MEMS, microreactors, microscaleheat exchangers, etc. A comprehensive understanding of dissipation mechanisms for fluid flow in microchannels is required to accurately predict the behavior in these small systems. Tests were performed using a constant pressure potential created by two immiscible fluids juxtaposed in a microchannel. This study focused on the flow and dissipation mechanisms in round and square microchannels. There are four major dissipation mechanisms in slug flow; wall shear, dissipation at the contact line, menisci interaction and the stretching of the interface. A force balance between the internal driving potential, viscous drag and interface stretching was used to develop a model for the prediction of the velocity of a bislug in a microchannel. Interface stretching is a dissipation mechanism that has been included due to the unique system properties and becomes increasingly more important as the bislug decreases in length.

Mixing-cell boundary conditions and apparent mass balance errors for advective-dispersive solute transport

In many field or laboratory situations, well-mixed reservoirs like, for instance, injection or detection wells and gas distribution or sampling chambers define boundaries of transport domains. Exchange of solutes or gases across such boundaries can occur through advective or diffusive processes. First we analyzed situations, where the inlet region consists of a well-mixed reservoir, in a systematic way by interpreting them in terms of injection type. Second, we discussed the mass balance errors that seem to appear in case of resident injections. Mixing cells (MC) can be coupled mathematically in different ways to a domain where advective-dispersive transport occurs: by assuming a continuous solute flux at the interface (flux injection, MC-FI), or by assuming a continuous resident concentration (resident injection). In the latter case, the flux leaving the mixing cell can be defined in two ways: either as the value when the interface is approached from the mixing-cell side (MC-RT -), or as the value when it is approached from the column side (MC-RT +). Solutions of these injection types with constant or-in one case-distance-dependent transport parameters were compared to each other as well as to a solution of a two-layer system, where the first layer was characterized by a large dispersion coefficient. These solutions differ mainly at small Peclet numbers. For most real situations, the model for resident injection MC-RI + is considered to be relevant. This type of injection was modeled with a constant or with an exponentially varying dispersion coefficient within the porous medium. A constant dispersion coefficient will be appropriate for gases because of the Eulerian nature of the usually dominating gaseous diffusion coefficient, whereas the asymptotically growing dispersion coefficient will be more appropriate for solutes due to the Lagrangian nature of mechanical dispersion, which evolves only with the fluid flow. Assuming a continuous resident concentration at the interface between a mixing cell and a column, as in case of the MC-RI + model, entails a flux discontinuity. This flux discontinuity arises inherently from the definition of a mixing cell: the mixing process is included in the balance equation, but does not appear in the description of the flux through the mixing cell. There, only convection appears because of the homogeneous concentration within the mixing cell. Thus, the solute flux through a mixing cell in close contact with a transport domain is generally underestimated. This leads to (apparent) mass balance errors, which are often reported for similar situations and erroneously used to judge the validity of such models. Finally, the mixing cell model MC-RI + defines a universal basis regarding the type of solute injection at a boundary. Depending on the mixing cell parameters, it represents, in its limits, flux as well as resident injections. (C) 1998 Elsevier Science B.V. All rights reserved.

Context-aware Adaptation Mechanism for Video Dissemination over Flying Ad-Hoc Networks

The user experience on watching live video se- quences transmitted over a Flying Ad-Hoc Networks (FANETs) must be considered to drop packets in overloaded queues, in scenarios with high buffer overflow and packet loss rate. In this paper, we introduce a context-aware adaptation mechanism to manage overloaded buffers. More specifically, we propose a utility function to compute the dropping probability of each packet in overloaded queues based on video context information, such as frame importance, packet deadline, and sensing relevance. In this way, the proposed mechanism drops the packet that adds the minimum video distortion. Simulation evaluation shows that the proposed adaptation mechanism provides real-time multimedia dissemination with QoE support in a multi-hop, multi-flow, and mobile network environments.

