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.

Stability of nonlinear difference inclusions

The stability of difference inclusions x(k+1) is an element of F(x(k)) is studied, where F(x) = {F(x, gimel) : is an element of Lambda} and the selections F(., gimel) : E -->E assume values in a Banach space E, partially ordered by a cone K. It is assumed that the operators F(.,gimel) are heterotone or pseudoconcave. The main results concern asymptotically stable absorbing sets, and include the case of a single equilibrium point. The results are applied to a number of practical problems.

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.

Estimates of the real structured radius of stability of linear dynamic systems

A question is examined as to estimates of the norms of perturbations of a linear stable dynamic system, under which the perturbed system remains stable in a situation R:here a perturbation has a fixed structure.

The acquisition of movement skills: Practice enhances the dynamic stability of bimanual coordination

During bimanual movements, two relatively stable inherent patterns of coordination (in-phase and anti-phase) are displayed (e.g., Kelso, Am. J. Physiol. 246 (1984) R1000). Recent research has shown that new patterns of coordination can be learned. For example, following practice a 90 degrees out-of-phase pattern can emerge as an additional, relatively stable, state (e.g., Zanone & Kelso, J. Exp. Psychol.: Human Performance and Perception 18 (1992) 403). On this basis, it has been concluded that practice leads to the evolution and stabilisation of the newly learned pattern and that this process of learning changes the entire attractor layout of the dynamic system. A general feature of such research has been to observe the changes of the targeted pattern's stability characteristics during training at a single movement frequency. The present study was designed to examine how practice affects the maintenance of a coordinated pattern as the movement frequency is scaled. Eleven volunteers were asked to perform a bimanual forearm pronation-supination task. Time to transition onset was used as an index of the subjects' ability to maintain two symmetrically opposite coordinated patterns (target task - 90 degrees out-of-phase - transfer task - 270 degrees out-of-phase). Their ability to maintain the target task and the transfer task were examined again after five practice sessions each consisting of 15 trials of only the 90 degrees out-of-phase pattern. Concurrent performance feedback (a Lissajous figure) was available to the participants during each practice trial. A comparison of the time to transition onset showed that the target task was more stable after practice (p = 0.025). These changes were still observed one week (p = 0.05) and two months (p = 0.075) after the practice period. Changes in the stability of the transfer task were not observed until two months after practice (p = 0.025). Notably, following practice, transitions from the 90 degrees pattern were generally to the anti-phase (180 degrees) pattern, whereas, transitions from the 270 degrees pattern were to the 90 degrees pattern. These results suggest that practice does improve the stability of a 90 degrees pattern, and that such improvements are transferable to the performance of the unpractised 270 degrees pattern. In addition, the anti-phase pattern remained more stable than the practised 90 degrees pattern throughout. (C) 2001 Elsevier Science B.V. All rights reserved.

Let your feet do the walking: constraints on the stability of bipedal coordination

In this paper we consider whether the behaviour of the neural circuitry that controls lower limb movements in humans is shaped primarily by the spatiotemporal characteristics of bipedal gait patterns, or by selective pressures that are sensitive to considerations of balance and energetics. During the course of normal locomotion, the full dynamics of the neural circuitry are masked by the inertial properties of the limbs. In the present study, participants executed bipedal movements in conditions in which their feet were either unloaded or subject to additional inertial loads. Two patterns of rhythmic coordination were examined. In the in-phase mode, participants were required to flex their ankles and extend their ankles in synchrony. In the out-of-phase mode, the participants flexed one ankle while extending the other and vice versa. The frequency of movement was increased systematically throughout each experimental trial. All participants were able to maintain both the in-phase and the out-of-phase mode of coordination, to the point at which they could no longer increase their frequency of movement. Transitions between the two modes were not observed, and the stability of the out-of-phase and in-phase modes of coordination was equivalent at all movement frequencies. These findings indicate that, in humans, the behaviour of the neural circuitry underlying coordinated movements of the lower limbs is not constrained strongly by the spatiotemporal symmetries of bipedal gait patterns.

Stickiness in foods: A review of mechanisms and test methods

Problems associated with the stickiness of food in processing and storage practices along with its causative factors are outlined. Fundamental mechanisms that explain why and how food products become sticky are discussed. Methods currently in use for characterizing and overcoming stickiness problems in food processing and storage operations are described. The use of glass transition temperature-based model, which provides a rational basis for understanding and characterizing the stickiness of many food products, is highlighted.

