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.

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.

Three-point boundary value problems for second-order, ordinary, differential equations

We establish existence results for solutions to three-point boundary value problems for nonlinear, second-order, ordinary differential equations with nonlinear boundary conditions. (C) 2001 Elsevier Science Ltd. All rights reserved.

Differential inclusions and robust control theory

Uncontrolled systems (x) over dot is an element of Ax, where A is a non-empty compact set of matrices, and controlled systems (x) over dot is an element of Ax + Bu are considered. Higher-order systems 0 is an element of Px - Du, where and are sets of differential polynomials, are also studied. It is shown that, under natural conditions commonly occurring in robust control theory, with some mild additional restrictions, asymptotic stability of differential inclusions is guaranteed. The main results are variants of small-gain theorems and the principal technique used is the Krasnosel'skii-Pokrovskii principle of absence of bounded solutions.

Stability of linear difference and differential inclusions

Any given n X n matrix A is shown to be a restriction, to the A-invariant subspace, of a nonnegative N x N matrix B of spectral radius p(B) arbitrarily close to p(A). A difference inclusion x(k+1) is an element of Ax(k), where A is a compact set of matrices, is asymptotically stable if and only if A can be extended to a set B of nonnegative matrices B with \ \B \ \ (1) < 1 or \ \B \ \ (infinity) < 1. Similar results are derived for differential inclusions.

Stiffly accurate Runge-Kutta methods for stiff stochastic differential equations

In this paper we discuss implicit methods based on stiffly accurate Runge-Kutta methods and splitting techniques for solving Stratonovich stochastic differential equations (SDEs). Two splitting techniques: the balanced splitting technique and the deterministic splitting technique, are used in this paper. We construct a two-stage implicit Runge-Kutta method with strong order 1.0 which is corrected twice and no update is needed. The stability properties and numerical results show that this approach is suitable for solving stiff SDEs. (C) 2001 Elsevier Science B.V. All rights reserved.

Earth pressure on cantilever walls at design retained heights

There are many methods for the analysis and design of embedded cantilever retaining walls. They involve various different simplifications of the pressure distribution to allow calculation of the limiting equilibrium retained height and the bending moment when the retained height is less than the limiting equilibrium value, i.e. the serviceability case. Recently, a new method for determining the serviceability earth pressure and bending moment has been proposed. This method makes an assumption defining the point of zero net pressure. This assumption implies that the passive pressure is not fully mobilised immediately below the excavation level. The finite element analyses presented in this paper examine the net pressure distribution on walls in which the retained height is less, than the limiting equilibrium value. The study shows that for all practical walls, the earth pressure distributions on the front and back of the wall are at their limit values, Kp and K-a respectively, when the lumped factor of safety F-r is less than or equal to2.0. A rectilinear net pressure distribution is proposed that is intuitively logical. It produces good predictions of the complete bending moment diagram for walls in the service configuration and the proposed method gives results that have excellent agreement with centrifuge model tests. The study shows that the method for determining the serviceability bending moment suggested by Padfield and Mair(1) in the CIRIA Report 104 gives excellent predictions of the maximum bending moment in practical cantilever walls. It provides the missing data that have been needed to verify and justify the CIRIA 104 method.

Mid-thoracic tenderness: a comparison of pressure pain threshold between spinal regions, in asymptomatic subjects

Palpation for tenderness forms an important part of the manual therapy assessment for musculoskeletal dysfunction, In conjunction with other testing procedures it assists in establishing the clinical diagnosis. Tenderness in the thoracic spine has been reported in the literature as a clinical feature in musculoskeletal conditions where pain and dysfunction are located primarily in the upper quadrant. This study aimed to establish whether pressure pain thresholds (PPTs) of the mid-thoracic region of asymptomatic subjects were naturally lower than those of the cervical and lumbar areas. A within-subject study design was used to examine PPT at four spinal levels C6, T4, T6, and L4 in 50 asymptomatic volunteers. Results showed significant (P < 0.001) regional differences. PPT values increased in a caudal direction. The cervical region had the lowest PPT scores, that is was the most tender. Values increased in the thoracic region and were highest in the lumbar region. This study contributes to the normative data on spinal PPT values and demonstrates that mid-thoracic tenderness relative to the cervical spine is not a normal finding in asymptomatic subjects. (C) 2001 Harcourt Publishers Ltd.