Superior functional outcome after radical cystectomy and orthotopic bladder substitution with restrictive intraoperative fluid management: a followup study of a randomized clinical trial

PURPOSE Continuous intraoperative norepinephrine infusion combined with restrictive deferred hydration improves surgical field visibility, and significantly decreases intraoperative blood loss and postoperative complications in patients undergoing radical cystectomy and urinary diversion. We determined whether the intraoperative fluid regimen would affect functional results (continence and erectile function) 1 year after orthotopic ileal bladder substitution. MATERIALS AND METHODS We analyzed a subgroup of 93 patients who received an ileal orthotopic bladder substitute. The subgroup was part of a randomized trial in 167 patients initially allocated to continuous norepinephrine administration starting with 2 μg/kg per hour combined with 1 ml/kg per hour initially and 3 ml/kg per hour crystalloid infusion after cystectomy (norepinephrine/low volume group of 51) or a standard crystalloid infusion of 6 ml/kg per hour throughout surgery (42 controls). We prospectively assessed daytime and nighttime continence, and erectile function 1 year postoperatively in the 93-patient subgroup. RESULTS Daytime continence was reported by 44 of 51 patients (86%) in the norepinephrine/low volume group and by 27 of 42 controls (64%) (p = 0.016), and nighttime continence was reported by 38 (75%) and 25 (60%), respectively (p = 0.077). Erectile function recovery was reported by 26 of 33 preoperatively potent patients (79%) in the norepinephrine/low volume group and by 11 of 29 controls (38%) (p = 0.002). CONCLUSIONS Patients who undergo radical cystectomy and orthotopic bladder substitution with continuous norepinephrine infusion and restrictive hydration during surgery have significantly better daytime continence and erectile function 1 year postoperatively.

Sediment mobilization deposits from episodic subsurface fluid flow—A new tool to reveal long-term earthquake records?

Subsurface fluid flow can be affected by earthquakes; increased spring activity, mud vol- cano eruptions, groundwater fluctuations, changes in geyser frequency, and other forms of altered subsurface fluid flow have been documented during, after, or even prior to seismic shaking. Recently discovered giant pockmarks on the bottom of Lake Neuchâtel, Switzerland, are the lake-floor expression of subsurface fluid flow. They discharge groundwater from the Jura Mountains karstic aquifers and experience episodically increased subsurface fluid flow documented by subsurface sediment mobilization deposits at the levees of the pockmarks. In this study, we present the spatio-temporal distribution of event deposits from these phases of sediment expulsion and of multiple time-correlative mass-transport deposits. We report five striking instances of concurrent multiple subsurface sediment deposits and multiple mass- transport deposits since late glacial times, for which we propose past earthquakes as a trigger. Comparison of this new event catalogue with historic earthquakes and other independent paleoseismic records suggests that initiation of sediment expulsion requires a minimum mac- roseismic intensity of VII. Thus, our study presents for the first time sedimentary deposits resulting from increased subsurface fluid flow as a paleoseismic proxy.

Effects of Estrogen on Muscle Damage in Response to an Acute Resistance Exercise Protocol