Techniques to determine ignition, flame stability and burnout of blended coals in p.f. power station boilers

The blending of coals has become popular to improve the performance of coals, to meet specifications of power plants and, to reduce the cost of coals, This article reviews the results and provides new information on ignition, flame stability, and carbon burnout studies of blended coals. The reviewed studies were conducted in laboratory-, pilot-, and full-scale facilities. The new information was taken in pilot-scale studies. The results generally show that blending a high-volatile coal with a low-volatile coal or anthracite can improve the ignition, flame stability and burnout of the blends. This paper discusses two general methods to predict the performance of blended coals: (1) experiment; and (2) indices. Laboratory- and pilot-scale tests, at least, provide a relative ranking of the combustion performance of coal/blends in power station boilers. Several indices, volatile matter content, heating value and a maceral index, can be used to predict the relative ranking of ignitability and flame stability of coals and blends. The maceral index, fuel ratio, and vitrinite reflectance can also be used to predict the absolute carbon burnout of coal and blends within limits. (C) 2000 Elsevier Science Ltd. All rights reserved.

The insulin hypoglycemia test: Hypoglycemic criteria and reproducibility

The insulin hypoglycemia test (IHT) is widely regarded as the 'gold standard' for dynamic stimulation of the hypothalamic-pituitary-adrenal (HPA) axis. This study aimed to investigate the temporal relationship between a rapid decrease in plasma glucose and the corresponding rise in plasma adenocorticotropic hormone (ACTH), and to assess the reproducibility of hormone responses to hypoglycemia in normal humans. Ten normal subjects underwent IHTs, using an insulin dose of 0.15 U/kg. Of these, eight had a second IHT (IHT2) and three went on to a third test (IHT3). Plasma ACTH and cortisol were measured at 15-min intervals and, additionally, in four IHT2s and the three IHT3s, ACTH was measured at 2.5- or 5-min intervals. Mean glucose nadirs and mean ACTH and cortisol responses were not significantly different between IHT1, IHT2 and IHT3. Combined data from all 21 tests showed the magnitude of the cortisol responses, but not the ACTH responses, correlated significantly with the depth and duration of hypoglycemia. All subjects achieved glucose concentrations of of less than or equal to 1.6 mmol/l before any detectable rise in ACTH occurred. In the seven tests performed with frequent sampling, an ACTH rise never preceeded the glucose nadir, but occurred at the nadir, or up to 15 min after. On repeat testing, peak ACTH levels varied markedly within individuals, whereas peak cortisol levels were more reproducible (mean coefficient of variation 7%). In conclusion, hypoglycemia of less than or equal to 1.6 mmol/l was sufficient to cause stimulation of the HPA axis in all 21 IHTs conducted in normal subjects. Nonetheless; our data cannot reveal whether higher glucose nadirs would stimulate increased HPA axis activity in all subjects. Overall, the cortisol response to hypoglycemia is more reproducible than the ACTH response but, in an individual subject, the difference in peak cortisol between two IHTs may exceed 100 nmol/l.

A test of the ash-free dry weight technique on the developmental stages of Patiriella spp. (Echinodermata : Asteroidea)

Determination of the ash-free dry weight (AFDW) of marine specimens requires samples to be rinsed, soaked, and centrifuged. Problems associated with this technique were examined with the developmental stages of seastar species (Patiriella) with different modes of development. The influence of three rinsing solutions (ammonium formate [AF], filtered seawater [FSW], and reverse osmosis water [RO]) was assessed. The hypothesis that the AFDW technique is a measure of organic material was addressed by drying inorganic salts. Developmental stages of Patiriella calcar rinsed in FSW were twice as heavy as those rinsed in RO or AE indicating that samples should be rinsed in RO or AF before weighing. Soaking treatments had a significant effect on the AFDW of samples of P. calcar (planktonic developer), indicating that the rinsing period should be brief. Zygotes of Patiriella re gularis (planktonic developer) were significantly heavier than ova or gastrulae, regardless of treatment. In contrast, there were no significant differences in the AFDW of any stages or treatments of Patiriella exigua (benthic developer). This may be due to the presence of a modified fertilization envelope, which protects these benthic embryos. Inorganic salts with water of crystallization and FSW lost 20-75% and 14% of their dry weight, respectively, after ashing. We propose that salt ions may retain water, which does not evaporate during drying but is lost during ashing, resulting in the overestimation of sample AFDW. If a similar process occurs in the developmental stages of marine invertebrates, changes in the intracellular ionic composition through development may result in inaccurate estimates of biomass.