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.

Intermittent spike-wave dynamics in a heterogeneous, spatially extended neural mass model

Generalised epileptic seizures are frequently accompanied by sudden, reversible transitions from low amplitude, irregular background activity to high amplitude, regular spike-wave discharges (SWD) in the EEG. The underlying mechanisms responsible for SWD generation and for the apparently spontaneous transitions to SWD and back again are still not fully understood. Specifically, the role of spatial cortico-cortical interactions in ictogenesis is not well studied. We present a macroscopic, neural mass model of a cortical column which includes two distinct time scales of inhibition. This model can produce both an oscillatory background and a pathological SWD rhythm. We demonstrate that coupling two of these cortical columns can lead to a bistability between out-of-phase, low amplitude background dynamics and in-phase, high amplitude SWD activity. Stimuli can cause state-dependent transitions from background into SWD. In an extended local area of cortex, spatial heterogeneities in a model parameter can lead to spontaneous reversible transitions from a desynchronised background to synchronous SWD due to intermittency. The deterministic model is therefore capable of producing absence seizure-like events without any time dependent adjustment of model parameters. The emergence of such mechanisms due to spatial coupling demonstrates the importance of spatial interactions in modelling ictal dynamics, and in the study of ictogenesis.

Excitability and recruitment patterns of spinal motoneurons in human sleep as assessed by F-wave recordings

This study examines the excitability and recruitment of spinal motoneurons in human sleep. The main objective was to assess whether supraspinal inhibition affects the different subpopulations of the compound spinal motoneuron pool in the same way or rather in a selective fashion in the various sleep stages. To this end, we studied F-conduction velocities (FCV) and F-tacheodispersion alongside F-amplitudes and F-persistence in 22 healthy subjects in sleep stages N2, N3 (slow-wave sleep), REM and in wakefulness. Stimuli were delivered on the ulnar nerve, and F-waves were recorded from the first dorsal interosseus muscle. Repeated sets of stimuli were stored to obtain at least 15 F-waves for each state of vigilance. F-tacheodispersion was calculated based on FCVs using the modified Kimura formula. Confirming the only previous study, excitability of spinal motoneurons was generally decreased in all sleep stages compared with wakefulness as indicated by significantly reduced F-persistence and F-amplitudes. More importantly, F-tacheodispersion showed a narrowed range of FCV in all sleep stages, most prominently in REM. In non-REM, this narrowed range was associated with a shift towards significantly decreased maximal FCV and mean FCV as well as with a trend towards lower minimal FCV. In REM, the lowering of mean FCV was even more pronounced, but contrary to non-REM sleep without a shift of minimal and maximal FCV. Variations in F-tacheodispersion between sleep stages suggest that different supraspinal inhibitory neuronal circuits acting on the spinal motoneuron pool may contribute to muscle hypotonia in human non-REM sleep and to atonia in REM sleep.

Histomorphologic evaluation of extracorporeal shock wave therapy of the fourth metatarsal bone and the origin of the suspensory ligament in horses without lameness

OBJECTIVE: To determine via histologic examination and scintigraphy the effect of focused extracorporeal shock wave therapy (ESWT) on normal bone and the bone-ligament interface in horses. ANIMALS: 6 horses without lameness. PROCEDURE: Origins of the suspensory ligament at the metacarpus (35-mm probe depth) and fourth metatarsal bone (5-mm probe depth) were treated twice (days 0 and 16) with 2,000 shocks (energy flux density, 0.15 mJ/mm2). One forelimb and 1 hind limb were randomly treated, and the contralateral limbs served as nontreated controls. Bone scans were performed on days -1 (before ESWT), 3, 16, and 19. Histomorphologic studies of control and treated tissues were performed on day 30. RESULTS: ESWT significantly increased the number of osteoblasts but caused no damage to associated soft tissue structures and did not induce cortical microfractures. A significant correlation between osteoblast numbers and radiopharmaceutical uptake was noticed on lateral views of the hind limb on days 3 and 16 and on caudal views of the forelimb on day 3. CONCLUSIONS AND CLINICAL RELEVANCE: Results suggested that ESWT has the potential to increase osteoblast numbers in horses. The correlation between increased osteoblast numbers and radio-pharmaceutical uptake 3 days and 16 days after the first ESWT suggested that stimulation of osteogenesis occurred soon after ESWT. No damage to bone or the bone-ligament interface should occur at the settings used in this study, and ESWT can therefore be administered safely in horses.