Creatine Kinase (CK) is used as a measure of exercise-induced muscle membrane damage. During acute eccentric (muscle lengthening) exercise, muscle sarcolemma, sarcoplasmic reticulum, and Z-lines are damaged, thus causing muscle proteins and enzymes to leak into the interstitial fluid. Strenuous eccentric exercise produces an elevation of oxygen free radicals, which further increases muscle damage. Muscle soreness and fatigue can be attributed to this membrane damage. Estradiol, however, may preserve membrane stability post-exercise (Brancaccio, Maffulli, & Limongelli, 2007; Carter, Dobridge, & Hackney, 2001; Tiidus, 2001). Because estradiol has a similar structure to Vitamin E, which is known to have antioxidant properties, and both are known to affect membrane structure, researchers have proposed that estrogen acts as an antioxidant to provide a protective effect on the post-exercise muscle of women (Sandoval & Matt, 2002). As a result, it has been postulated that muscles in women incur less damage in response to an acute strenuous exercise as compared to men. PURPOSE: To determine if circulating estrogen concentrations are related to muscle damage, as measured by creatine kinase activity and to determine gender differences in creatine kinase as a marker of muscle damage in response to an acute heavy resistance exercise protocol. METHODS: 7 healthy, resistance-trained, eumenhorrheic women (23±3 y, 169±9.1 cm, 66.4±10.5 kg) and 8 healthy, resistance-trained men (25±5 y, 178±6.7 cm, 82.3±9.33 kg) volunteered to participate in the study. Subjects performed an Acute Resistance Exercise Test (ARET) consisting of 6 sets of 5 repetitions Smith machine squats at 90% of their previously determined 1-RM. Blood samples were taken pre-, mid-, post-, 1 hour post-, 6 hours post-, and 24 hours post-exercise. Samples were stored at -80ºC until analyzed. Serum creatine kinase was measured using an assay kit from Genzyme (Framingham, MA). Serum estradiol was measured by an ELISA from GenWay (San Diego, CA). Estradiol b-receptor presence on granulocytes was measured via flow cytometry using primary antibodies from Abcam (Cambridge, MA) and PeCy7 antibodies (secondary) from Santa Cruz (Santa Cruz, CA). RESULTS: No significant correlations between estrogen and CK response were found after an acute resistant exercise protocol. Moreover, no significant change in estradiol receptors were expressed on granulocytes after exercise. Creatine Kinase response, however, differed significantly between genders. Men had higher resting CK concentrations throughout all time points. Creatine Kinase response increased significantly after exercise in both men and women (p=0.008, F=9.798). Men had a significantly higher CK response at 24 hours post exercise than women. A significant condition/sex/time interaction was exhibited in CK response (p=0.02, F=4.547). Perceived general soreness presented a significant condition, sex interaction (p=0.01, F=9.532). DISCUSSION: Although no estradiol and CK response correlations were found in response to exercise, a significant difference in creatine kinase activity was present between men and women. This discrepancy of our results and findings in the literature may be due to the high variability between subjects in creatine kinase activity as well as estrogen concentrations. The lack of significance in change of estradiol receptor expression on granulocytes in response to exercise may be due to intracellular estradiol receptor staining and non-specific gating for granulocytes rather than additional staining for neutrophil markers. Because neutrophils are the initial cells present in the inflammatory response after strenuous exercise, staining for estrogen receptors on this cell type may allow for a better understanding of the effect of estrogen and its hypothesized protective effect against muscle damage. Furthermore, the mechanism of action may include estradiol receptor expression on the muscle fiber itself may play a role in the protective effects of estradiol rather than or in addition to expression on neutrophils. We have shown here that gender differences occur in CK activity as a marker of muscle damage in response to strenuous eccentric exercise, but may not be the result of estradiol concentration or estradiol receptor expression on granulocytes. Other variables should be examined in order to determine the mechanism involved in the difference in creatine kinase as a marker of muscle damage between men and women after heavy resistance exercise.

Diversity in T cell costimulation by alpha4beta1 integrin

T cell activation requires antigen-specific T cell receptor signals that spatially and temporally coincide with a second costimulatory signal. CD28 and α4β1 integrin both function as T cell costimulators, but their individual mechanisms remain elusive. By directly comparing CD3-dependent functions and signaling pathways employed by these two costimulatory receptors, aspects of their individual signaling mechanisms are explored. We determined that CD28 and α4β1 integrins both use Src-family kinase Lck and MAPK Erk, but to different extents and functional ends. After identifying functional differences between CD28 and integrin costimulatory pathways, the focus of the study turned to integrin signaling in naïve and memory T cell subsets. CD45RO T cells are fully co-activated by natural β1 integrin ligands fibronectin (FN) and VCAM-1, β1 monoclonal antibody 33B6, as well as α4β1 monoclonal antibody 19H8 which binds a combinatorial epitope of the α4β1 heterodimer. While CD28 fully costimulates CD45RA T cells, the degree of activation from integrin ligands varies. FN costimulates CD3-dependent proliferation, IL-2 secretion, and early activation markers CD25 and CD69. However, β1 antibody 33B6, which binds to the same T cell integrins (α4β1 and α5β1) as natural ligand FN, failed to costimulate proliferation or IL-2 in the CD45RA subset, but retained the ability to regulate CD25 and CD69. Unique aspects of 19H8 signaling involve early Erk activation and IL-2 independent proliferation. Signaling defects through 33B6 ligation correlates with poor adhesion under fluid flow conditions, suggesting a cytoskeletal basis for signaling. All together, these data provide evidence for a mechanism of α4β1 integrin signaling and describe functional differences between naïve and memory T cells. ^

