IMEX finite volume methods for the shallow water equations

Die Flachwassergleichungen (SWE) sind ein hyperbolisches System von Bilanzgleichungen, die adäquate Approximationen an groß-skalige Strömungen der Ozeane, Flüsse und der Atmosphäre liefern. Dabei werden Masse und Impuls erhalten. Wir unterscheiden zwei charakteristische Geschwindigkeiten: die Advektionsgeschwindigkeit, d.h. die Geschwindigkeit des Massentransports, und die Geschwindigkeit von Schwerewellen, d.h. die Geschwindigkeit der Oberflächenwellen, die Energie und Impuls tragen. Die Froude-Zahl ist eine Kennzahl und ist durch das Verhältnis der Referenzadvektionsgeschwindigkeit zu der Referenzgeschwindigkeit der Schwerewellen gegeben. Für die oben genannten Anwendungen ist sie typischerweise sehr klein, z.B. 0.01. Zeit-explizite Finite-Volume-Verfahren werden am öftersten zur numerischen Berechnung hyperbolischer Bilanzgleichungen benutzt. Daher muss die CFL-Stabilitätsbedingung eingehalten werden und das Zeitinkrement ist ungefähr proportional zu der Froude-Zahl. Deswegen entsteht bei kleinen Froude-Zahlen, etwa kleiner als 0.2, ein hoher Rechenaufwand. Ferner sind die numerischen Lösungen dissipativ. Es ist allgemein bekannt, dass die Lösungen der SWE gegen die Lösungen der Seegleichungen/ Froude-Zahl Null SWE für Froude-Zahl gegen Null konvergieren, falls adäquate Bedingungen erfüllt sind. In diesem Grenzwertprozess ändern die Gleichungen ihren Typ von hyperbolisch zu hyperbolisch.-elliptisch. Ferner kann bei kleinen Froude-Zahlen die Konvergenzordnung sinken oder das numerische Verfahren zusammenbrechen. Insbesondere wurde bei zeit-expliziten Verfahren falsches asymptotisches Verhalten (bzgl. der Froude-Zahl) beobachtet, das diese Effekte verursachen könnte.Ozeanographische und atmosphärische Strömungen sind typischerweise kleine Störungen eines unterliegenden Equilibriumzustandes. Wir möchten, dass numerische Verfahren für Bilanzgleichungen gewisse Equilibriumzustände exakt erhalten, sonst können künstliche Strömungen vom Verfahren erzeugt werden. Daher ist die Quelltermapproximation essentiell. Numerische Verfahren die Equilibriumzustände erhalten heißen ausbalanciert.rnrnIn der vorliegenden Arbeit spalten wir die SWE in einen steifen, linearen und einen nicht-steifen Teil, um die starke Einschränkung der Zeitschritte durch die CFL-Bedingung zu umgehen. Der steife Teil wird implizit und der nicht-steife explizit approximiert. Dazu verwenden wir IMEX (implicit-explicit) Runge-Kutta und IMEX Mehrschritt-Zeitdiskretisierungen. Die Raumdiskretisierung erfolgt mittels der Finite-Volumen-Methode. Der steife Teil wird mit Hilfe von finiter Differenzen oder au eine acht mehrdimensional Art und Weise approximniert. Zur mehrdimensionalen Approximation verwenden wir approximative Evolutionsoperatoren, die alle unendlich viele Informationsausbreitungsrichtungen berücksichtigen. Die expliziten Terme werden mit gewöhnlichen numerischen Flüssen approximiert. Daher erhalten wir eine Stabilitätsbedingung analog zu einer rein advektiven Strömung, d.h. das Zeitinkrement vergrößert um den Faktor Kehrwert der Froude-Zahl. Die in dieser Arbeit hergeleiteten Verfahren sind asymptotisch erhaltend und ausbalanciert. Die asymptotischer Erhaltung stellt sicher, dass numerische Lösung das "korrekte" asymptotische Verhalten bezüglich kleiner Froude-Zahlen besitzt. Wir präsentieren Verfahren erster und zweiter Ordnung. Numerische Resultate bestätigen die Konvergenzordnung, so wie Stabilität, Ausbalanciertheit und die asymptotische Erhaltung. Insbesondere beobachten wir bei machen Verfahren, dass die Konvergenzordnung fast unabhängig von der Froude-Zahl ist.