Effect of short-wave (6-22 MHz) magnetic fields on sleep quality and melatonin cycle in humans: the Schwarzenburg shut-down study

This paper describes the results of a unique "natural experiment" of the operation and cessation of a broadcast transmitter with its short-wave electromagnetic fields (6-22 MHz) on sleep quality and melatonin cycle in a general human population sample. In 1998, 54 volunteers (21 men, 33 women) were followed for 1 week each before and after shut-down of the short-wave radio transmitter at Schwarzenburg (Switzerland). Salivary melatonin was sampled five times a day and total daily excretion and acrophase were estimated using complex cosinor analysis. Sleep quality was recorded daily using a visual analogue scale. Before shut down, self-rated sleep quality was reduced by 3.9 units (95% CI: 1.7-6.0) per mA/m increase in magnetic field exposure. The corresponding decrease in melatonin excretion was 10% (95% CI: -32 to 20%). After shutdown, sleep quality improved by 1.7 units (95% CI: 0.1-3.4) per mA/m decrease in magnetic field exposure. Melatonin excretion increased by 15% (95% CI: -3 to 36%) compared to baseline values suggesting a rebound effect. Stratified analyses showed an exposure effect on melatonin excretion in poor sleepers (26% increase; 95% CI: 8-47%) but not in good sleepers. Change in sleep quality and melatonin excretion was related to the extent of magnetic field reduction after the transmitter's shut down in poor but not good sleepers. However, blinding of exposure was not possible in this observational study and this may have affected the outcome measurements in a direct or indirect (psychological) way.

Calcium waves driven by "sensitization" wave-fronts

OBJECTIVE: Cellular Ca(2+) waves are understood as reaction-diffusion systems sustained by Ca(2+)-induced Ca(2+) release (CICR) from Ca(2+) stores. Given the recently discovered sensitization of Ca(2+) release channels (ryanodine receptors; RyRs) of the sarcoplasmic reticulum (SR) by luminal SR Ca(2+), waves could also be driven by RyR sensitization, mediated by SR overloading via Ca(2+) pump (SERCA), acting in tandem with CICR. METHODS: Confocal imaging of the Ca(2+) indicator fluo-3 was combined with UV-flash photolysis of caged compounds and the whole-cell configuration of the patch clamp technique to carry out these experiments in isolated guinea pig ventricular cardiomyocytes. RESULTS: Upon sudden slowing of the SERCA in cardiomyocytes with a photoreleased inhibitor, waves indeed decelerated immediately. No secondary changes of Ca(2+) signaling or SR Ca(2+) content due to SERCA inhibition were observed in the short time-frame of these experiments. CONCLUSIONS: Our findings are consistent with Ca(2+) loading resulting in a zone of RyR 'sensitization' traveling within the SR, but inconsistent with CICR as the predominant mechanism driving the Ca(2+) waves. This alternative mode of RyR activation is essential to fully conceptualize cardiac arrhythmias triggered by spontaneous Ca(2+) release.

Time-domain modeling of high-frequency electromagnetic wave propagation, overhead wires, and earth

Prediction of radiated fields from transmission lines has not previously been studied from a panoptical power system perspective. The application of BPL technologies to overhead transmission lines would benefit greatly from an ability to simulate real power system environments, not limited to the transmission lines themselves. Presently circuitbased transmission line models used by EMTP-type programs utilize Carson’s formula for a waveguide parallel to an interface. This formula is not valid for calculations at high frequencies, considering effects of earth return currents. This thesis explains the challenges of developing such improved models, explores an approach to combining circuit-based and electromagnetics modeling to predict radiated fields from transmission lines, exposes inadequacies of simulation tools, and suggests methods of extending the validity of transmission line models into very high frequency ranges. Electromagnetics programs are commonly used to study radiated fields from transmission lines. However, an approach is proposed here which is also able to incorporate the components of a power system through the combined use of EMTP-type models. Carson’s formulas address the series impedance of electrical conductors above and parallel to the earth. These equations have been analyzed to show their inherent assumptions and what the implications are. Additionally, the lack of validity into higher frequencies has been demonstrated, showing the need to replace Carson’s formulas for these types of studies. This body of work leads to several conclusions about the relatively new study of BPL. Foremost, there is a gap in modeling capabilities which has been bridged through integration of circuit-based and electromagnetics modeling, allowing more realistic prediction of BPL performance and radiated fields. The proposed approach is limited in its scope of validity due to the formulas used by EMTP-type software. To extend the range of validity, a new set of equations must be identified and implemented in the approach. Several potential methods of implementation have been explored. Though an appropriate set of equations has not yet been identified, further research in this area will benefit from a clear depiction of the next important steps and how they can be accomplished. Prediction of radiated fields from transmission lines has not previously been studied from a panoptical power system perspective. The application of BPL technologies to overhead transmission lines would benefit greatly from an ability to simulate real power system environments, not limited to the transmission lines themselves. Presently circuitbased transmission line models used by EMTP-type programs utilize Carson’s formula for a waveguide parallel to an interface. This formula is not valid for calculations at high frequencies, considering effects of earth return currents. This thesis explains the challenges of developing such improved models, explores an approach to combining circuit-based and electromagnetics modeling to predict radiated fields from transmission lines, exposes inadequacies of simulation tools, and suggests methods of extending the validity of transmission line models into very high frequency ranges. Electromagnetics programs are commonly used to study radiated fields from transmission lines. However, an approach is proposed here which is also able to incorporate the components of a power system through the combined use of EMTP-type models. Carson’s formulas address the series impedance of electrical conductors above and parallel to the earth. These equations have been analyzed to show their inherent assumptions and what the implications are. Additionally, the lack of validity into higher frequencies has been demonstrated, showing the need to replace Carson’s formulas for these types of studies. This body of work leads to several conclusions about the relatively new study of BPL. Foremost, there is a gap in modeling capabilities which has been bridged through integration of circuit-based and electromagnetics modeling, allowing more realistic prediction of BPL performance and radiated fields. The proposed approach is limited in its scope of validity due to the formulas used by EMTP-type software. To extend the range of validity, a new set of equations must be identified and implemented in the approach. Several potential methods of implementation have been explored. Though an appropriate set of equations has not yet been identified, further research in this area will benefit from a clear depiction of the next important steps and how they can be accomplished.