Interstitial water d13C and sediment geochemistry of ODP Leg 166 sites

A review of interstitial water samples collected from Sites 1003-1007 of the Bahamas Transect along with a shore-based analysis of oxygen and carbon isotopes, minor and trace elements, and sediment chemistry are presented. Results indicate that the pore-fluid profiles in the upper 100 meters below seafloor (mbsf) are marked by shifts between 20 and 40 mbsf that are thought to be caused by changes in sediment reactivity, sedimentation rates, and the influence of strong bottom currents that have been active since the late Pliocene. Pore-fluid profiles in the lower Pliocene-Miocene sequences are dominated by diffusion and do not show significant evidence of subsurface advective flow. Deeper interstitial waters are believed to be the in situ fluids that have evolved through interaction with sediments and diffusion. Pore-fluid chemistry is strongly influenced by carbonate recrystallization processes. Increases in pore-fluid Cl- and Na+ with depth are interpreted to result mainly from carbonate remineralization reactions that are most active near the platform margin. A lateral gradient in detrital clay content observed along the transect, leads to an overall lower carbonate reactivity, and enhances preservation of metastable aragonite further away from the platform margin. Later stage burial diagenesis occurs at slow rates and is limited by the supply of reactive elements through diffusion.

Chemistry and age determination of basement fluids from Juan de Fuca Ridge

The geochemical implications of thermally driven flow of seawater through oceanic crust on the mid-ocean ridge flank have been examined on a well-studied 80 km transect across the eastern flank of the Juan de Fuca Ridge at 48°N, using porewater and basement fluid samples obtained on ODP Leg 168. Fluid flow is recognised by near-basement reversals in porewater concentration gradients from altered values in the sediment section to seawater-like values in basaltic basement. In general, the basement fluids become more geochemically evolved with distance from the ridge and broadly follow basement temperature which ranges from not, vert, similar16° to 63°C. Although thermal effects of advective heat exchange are only seen within 20 km east of where basement is exposed near the ridge crest, chemical reactivity extends to all sites. Seawater passing through oceanic crust has reacted with basement rocks leading to increases in Ca2+ and decreases in alkalinity, Mg2+, Na+, K+, SO42- and delta18O. Sr isotope exchange between seawater and oceanic crust off axis is unequivocally demonstrated with endmember 87Sr/86Sr ~ 0.707. Evidence of more evolved fluids is seen at sites where rapid upwelling of fluids through sediments occurs. Chlorinities of the basement fluids are consistent with post-glacial seawater and thus a short residence time in the crust. Rates of lateral flow have been by estimated by modelling porewater sulphate gradients, using Cl as a glacial chronometer, and from radiocarbon dating of basal fluids. All three methods reveal fluid flow with 14C ages less than 10,000 yr and particle velocities of ~1-5 m/yr, in agreement with thermally constrained volumetric flow rates through a ~600 m thick permeable layer of ~10% porosity. Delta(element)/Delta(heat) extraction ratios are similar to values for ridge-crest hydrothermal systems.

