The composite Euler method for stiff stochastic differential equations

In this paper we present the composite Euler method for the strong solution of stochastic differential equations driven by d-dimensional Wiener processes. This method is a combination of the semi-implicit Euler method and the implicit Euler method. At each step either the semi-implicit Euler method or the implicit Euler method is used in order to obtain better stability properties. We give criteria for selecting the semi-implicit Euler method or the implicit Euler method. For the linear test equation, the convergence properties of the composite Euler method depend on the criteria for selecting the methods. Numerical results suggest that the convergence properties of the composite Euler method applied to nonlinear SDEs is the same as those applied to linear equations. The stability properties of the composite Euler method are shown to be far superior to those of the Euler methods, and numerical results show that the composite Euler method is a very promising method. (C) 2001 Elsevier Science B.V. All rights reserved.

Renal structural and functional repair in a mouse model of reversal of ureteral obstruction

The end point of immune and nonimmune renal injury typically involves glomerular and tubulointerstitial fibrosis. Although numerous studies have focused on the events that lead to renal fibrosis, less is known about the mechanisms that promote cellular repair and tissue remodeling. Described is a model of renal injury and repair after the reversal of unilateral ureteral obstruction (UUO) in male C57b1/6J mice. Male mice (20 to 25 g) underwent 10 d of UUO with or without 1, 2, 4, or 6 wk of reversal of UUO (R-UUO). UUO resulted in cortical tubular cell atrophy and tubular dilation in conjunction with an almost complete ablation of the outer medulla. This was associated with interstitial macrophage infiltration; increased hydroxyproline content; and upregulated type I, III, IV, and V collagen expression. The volume density of kidney occupied by renal tubules that exhibited a brush border was measured as an assessment of the degree of repair after R-UUO. After 6 wk of R-UUO, there was an increase in the area of kidney occupied by repaired tubules (83.7 +/- 5.9%), compared with 10 d UUO kidneys (32.6 +/- 7.3%). This coincided with reduced macrophage numbers, decreased hydroxyproline content, and reduced collagen accumulation and interstitial matrix expansion, compared with obstructed kidneys from UUO mice. GFR in the 6-wk R-UUO kidneys was restored to 43 to 88% of the GFR in the contralateral unobstructed kidneys. This study describes the regenerative potential of the kidney after the established interstitial matrix expansion and medullary ablation associated with UUO in the adult mouse.

The Equilibrium Flux Method for the calculation of flows with non-equilbrium chemical reactions

The Equilibrium Flux Method [1] is a kinetic theory based finite volume method for calculating the flow of a compressible ideal gas. It is shown here that, in effect, the method solves the Euler equations with added pseudo-dissipative terms and that it is a natural upwinding scheme. The method can be easily modified so that the flow of a chemically reacting gas mixture can be calculated. Results from the method for a one-dimensional non-equilibrium reacting flow are shown to agree well with a conventional continuum solution. Results are also presented for the calculation of a plane two-dimensional flow, at hypersonic speed, of a dissociating gas around a blunt-nosed body.

Theory manual to OctVCE – a cartesian cell CFD code with special application to blast wave problems, Department of Mechanical Engineering Report 2007/12

OctVCE is a cartesian cell CFD code produced especially for numerical simulations of shock and blast wave interactions with complex geometries, in particular, from explosions. Virtual Cell Embedding (VCE) was chosen as its cartesian cell kernel for its simplicity and sufficiency for practical engineering design problems. The code uses a finite-volume formulation of the unsteady Euler equations with a second order explicit Runge-Kutta Godonov (MUSCL) scheme. Gradients are calculated using a least-squares method with a minmod limiter. Flux solvers used are AUSM, AUSMDV and EFM. No fluid-structure coupling or chemical reactions are allowed, but gas models can be perfect gas and JWL or JWLB for the explosive products. This report also describes the code’s ‘octree’ mesh adaptive capability and point-inclusion query procedures for the VCE geometry engine. Finally, some space will also be devoted to describing code parallelization using the shared-memory OpenMP paradigm. The user manual to the code is to be found in the companion report 2007/13.