Analysis of transient eddy currents in MRI using a cylindrical FDTD method

Most magnetic resonance imaging (MRI) spatial encoding techniques employ low-frequency pulsed magnetic field gradients that undesirably induce multiexponentially decaying eddy currents in nearby conducting structures of the MRI system. The eddy currents degrade the switching performance of the gradient system, distort the MRI image, and introduce thermal loads in the cryostat vessel and superconducting MRI components. Heating of superconducting magnets due to induced eddy currents is particularly problematic as it offsets the superconducting operating point, which can cause a system quench. A numerical characterization of transient eddy current effects is vital for their compensation/control and further advancement of the MRI technology as a whole. However, transient eddy current calculations are particularly computationally intensive. In large-scale problems, such as gradient switching in MRI, conventional finite-element method (FEM)-based routines impose very large computational loads during generation/solving of the system equations. Therefore, other computational alternatives need to be explored. This paper outlines a three-dimensional finite-difference time-domain (FDTD) method in cylindrical coordinates for the modeling of low-frequency transient eddy currents in MRI, as an extension to the recently proposed time-harmonic scheme. The weakly coupled Maxwell's equations are adapted to the low-frequency regime by downscaling the speed of light constant, which permits the use of larger FDTD time steps while maintaining the validity of the Courant-Friedrich-Levy stability condition. The principal hypothesis of this work is that the modified FDTD routine can be employed to analyze pulsed-gradient-induced, transient eddy currents in superconducting MRI system models. The hypothesis is supported through a verification of the numerical scheme on a canonical problem and by analyzing undesired temporal eddy current effects such as the B-0-shift caused by actively shielded symmetric/asymmetric transverse x-gradient head and unshielded z-gradient whole-body coils operating in proximity to a superconducting MRI magnet.

Data compilation on the biological response to ocean acidification: environmental and experimental context of data sets and related literature

The exponential growth of studies on the biological response to ocean acidification over the last few decades has generated a large amount of data. To facilitate data comparison, a data compilation hosted at the data publisher PANGAEA was initiated in 2008 and is updated on a regular basis (doi:10.1594/PANGAEA.149999). By January 2015, a total of 581 data sets (over 4 000 000 data points) from 539 papers had been archived. Here we present the developments of this data compilation five years since its first description by Nisumaa et al. (2010). Most of study sites from which data archived are still in the Northern Hemisphere and the number of archived data from studies from the Southern Hemisphere and polar oceans are still relatively low. Data from 60 studies that investigated the response of a mix of organisms or natural communities were all added after 2010, indicating a welcomed shift from the study of individual organisms to communities and ecosystems. The initial imbalance of considerably more data archived on calcification and primary production than on other processes has improved. There is also a clear tendency towards more data archived from multifactorial studies after 2010. For easier and more effective access to ocean acidification data, the ocean acidification community is strongly encouraged to contribute to the data archiving effort, and help develop standard vocabularies describing the variables and define best practices for archiving ocean acidification data.

Bounding the stability and rupture condition of emulsion and foam films

A scaling law is presented that provides a complete solution to the equations bounding the stability and rupture of thin films. The scaling law depends on the fundamental physicochemical properties of the film and interface to calculate bounds for the critical thickness and other key film thicknesses, the relevant waveforms associated with instability and rupture, and film lifetimes. Critical thicknesses calculated from the scaling law are shown to bound the values reported in the literature for numerous emulsion and foam films. The majority of critical thickness values are between 15 to 40% lower than the upper bound critical thickness provided by the scaling law.