Influence of deceleration profiles on occupant velocity differential and injury potential

This paper compares two hypothetical and identical vehicle deceleration profiles mirrored in time, one linearly descending with time and the other linearly ascending with time. The differences of such profiles on occupant velocity differential and by implication, injury levels at the point of occupant impact are presented. An indifference point is established to assist in comparing which occupant body part will benefit from the altered crash pulse. It is shown that for occupant proximity distances below the indifference point, an ascending profile results in lower injury risk. Above the indifference point, the result is reversed.

Differential perturbation of neuronal and glial glutamate transport systems in retinal ischaemia

Glutamate is the major excitatory neurotransmitter in the retina and is removed from the extracellular space by an energy-dependent process involving neuronal and glial cell transporters. The radial glial Muller cells express the glutamate transporter, GLAST, and preferentially accumulate glutamate. However, during an ischaemic episode, extracellular glutamate concentrations may rise to excitotoxic levels. Is this catastrophic rise in extracellular glutamate due to a failure of GLAST? Using immunocytochemistry, we monitored the transport of the glutamate transporter substrate, D-aspartate, in the retina under normal and ischaemic conditions. Two models of compromised retinal perfusion were compared: (1) Anaesthetised rats had their carotid arteries occluded for 7 days to produce a chronic reduction in retinal blood flow. Retinal function was assessed by electroretinography. D-aspartate was injected into the eye for 45 min, Following euthanasia, the retina was processed for D-aspartate. GLAST and glutamate immunocytochemistry. Although reduced retinal perfusion suppresses the electroretinogram b-wave, neither retinal histology, GLAST expression, nor the ability of Muller cells to uptake D-aspartate is affected. As this insult does not appear to cause excitotoxic neuronal damage, these data suggest that GLAST function and glutamate clearance are maintained during periods of reduced retinal perfusion. (2) Occlusion of the central retinal artery for 60 min abolishes retinal perfusion, inducing histological damage and electroretinogram suppression. Although GLAST expression appears to be normal. its ability to transport D-aspartate into Muller cells is greatly reduced. Interestingly, D-aspartate is transported into neuronal cells, i.e. photoreceptors, bipolar and ganglion cells. This suggests that while GLAST is vitally important for the clearance of excess extracellular glutamate, its capability to sustain inward transport is particularly susceptible to an acute ischaemic attack. Manipulation of GLAST function could alleviate the degeneration and blindness that result from ischaemic retinal disease. (C) 2001 Elsevier Science Ltd, All rights reserved.

Differential inhibition of human CYP1A1 AND CYP1A2 by quinidine and quinine.

The inhibition of recombinant CYP1A1 and CYP1A2 activity by quinidine and quinine was evluated using ethoxyresorufin O -deethylation, phenacetin O -deethylation and propranolol desisopropylation as probe catalytic pathways. 2. With substrate concentrations near the K m of catalysis, both quinidine and quinine potently inhibited CYP1A1 activity with [ I ] 0.5 ~ 1-3 μM, whereas in contrast, there was little inhibition of CYP1A2 activity. The Lineweaver-Burk plots with varying inhibitor concentrations suggested that inhibition by quinidine and quinine was competitive. 3. There was only trace metabolism of quinidine by recombinant CYP1A1, whereas rat liver microsomes as a control showed extensive consumption of quinidine and metabolite production. 4. This work suggests that quinidine is a non-classical inhibitor of CYP1A1 and that it is not as highly specific at inhibiting CYP2D6 as previously thought.

The measurement of Pitot pressure in high enthalpy expansion tubes

Expansion tubes operating at total flow enthalpies of 100 MJ kg(-1) or more have characteristical test times of 30-50 mus. Under these conditions, the response time of the Pitot pressure measuring device is critical when performing flow calibration studies. The conventional technique of using a commercial pressure transducer protected by shielding has not always proven to be effective, due to the relatively large (and variable) response time caused by the shielding. A device called the stress wave bar gauge has been designed and calibrated and shown to be an effective way to measure the Pitot pressure with a response time of only 2-3 mus.