User guide for shock and blast simulation with the OctVCE code (version 3.5+), Department of Mechanical Engineering Report 2007/13

OctVCE is a cartesian cell CFD code produced especially for numerical simulations of shock and blast wave interactions with complex geometries. Virtual Cell Embedding (VCE) was chosen as its cartesian cell kernel as it is simple to code and sufficient for practical engineering design problems. This also makes the code much more ‘user-friendly’ than structured grid approaches as the gridding process is done automatically. The CFD methodology relies on a finite-volume formulation of the unsteady Euler equations and is solved using a standard explicit Godonov (MUSCL) scheme. Both octree-based adaptive mesh refinement and shared-memory parallel processing capability have also been incorporated. For further details on the theory behind the code, see the companion report 2007/12.

Alkyl halides, super hydrogen production and the pathogenesis of pneumatosis cystoides coli

Background and aims-The colons of patients with pneumatosis cystoides coli produce excessive H-2. Exposure to alkyl halides could explain this. Six consecutive patients who had pneumatosis cystoides coli while taking chloral hydrate (1-5+ g/day) are reported. Patients 2 and 3 were investigated after they had ceased chloral hydrate treatment. One produced methane, the other did not. (Pneumatosis cystoides coli patients are non-methanogenic according to the literature.) Both had overnight fasting breath H-2 of less than 10 ppm. A literature review disclosed just one patient who was using chloral at the time of diagnosed pneumatosis cystoides coli, but an epidemic of the disease in workers exposed to trichloroethylene. Methods-(i) In vitro experiments with human faeces: chloral or closely related alkyl halides were added to anaerobic faecal cultures derived from four methane-producing and three non-methanogenic human subjects. H-2 and CH4 gases were measured. (ii) In vivo animal experiment: chloral hydrate was added to drinking water of four Wistar rats, and faecal HI compared with control rats. Results-Alkyl halides increased H-2 up to 900 times in methanogenic and 10 times in non-methanogenic faecal cultures. The K-i of chloral was 0.2 mM. Methanogenesis was inhibited in concert with the increase in net H-2. In the rat experiment, chloral hydrate increased H-2 10 times, but did not cause pneumatosis. Conclusions-Chloral and trichloroethylene are alkyl halides chemically similar to chloroform, a potent inhibitor of H-2 consumption by methanogens and acetogens. These bacteria are the most important H-2-consuming species in the colon. It is postulated that exposure to these alkyl halides increases net H-2 production, which sets the scene for counterperfusion supersaturation and the formation of gas cysts. In recent times, very low prescribing rates for chloral have caused primary pneumatosis cystoides to become extremely rare. As with primary pneumatosis, secondary pneumatosis cystoides, which occurs if there is small bowel bacterial overgrowth distal to a proximally located gut obstruction, is predicted by counterperfusion supersaturation. Inherent unsaturation due to metabolism of O-2 is a safety factor, which could explain why gas bubbles do not form more often in tissue with high H-2 tension.

A computational study of shock speeds in high-performance shock tubes

This paper describes U2DE, a finite-volume code that numerically solves the Euler equations. The code was used to perform multi-dimensional simulations of the gradual opening of a primary diaphragm in a shock tube. From the simulations, the speed of the developing shock wave was recorded and compared with other estimates. The ability of U2DE to compute shock speed was confirmed by comparing numerical results with the analytic solution for an ideal shock tube. For high initial pressure ratios across the diaphragm, previous experiments have shown that the measured shock speed can exceed the shock speed predicted by one-dimensional models. The shock speeds computed with the present multi-dimensional simulation were higher than those estimated by previous one-dimensional models and, thus, were closer to the experimental measurements. This indicates that multi-dimensional flow effects were partly responsible for the relatively high shock speeds measured in the experiments.