Extracorporeal shock wave lithotripsy for distal ureteral calculi: what a powerful machine can achieve

PURPOSE: We assessed the efficacy of extracorporeal shock wave lithotripsy (ESWL, Dornier Medical Systems, Inc., Marietta, Georgia) for distal ureteral calculi with the HM3 (Dornier Medical Systems, Inc.) lithotriptor. MATERIALS AND METHODS: A total of 585 consecutive patients with distal ureteral calculi were treated with ESWL using an unmodified HM3 lithotriptor. Of these patients 67 referred for treatment only for whom no followup was available were excluded from further analysis. The remaining 518 cases were followed until they were radiologically documented to be stone-free or considered treatment failures. Before ESWL additional procedures were performed in 144 patients, including stone push back, ureteral catheter or Double-J (Medical Engineering Corp., New York, New York) stent placement, percutaneous nephrostomy, ureteral endoscopic maneuvers or stone basket manipulation. A total of 374 patients needed no preliminary treatment before ESWL. RESULTS: Of the 518 patients 469 (91%) were successfully treated with 1 ESWL session, while 49 (9%) needed 2 or 3. Manipulation after ESWL was performed in 22 cases, including stent placement, percutaneous nephrostomy, ureteral endoscopic stone removal and a stone basket procedure. On day 1 after ESWL 327 patients (63%) were stone-free, 158 (30%) had less than 5 mm. fragments and 33 (7%) had more than 5 mm. fragments. At 3 months the stone-free rate increased to 97%. CONCLUSIONS: These data show that ESWL for distal ureteral calculi with the powerful unmodified HM3 lithotriptor has a high success rate with a low rate of minimally traumatic manipulations before and after intervention. Results in terms of the re-treatment and stone-free rates are superior to those of any other second or third generation lithotriptor and comparable to the results of the best ureteroscopic series.

Tropopause level Rossby wave breaking in the Northern Hemisphere: a feature-based validation of the ECHAM5-HAM climate model

Breaking synoptic-scale Rossby waves (RWB) at the tropopause level are central to the daily weather evolution in the extratropics and the subtropics. RWB leads to pronounced meridional transport of heat, moisture, momentum, and chemical constituents. RWB events are manifest as elongated and narrow structures in the tropopause-level potential vorticity (PV) field. A feature-based validation approach is used to assess the representation of Northern Hemisphere RWB in present-day climate simulations carried out with the ECHAM5-HAM climate model at three different resolutions (T42L19, T63L31, and T106L31) against the ERA-40 reanalysis data set. An objective identification algorithm extracts RWB events from the isentropic PV field and allows quantifying the frequency of occurrence of RWB. The biases in the frequency of RWB are then compared to biases in the time mean tropopause-level jet wind speeds. The ECHAM5-HAM model captures the location of the RWB frequency maxima in the Northern Hemisphere at all three resolutions. However, at coarse resolution (T42L19) the overall frequency of RWB, i.e. the frequency averaged over all seasons and the entire hemisphere, is underestimated by 28%.The higher-resolution simulations capture the overall frequency of RWB much better, with a minor difference between T63L31 and T106L31 (frequency errors of −3.5 and 6%, respectively). The number of large-size RWB events is significantly underestimated by the T42L19 experiment and well represented in the T106L31 simulation. On the local scale, however, significant differences to ERA-40 are found in the higher-resolution simulations. These differences are regionally confined and vary with the season. The most striking difference between T106L31 and ERA-40 is that ECHAM5-HAM overestimates the frequency of RWB in the subtropical Atlantic in all seasons except for spring. This bias maximum is accompanied by an equatorward extension of the subtropical westerlies.