Numerical Error Prediction and its applications in CFD using tau-estimation

Nowadays, Computational Fluid Dynamics (CFD) solvers are widely used within the industry to model fluid flow phenomenons. Several fluid flow model equations have been employed in the last decades to simulate and predict forces acting, for example, on different aircraft configurations. Computational time and accuracy are strongly dependent on the fluid flow model equation and the spatial dimension of the problem considered. While simple models based on perfect flows, like panel methods or potential flow models can be very fast to solve, they usually suffer from a poor accuracy in order to simulate real flows (transonic, viscous). On the other hand, more complex models such as the full Navier- Stokes equations provide high fidelity predictions but at a much higher computational cost. Thus, a good compromise between accuracy and computational time has to be fixed for engineering applications. A discretisation technique widely used within the industry is the so-called Finite Volume approach on unstructured meshes. This technique spatially discretises the flow motion equations onto a set of elements which form a mesh, a discrete representation of the continuous domain. Using this approach, for a given flow model equation, the accuracy and computational time mainly depend on the distribution of nodes forming the mesh. Therefore, a good compromise between accuracy and computational time might be obtained by carefully defining the mesh. However, defining an optimal mesh for complex flows and geometries requires a very high level expertize in fluid mechanics and numerical analysis, and in most cases a simple guess of regions of the computational domain which might affect the most the accuracy is impossible. Thus, it is desirable to have an automatized remeshing tool, which is more flexible with unstructured meshes than its structured counterpart. However, adaptive methods currently in use still have an opened question: how to efficiently drive the adaptation ? Pioneering sensors based on flow features generally suffer from a lack of reliability, so in the last decade more effort has been made in developing numerical error-based sensors, like for instance the adjoint-based adaptation sensors. While very efficient at adapting meshes for a given functional output, the latter method is very expensive as it requires to solve a dual set of equations and computes the sensor on an embedded mesh. Therefore, it would be desirable to develop a more affordable numerical error estimation method. The current work aims at estimating the truncation error, which arises when discretising a partial differential equation. These are the higher order terms neglected in the construction of the numerical scheme. The truncation error provides very useful information as it is strongly related to the flow model equation and its discretisation. On one hand, it is a very reliable measure of the quality of the mesh, therefore very useful in order to drive a mesh adaptation procedure. On the other hand, it is strongly linked to the flow model equation, so that a careful estimation actually gives information on how well a given equation is solved, which may be useful in the context of _ -extrapolation or zonal modelling. The following work is organized as follows: Chap. 1 contains a short review of mesh adaptation techniques as well as numerical error prediction. In the first section, Sec. 1.1, the basic refinement strategies are reviewed and the main contribution to structured and unstructured mesh adaptation are presented. Sec. 1.2 introduces the definitions of errors encountered when solving Computational Fluid Dynamics problems and reviews the most common approaches to predict them. Chap. 2 is devoted to the mathematical formulation of truncation error estimation in the context of finite volume methodology, as well as a complete verification procedure. Several features are studied, such as the influence of grid non-uniformities, non-linearity, boundary conditions and non-converged numerical solutions. This verification part has been submitted and accepted for publication in the Journal of Computational Physics. Chap. 3 presents a mesh adaptation algorithm based on truncation error estimates and compares the results to a feature-based and an adjoint-based sensor (in collaboration with Jorge Ponsín, INTA). Two- and three-dimensional cases relevant for validation in the aeronautical industry are considered. This part has been submitted and accepted in the AIAA Journal. An extension to Reynolds Averaged Navier- Stokes equations is also included, where _ -estimation-based mesh adaptation and _ -extrapolation are applied to viscous wing profiles. The latter has been submitted in the Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering. Keywords: mesh adaptation, numerical error prediction, finite volume Hoy en día, la Dinámica de Fluidos Computacional (CFD) es ampliamente utilizada dentro de la industria para obtener información sobre fenómenos fluidos. La Dinámica de Fluidos Computacional considera distintas modelizaciones de las ecuaciones fluidas (Potencial, Euler, Navier-Stokes, etc) para simular y predecir las fuerzas que actúan, por ejemplo, sobre una configuración de aeronave. El tiempo de cálculo y la precisión en la solución depende en gran