Effect of increased lung expansion on lung growth and development near midgestation in fetal sheep

Obstruction of the fetal trachea is a potent stimulus for fetal lung growth and may have therapeutic potential in human fetuses with lung hypoplasia. However, the effects of increased lung expansion on lung development near midgestation, which is the preferred timing for fetal intervention, have not been well studied. Our aim was to determine the effects of increased lung expansion on lung development at 75-90 d of gestation in fetal sheep. In three groups of fetuses (n = 4 for each), the trachea was occluded for either 10 [10-d tracheal occlusion (TO) group] or 15 d (15-d TO group) or left intact (control fetuses). TO for both 10 and 15 d caused fetal hydrops, resulting in significantly increased fetal body weights. Both periods of TO significantly increased total lung DNA contents from 99.8 +/- 10.1 to 246.0 +/- 5.3 and 246.9 +/- 48.7 mg in 10- and 15-d TO fetuses, respectively. TO for 10 and 15 d also increased airspace diameter, although the percentage of lung occupied by airspace was not increased in 10-d TO fetuses due to large increases in interairway distances; this resulted from a large increase in mesenchymal tissue. The interairway distances at 15 d of TO were reduced compared with the 10-d value but were still similar to 30% larger than control values. We conclude that TO at

Magnetic resonance imaging and diseases of the liver and biliary tract. Part 2. Magnetic resonance cholangiography and angiography and conclusions

Magnetic resonance cholangiography (MRC) relies on the strong T-2 signal from stationary liquids, in this case bile, to generate images. No contrast agents are required, and the failure rate and risk of serious complications is lower than with endoscopic retrograde cholangiopancreatography (ERCP). Data from MRC can be summated to produce an image much like the cholangiogram obtained by using ERCP. In addition, MRC and conventional MRI can provide information about the biliary and other anatomy above and below a biliary obstruction. This provides information for therapeutic intervention that is probably most useful for hilar and intrahepatic biliary obstruction. Magnetic resonance cholangiography appears to be similar to ERCP with respect to sensitivity and specificity in detecting lesions causing biliary obstruction, and in the diagnosis of choledocholithiasis. It is also suited to the assessment of biliary anatomy (including the assessment of surgical bile-duct injuries) and intrahepatic biliary pathology. However, ERCP can be therapeutic as well as diagnostic, and MRC should be limited to situations where intervention is unlikely, where intrahepatic or hilar pathology is suspected, to delineate the biliary anatomy prior to other interventions, or after failed or inadequate ERCP. Magnetic resonance angiography (MRA) relies on the properties of flowing liquids to generate images. It is particularly suited to assessment of the hepatic vasculature and appears as good as conventional angiography. It has been shown to be useful in delineating vascular anatomy prior to liver transplantation or insertion of a transjugular intrahepatic portasystemic shunt. Magnetic resonance angiography may also be useful in predicting subsequent variceal haemorrhage in patients with oesophageal varices. (C) 2000 Blackwell Science Asia Pty Ltd.

A numerical study of flexural buckling of foliated rock slopes

The occurrence of foliated rock masses is common in mining environment. Methods employing continuum approximation in describing the deformation of such rock masses possess a clear advantage over methods where each rock layer and each inter-layer interface (joint) is explicitly modelled. In devising such a continuum model it is imperative that moment (couple) stresses and internal rotations associated with the bending of the rock layers be properly incorporated in the model formulation. Such an approach will lead to a Cosserat-type theory. In the present model, the behaviour of the intact rock layer is assumed to be linearly elastic and the joints are assumed to be elastic-perfectly plastic. Condition of slip at the interfaces are determined by a Mohr-Coulomb criterion with tension cut off at zero normal stress. The theory is valid for large deformations. The model is incorporated into the finite element program AFENA and validated against an analytical solution of elementary buckling problems of a layered medium under gravity loading. A design chart suitable for assessing the stability of slopes in foliated rock masses against flexural buckling failure has been developed. The design chart is easy to use and provides a quick estimate of critical loading factors for slopes in foliated rock masses. It is shown that the model based on Euler's buckling theory as proposed by Cavers (Rock Mechanics and Rock Engineering 1981; 14:87-104) substantially overestimates the critical heights for a vertical slope and underestimates the same for sub-vertical slopes. Copyright (C) 2001 John Wiley & Sons, Ltd.