A comparison of estimated glomerular filtration rates using Cockcroft−Gault and the Chronic Kidney Disease Epidemiology Collaboration estimating equations in HIV infection

OBJECTIVES: The aim of this study was to determine whether the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI)- or Cockcroft-Gault (CG)-based estimated glomerular filtration rates (eGFRs) performs better in the cohort setting for predicting moderate/advanced chronic kidney disease (CKD) or end-stage renal disease (ESRD). METHODS: A total of 9521 persons in the EuroSIDA study contributed 133 873 eGFRs. Poisson regression was used to model the incidence of moderate and advanced CKD (confirmed eGFR < 60 and < 30 mL/min/1.73 m(2) , respectively) or ESRD (fatal/nonfatal) using CG and CKD-EPI eGFRs. RESULTS: Of 133 873 eGFR values, the ratio of CG to CKD-EPI was ≥ 1.1 in 22 092 (16.5%) and the difference between them (CG minus CKD-EPI) was ≥ 10 mL/min/1.73 m(2) in 20 867 (15.6%). Differences between CKD-EPI and CG were much greater when CG was not standardized for body surface area (BSA). A total of 403 persons developed moderate CKD using CG [incidence 8.9/1000 person-years of follow-up (PYFU); 95% confidence interval (CI) 8.0-9.8] and 364 using CKD-EPI (incidence 7.3/1000 PYFU; 95% CI 6.5-8.0). CG-derived eGFRs were equal to CKD-EPI-derived eGFRs at predicting ESRD (n = 36) and death (n = 565), as measured by the Akaike information criterion. CG-based moderate and advanced CKDs were associated with ESRD [adjusted incidence rate ratio (aIRR) 7.17; 95% CI 2.65-19.36 and aIRR 23.46; 95% CI 8.54-64.48, respectively], as were CKD-EPI-based moderate and advanced CKDs (aIRR 12.41; 95% CI 4.74-32.51 and aIRR 12.44; 95% CI 4.83-32.03, respectively). CONCLUSIONS: Differences between eGFRs using CG adjusted for BSA or CKD-EPI were modest. In the absence of a gold standard, the two formulae predicted clinical outcomes with equal precision and can be used to estimate GFR in HIV-positive persons.

Cardiac Shock Wave Therapy for Chronic Refractory Angina Pectoris. A Prospective Placebo-Controlled Randomized Trial

Background: Cardiac shock wave therapy (CSWT) delivered to the myocardium increases capillary density and regional myocardial blood flow in animal experiments. In addition, nonenzymatic nitric oxide production and the upregulation of vascular growth factor's mRNA by CSWT have been described. The aim of the study was therefore to test its potential to relieve symptoms in patients with chronic stable angina pectoris. Methods: Twenty-one patients (mean age 68.2 ± 8.3 years, 19 males) with chronic refractory angina pectoris and evidence of inducible myocardial ischemia during MIBI-SPECT imaging, were randomized into a treatment (n = 11) and a placebo arm (n = 10). The region of exercise-induced ischemia was treated with echocardiographic guidance during nine sessions over a period of 3 months. One session of CSWT consisted of 200 shots/spot (9--12 spots/session) with an energy intensity of 0.09 mJ/mm2. In the control group acoustic simulation was performed without energy application. Medication was kept unchanged during the whole treatment period. Results: In the treatment group, symptoms improved in 9/11 patients, and the ischemic threshold, determined by cardiopulmonary exercise stress testing, increased from 80 ± 28 to 95 ± 28 W (P= 0.036). In the placebo arm, only 2/10 patients reported an improvement and the ischemic threshold remained unchanged (98 ± 23 to 107 ± 23 W; P= 0.141). The items “physical functioning” (P= 0.043), “general health perception” (P= 0.046), and “vitality” (P= 0.035) of the SF-36 questionnaire significantly improved in the treatment arm, whereas in the placebo arm, no significant change was noted. Neither arrhythmias, troponin rise nor complications were observed during treatment. Conclusions: This placebo controlled trial shows a significant improvement in symptoms, quality of life parameters and ischemic threshold during exercise in patients with chronic refractory angina pectoris treated with CSWT. Thus, CSWT represents a new option for the treatment of patients with refractory AP.

Essential spectrum of systems of singular differential equations

In this paper we develop a new method to determine the essential spectrum of coupled systems of singular differential equations. Applications to problems from magnetohydrodynamics and astrophysics are given.