Stability analysis of core-annular flow and neutral stability wave number

A general transition criterion is proposed in order to locate the core-annular flow pattern in horizontal and vertical oil-water flows. It is based on a rigorous one-dimensional two-fluid model of liquid-liquid two-phase flow and considers the existence of critical interfacial wave numbers related to a non-negligible interfacial tension term to which the linear stability theory still applies. The viscous laminar-laminar flow problem is fully resolved and turbulence effects on the stability are analyzed through experimentally obtained shape factors. The proposed general transition criterion includes in its formulation the inviscid Kelvin-Helmholtz`s discriminator. If a theoretical maximum wavelength is considered as a necessary condition for stability, a stability criterion in terms of the Eotvos number is achieved. Effects of interfacial tension, viscosity ratio, density difference, and shape factors on the stability of core-annular flow are analyzed in detail. The more complete modeling allowed for the analysis of the neutral-stability wave number and the results strongly suggest that the interfacial tension term plays an indispensable role in the correct prediction of the stable region of core-annular flow pattern. The incorporation of a theoretical minimum wavelength into the transition model produced significantly better results. The criterion predictions were compared with recent data from the literature and the agreement is encouraging. (C) 2007 American Institute of Chemical Engineers.

Stability and in vitro penetration study of rutin incorporated in a cosmetic emulsion through an alternative model biomembrane

Rutin is employed as antioxidant and to prevent the capillary fragility and, when incorporated in cosmetic emulsions, it must target the action site. In vitro cutaneous penetration studies through human skin is the ideal situation, however, there are difficulties to obtain and to maintain this tissue viability. Among the membrane models, shed snake skin presents itself as pure stratum corneum, providing barrier function similar to human and it is obtained without the animal sacrifice. The objectives of this research were the development and stability evaluation of a cosmetic emulsion containing rutin and propylene glycol (penetration enhancer) and the evaluation or rutin in vitro cutaneous penetration and retention from the emulsion, employing an alternative model biomembrane. Emulsion was developed with rutin and propylene glycol, both at 5.0% w/w. Active substance presented on the formulation was quantified by a validated spectrophotometric method at 361.0 nm. Rutin Rutin cutaneous penetration and retention was performed in vertical diffusion cells with shed snake skin of Crotalus durissus, as alternative model biomembrane, and distilled water and ethanol 99.5% (1:1), as receptor fluid. The experiment was conducted for six hours, at 37.0 +/- 0.5 degrees C with constant stirring of 300 rpm. Spectrophotometry at 410.0 nm, previously validated, determined the active substance after cutaneous penetration/ retention. Emulsion did not promote rutin cutaneous penetration through C. durissus skin, retaining 0.931 +/- 0.0391 mu g rutin/mg shed snake skin. The referred formulation was chemically stable for 30 days after stored at 25.0 +/- 2.0 degrees C, 5.0 +/- 0.5 degrees C and 45.0 +/- 0.5 degrees C. In conclusion, it has not been verified the active cutaneous penetration through the model biomembrane, but only its retention on the Crotalus durissus stratum corneum, condition considered stable for 30 days.

The effects of viscous loading of the human forearm flexors on the stability of coordination

This experiment investigated whether the stability of rhythmic unimanual movements is primarily a function of perceptual/spatial orientation or neuro-mechanical in nature. Eight participants performed rhythmic flexion and extension movements of the left wrist for 30 s at a frequency of 2.25 Hz paced by an auditory metronome. Each participant performed 8 flex-on-the-beat trials and 8 extend-on-the-beat trials in one of two load conditions, loaded and unload. In the loaded condition, a servo-controlled torque motor was used to apply a small viscous load that resisted the flexion phase of the movement only. Both the amplitude and frequency of the movement generated in the loaded and unloaded conditions were statistically equivalent. However, in the loaded condition movements in which participants were required to flex-on-the-beat became less stable (more variable) while extend-on-the-beat movements remained unchanged compared with the unload condition. The small alteration in required muscle force was sufficient to result in reliable changes in movement stability even a situation where the movement kinematics were identical. These findings support the notion that muscular constraints, independent of spatial dependencies, can be sufficiently strong to reliably influence coordination in a simple unimanual task.