Intermittent heparinised saline flushes for maintaining indwelling peripheral and central intravenous catheters in diabetic dogs

Intermittent low-dose heparinised saline flushes were found to be efficacious for maintaining patency of indwelling peripheral and central intravenous catheters in diabetic dogs. The catheters were flushed with 1 mL of 1 U/mL heparinised saline every two hours immediately following blood sample collection, or every 12 hours when not being used for sampling. Central catheters were flushed with saline solution first to clear the line before instillation of the heparinised saline. Patency of 54/57 (95%) of the peripheral catheters and 30/32 (94%) of the central catheters was achieved for up to 36 hours and five days, respectively. No phlebitis, or local or systemic infections were observed and, in each case, catheter failure was attributable to obstruction or extravasation. It is unlikely that there will be any contraindications to this flushing technique and its introduction may improve intravenous catheter survival and reduce catheter-associated complications in hospitalised dogs.

Mucociliary clearance in patients with chronic asthma: Effects of beta(2) agonists

Chronic asthma is characterized by airway inflammation, mucus hypersecretion and impaired mucociliary clearance (MCC). We investigated baseline MCC and the acute effect of terbutaline in chronic asthmatics with sputum production while on long-term treatment with salmeterol in combination with inhaled corticosteroids (ICS). MCC was measured at baseline and in response to 1 mg terbutaline (or placebo) on three visits over 80 min in 16 asthmatics (52 +/- 13 years of age). Subjects who had greater than 10% absolute increase in MCC above baseline and placebo, after terbutaline, were categorized in group A and subjects who had less than 10% in group B. In group A subjects (n = 6), MCC increased from 23.7 +/- 4.0% at baseline to 43.7 +/- 4.9% with terbutaline (P < 0.0001) and to 34.4 +/- 5.7% with placebo (P < 0.01). In group B subjects (n = 10), MCC remained similar: 11.3 +/- 3.2% at initial baseline, 12.0 +/- 3.2% with terbutaline and 7.3 +/- 3.0% with placebo (P > 0.05). Group B subjects withdrew from all beta(2) agonists for a week and MCC was remeasured. After withdrawal, baseline MCC (7.0 +/- 1.8%) was similar to the initial baseline value (P > 0.1) and MCC with terbutaline (15.8 +/- 4.9%) was greater than baseline (P < 0.005) but remained abnormal in most subjects. Baseline percentage predicted FEV1 and FEF25-75% were 77.3 +/- 7.2 and 41.7 +/- 5.6 in group A and 59.9 +/- 8.1 and 29.5 +/- 8.4 in group B subjects, respectively. MCC was impaired in most of these asthmatics with persistent airway obstruction and sputum production, despite regular treatment with ICS and salmeterol. In addition, there was little or no stimulation of MCC acutely after terbutaline in most of these asthmatics.

Implicit Taylor methods for stiff stochastic differential equations

In this paper we discuss implicit Taylor methods for stiff Ito stochastic differential equations. Based on the relationship between Ito stochastic integrals and backward stochastic integrals, we introduce three implicit Taylor methods: the implicit Euler-Taylor method with strong order 0.5, the implicit Milstein-Taylor method with strong order 1.0 and the implicit Taylor method with strong order 1.5. The mean-square stability properties of the implicit Euler-Taylor and Milstein-Taylor methods are much better than those of the corresponding semi-implicit Euler and Milstein methods and these two implicit methods can be used to solve stochastic differential equations which are stiff in both the deterministic and the stochastic components. Numerical results are reported to show the convergence properties and the stability properties of these three implicit Taylor methods. The stability analysis and numerical results show that the implicit Euler-Taylor and Milstein-Taylor methods are very promising methods for stiff stochastic differential equations.