medida de los modelos utilizados, así como de la dimensión espacial del problema considerado. Mientras que modelos simples basados en flujos perfectos, como modelos de flujos potenciales, se pueden resolver rápidamente, por lo general aducen de una baja precisión a la hora de simular flujos reales (viscosos, transónicos, etc). Por otro lado, modelos más complejos tales como el conjunto de ecuaciones de Navier-Stokes proporcionan predicciones de alta fidelidad, a expensas de un coste computacional mucho más elevado. Por lo tanto, en términos de aplicaciones de ingeniería se debe fijar un buen compromiso entre precisión y tiempo de cálculo. Una técnica de discretización ampliamente utilizada en la industria es el método de los Volúmenes Finitos en mallas no estructuradas. Esta técnica discretiza espacialmente las ecuaciones del movimiento del flujo sobre un conjunto de elementos que forman una malla, una representación discreta del dominio continuo. Utilizando este enfoque, para una ecuación de flujo dado, la precisión y el tiempo computacional dependen principalmente de la distribución de los nodos que forman la malla. Por consiguiente, un buen compromiso entre precisión y tiempo de cálculo se podría obtener definiendo cuidadosamente la malla, concentrando sus elementos en aquellas zonas donde sea estrictamente necesario. Sin embargo, la definición de una malla óptima para corrientes y geometrías complejas requiere un nivel muy alto de experiencia en la mecánica de fluidos y el análisis numérico, así como un conocimiento previo de la solución. Aspecto que en la mayoría de los casos no está disponible. Por tanto, es deseable tener una herramienta que permita adaptar los elementos de malla de forma automática, acorde a la solución fluida (remallado). Esta herramienta es generalmente más flexible en mallas no estructuradas que con su homóloga estructurada. No obstante, los métodos de adaptación actualmente en uso todavía dejan una pregunta abierta: cómo conducir de manera eficiente la adaptación. Sensores pioneros basados en las características del flujo en general, adolecen de una falta de fiabilidad, por lo que en la última década se han realizado grandes esfuerzos en el desarrollo numérico de sensores basados en el error, como por ejemplo los sensores basados en el adjunto. A pesar de ser muy eficientes en la adaptación de mallas para un determinado funcional, este último método resulta muy costoso, pues requiere resolver un doble conjunto de ecuaciones: la solución y su adjunta. Por tanto, es deseable desarrollar un método numérico de estimación de error más asequible. El presente trabajo tiene como objetivo estimar el error local de truncación, que aparece cuando se discretiza una ecuación en derivadas parciales. Estos son los términos de orden superior olvidados en la construcción del esquema numérico. El error de truncación proporciona una información muy útil sobre la solución: es una medida muy fiable de la calidad de la malla, obteniendo información que permite llevar a cabo un procedimiento de adaptación de malla. Está fuertemente relacionado al modelo matemático fluido, de modo que una estimación precisa garantiza la idoneidad de dicho modelo en un campo fluido, lo que puede ser útil en el contexto de modelado zonal. Por último, permite mejorar la precisión de la solución resolviendo un nuevo sistema donde el error local actúa como término fuente (_ -extrapolación). El presenta trabajo se organiza de la siguiente manera: Cap. 1 contiene una breve reseña de las técnicas de adaptación de malla, así como de los métodos de predicción de los errores numéricos. En la primera sección, Sec. 1.1, se examinan las estrategias básicas de refinamiento y se presenta la principal contribución a la adaptación de malla estructurada y no estructurada. Sec 1.2 introduce las definiciones de los errores encontrados en la resolución de problemas de Dinámica Computacional de Fluidos y se examinan los enfoques más comunes para predecirlos. Cap. 2 está dedicado a la formulación matemática de la estimación del error de truncación en el contexto de la metodología de Volúmenes Finitos, así como a un procedimiento de verificación completo. Se estudian varias características que influyen en su estimación: la influencia de la falta de uniformidad de la malla, el efecto de las no linealidades del modelo matemático, diferentes condiciones de contorno y soluciones numéricas no convergidas. Esta parte de verificación ha sido presentada y aceptada para su publicación en el Journal of Computational Physics. Cap. 3 presenta un algoritmo de adaptación de malla basado en la estimación del error de truncación y compara los resultados con sensores de featured-based y adjointbased (en colaboración con Jorge Ponsín del INTA). Se consideran casos en dos y tres dimensiones, relevantes para la validación en la industria aeronáutica. Este trabajo ha sido presentado y aceptado en el AIAA Journal. También se incluye una extensión de estos métodos a las ecuaciones RANS (Reynolds Average Navier- Stokes), en donde adaptación de malla basada en _ y _ -extrapolación son aplicados a perfiles con viscosidad de alas. Este último trabajo se ha presentado en los Actas de la Institución de Ingenieros Mecánicos, Parte G: Journal of Aerospace Engineering. Palabras clave: adaptación de malla, predicción del error numérico, volúmenes finitos