Mechanical stability of adhesives under water storage

Objectives. To evaluate the effects of storage condition (wet or dry) and storage time (24 h and 3 months) on the ultimate tensile strength (UTS) of Single Bond (SB), 3M-ESPE; Opti Bond Solo Plus (OB), Kerr; One Step (OS), Bisco, and Prime & Bond NT (PB), Dentsply adhesive resins. Methods. Hourglass-shaped specimens were obtained from a metallic matrix. Each adhesive was dispensed to fill the molds completely and left undisturbed in a dark chamber for 4 min at 37 degrees C for solvent evaporation. They were individually light-cured for 80 s at 500 mW/cm(2) and randomly divided into three groups: 24 h of water storage; 3 months of water storage; 3 months of dry storage. The specimens were tested in tension at 0.5 mm/min using the microtensile method and data were analyzed by two-way ANOVA and SNK tests for each material. Results. Water storage for 3 months did not cause significant changes in the UTS of any of the adhesives (p-value). Values for water storage ranged from 25.9 MPa for Single Bond at 24 h to 32.7 MPa for Prime & Bond NT after 3 months. Dry storage for 3 months yielded significantly higher UTS for most adhesives, which ranged from approximately 20% for Opti Bond to 160% higher values for Single Bond compared to their 3 months wet storage values. Conclusion. The effects of storage condition and time on the UTS of adhesives were material-dependent. (C) 2009 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

The influence of storage condition and duration on the resistance to fracture of different fiber post systems

Purpose: To evaluate the effects of storage condition and duration on the resistance to fracture of different fiber post systems (and to morphologically assess the post structure before and after storage. Methods: Three types of fiber posts (DT Light Post, GC Post, FRC Postect Plus) were divided in different groups (n=12) according to the storage condition (dry at 37 degrees C; saline water at 37 degrees C; mineral oil at 37 degrees C and storage inside the roots of extracted human teeth immersed in saline water at 37 degrees C and duration (6, 12 months). A universal testing machine loading at a 90 degrees angle was employed for the three-point bending test. The test was carried out until fracture of the post. A 3-way ANOVA and Tukey`s test (alpha= 0.05) were used to compare the effect of the experimental factors on the fracture strength. Two posts of each group were observed before and after the storage using a scanning electron microscope. Results: Storage condition and post type had a significant effect on post fracture strength (P< 0.05). The interaction between these factors was significant (P< 0.05). Water storage significantly decreased the fracture strength, regardless of the post type and the storage duration. Storage inside roots, in oil, and at dry conditions did not significantly affect post fracture strength. SEM micrographs revealed voids between fibers and resin matrix for posts stored in water. Posts stored under the other conditions showed a compact matrix without porosities. (Am J Dent 2009;22:366-370).

Changes in postural stability in women aged 20 to 80 years

Background. A study of postural stability was undertaken to identify the relationship between vision and support surface across age decades. Understanding when reliance on vision for postural stability emerges and the support conditions contributing to this instability may provide the evidence required to introduce falls-prevention strategies in younger age decades. Methods. We measured postural stability in 453 women aged 20 to 80 years using the Balance Master force-plate system while the women performed the modified Clinical Test for the Sensory Interaction and Balance (firm and foam surfaces, eyes open and closed) and the Single-Limb Stance Test (eyes open and closed). Results. Women in their 60s and 70s were more unstable than younger women in bilateral stance on a firm surface with the eyes closed. This instability was evident from the 50s when a foam surface was introduced and from the 40s when single-limb stance was tested with eyes closed. A further decline in stability was demonstrated for each subsequent decade when the eyes were closed in single-limb stance. Conclusions. Age, visual condition, and support surface were significant variables influencing postural stability in women. Reliance on vision for postural stability was evident for women from the 40s when single-limb stance was tested, from the 50s when bilateral stance on foam was tested, and from the 60s when a firm surface was used. The cause(s) of this decline in stability requires further investigation, and screening for postural instability between the ages of 40 and 60 is advocated.

Stability of the tree-level vacuum in two Higgs doublet models against charge or CP spontaneous violation

We show that in two Higgs doublet models at tree-level the potential minimum preserving electric charge and CP symmetries, when it exists, is the global one. Furthermore, we derived a very simple condition, involving only the coefficients of the quartic terms of the potential, that guarantees spontaneous CP breaking. (C) 2004 Elsevier B.V. All rights reserved.

The effect of metal transfer stability (spattering) on fume generation, morphology and composition in short-circuit MAG welding

The main objective of this work was to evaluate the hypothesis that the greater transfer stability leads also to less volume of fumes. Using an Ar + 25%CO2 blend as shielding gas and maintaining constant the average current, wire feed speed and welding speed, bead-on-plate welds were carried out with plain carbon steel solid wire. The welding voltage was scanned to progressively vary the transfer stability. Using two conditions of low stability and one with high stability, fume generation was evaluated by means of the AWS F1.2:2006 standard. The influence of these conditions on fume morphology and composition was also verified. A condition with greater transfer stability does not generate less fume quantity, despite the fact that this condition produces fewer spatters. Other factors such as short-circuit current, arcing time, droplet diameters and arc length are the likely governing factors, but in an interrelated way. Metal transfer stability does not influence either the composition or the size/morphology of fume particulates. (c) 2014 Elsevier B.V. All rights reserved.

A new empirical system for rock slope stability analysis in exploitation stage

An empirical system was developed to obtain a quality index for rock slopes in road infrastructures, named Slope Quality Index (SQI), and it was applied to a set of real slopes.The SQI is supported in nine factors affecting slope stability that contemplate the evaluation of different parameters. Consequently, each factor is classified by the degree of importance and influence by assigned weights. These weights were established through a statistical analysis of replies to a survey that was distributed to several experienced professionals in the field. The proposed SQI varies between1 and 5, corresponding to slopes in very good and very bad condition state, respectively. Besides the advantage linked to a quantitative and qualitative evaluation of slopes, theSQI also allows identifying the most critical factors on the slope stability, which is a fundamental issue for an efficient management of the slope network in the road infrastructure, namely in the planning of conservation and maintenance operations.

Stability and manipulation in representative democracies

This paper is devoted to the analysis of all constitutions equipped with electoral systems involving two step procedures. First, one candidate is elected in every jurisdiction by the electors in that jurisdiction, according to some aggregation procedure. Second, another aggregation procedure collects the names of the jurisdictional winners in order to designate the final winner. It appears that whenever individuals are allowed to change jurisdiction when casting their ballot, they are able to manipulate the result of the election except in very few cases. When imposing a paretian condition on every jurisdictions voting rule, it is shown that, in the case of any finite number of candidates, any two steps voting rule that is not manipulable by movement of the electors necessarily gives to every voter the power of overruling the unanimity on its own. A characterization of the set of these rules is next provided in the case of two candidates.

Embolization for multicompartmental bleeding in patients in hemodynamically unstable condition: prognostic factors and outcome.

PURPOSE: To determine prognostic factors and evaluate outcomes of transcatheter arterial embolization in severely injured patients in hemodynamically unstable condition with multicompartmental bleeding.¦MATERIALS AND METHODS: Between June 2000 and May 2008, 36 consecutive patients treated with transcatheter arterial embolization for major retroperitoneal bleeding associated with at least one additional source of bleeding were retrospectively reviewed. Mean Injury Severity Score (ISS) was 49.4 ± 15.8. Univariate and multivariate analyses were performed to identify parameters associated with failure of embolization, need for additional surgery to control bleeding, and fatal outcome at 30 d.¦RESULTS: Embolization was technically successful in 35 of 36 patients (97.2%) and resulted in immediate and sustained (> 24 h) hemodynamic improvement in 29 (80.5%). Additional hemostatic surgery was necessary after embolization in six patients (16.6%). Fifteen patients (41.6%) died within 30 d. Failure to restore hemodynamic stability was correlated with the rate of administration of packed red blood cells (P = .014), rate of administration of fresh frozen plasma (FFP; P = .031), and systolic blood pressure (SBP) immediately before embolization (P = .002). The need for additional surgery was correlated with FFP administration rate before embolization (P = .0002) and hemodynamic success (P = .003). Death was correlated with Glasgow Coma Scale score at admission (P = .001), ISS (P = .014), New Injury Severity Score (P = .016), number of injured sites (P = .012), SBP before embolization (P = .042), need for vasopressive drugs before embolization (P = .037), and hemodynamic success (P = .0004).¦CONCLUSIONS: In patients in hemodynamically unstable condition, transcatheter arterial embolization effectively controls bleeding and improves hemodynamic stability. Immediate survival is related to hemodynamic condition before embolization, and 30-d mortality is mainly related to associated brain trauma.