Adams-Type Methods for the Numerical Solution of Stochastic Ordinary Differential Equations

Stochastic differential equations (SDEs) arise fi om physical systems where the parameters describing the system can only be estimated or are subject to noise. There has been much work done recently on developing numerical methods for solving SDEs. This paper will focus on stability issues and variable stepsize implementation techniques for numerically solving SDEs effectively. (C) 2000 Elsevier Science B.V. All rights reserved.

Efficient solution of multiple cracks in great number using eigen COD boundary integral equations with iteration procedure

A newly developed computational approach is proposed in the paper for the analysis of multiple crack problems based on the eigen crack opening displacement (COD) boundary integral equations. The eigen COD particularly refers to a crack in an infinite domain under fictitious traction acting on the crack surface. With the concept of eigen COD, the multiple cracks in great number can be solved by using the conventional displacement discontinuity boundary integral equations in an iterative fashion with a small size of system matrix to determine all the unknown CODs step by step. To deal with the interactions among cracks for multiple crack problems, all cracks in the problem are divided into two groups, namely the adjacent group and the far-field group, according to the distance to the current crack in consideration. The adjacent group contains cracks with relatively small distances but strong effects to the current crack, while the others, the cracks of far-field group are composed of those with relatively large distances. Correspondingly, the eigen COD of the current crack is computed in two parts. The first part is computed by using the fictitious tractions of adjacent cracks via the local Eshelby matrix derived from the traction boundary integral equations in discretized form, while the second part is computed by using those of far-field cracks so that the high computational efficiency can be achieved in the proposed approach. The numerical results of the proposed approach are compared not only with those using the dual boundary integral equations (D-BIE) and the BIE with numerical Green's functions (NGF) but also with those of the analytical solutions in literature. The effectiveness and the efficiency of the proposed approach is verified. Numerical examples are provided for the stress intensity factors of cracks, up to several thousands in number, in both the finite and infinite plates.

Efficient solution of two-sided nonlinear space-fractional diffusion equations using fast Poisson preconditioners

We develop a fast Poisson preconditioner for the efficient numerical solution of a class of two-sided nonlinear space fractional diffusion equations in one and two dimensions using the method of lines. Using the shifted Gr¨unwald finite difference formulas to approximate the two-sided(i.e. the left and right Riemann-Liouville) fractional derivatives, the resulting semi-discrete nonlinear systems have dense Jacobian matrices owing to the non-local property of fractional derivatives. We employ a modern initial value problem solver utilising backward differentiation formulas and Jacobian-free Newton-Krylov methods to solve these systems. For efficient performance of the Jacobianfree Newton-Krylov method it is essential to apply an effective preconditioner to accelerate the convergence of the linear iterative solver. The key contribution of our work is to generalise the fast Poisson preconditioner, widely used for integer-order diffusion equations, so that it applies to the two-sided space fractional diffusion equation. A number of numerical experiments are presented to demonstrate the effectiveness of the preconditioner and the overall solution strategy.

The analytical solution and numerical solution of the fractional diffusion-wave equation with damping

Fractional partial differential equations have been applied to many problems in physics, finance, and engineering. Numerical methods and error estimates of these equations are currently a very active area of research. In this paper we consider a fractional diffusionwave equation with damping. We derive the analytical solution for the equation using the method of separation of variables. An implicit difference approximation is constructed. Stability and convergence are proved by the energy method. Finally, two numerical examples are presented to show the effectiveness of this approximation.

Numerical solution of an optimal control model of dendritic cell treatment of a growing tumour

A new optimal control model of the interactions between a growing tumour and the host immune system along with an immunotherapy treatment strategy is presented. The model is based on an ordinary differential equation model of interactions between the growing tu- mour and the natural killer, cytotoxic T lymphocyte and dendritic cells of the host immune system, extended through the addition of a control function representing the application of a dendritic cell treat- ment to the system. The numerical solution of this model, obtained from a multi species Runge–Kutta forward-backward sweep scheme, is described. We investigate the effects of varying the maximum al- lowed amount of dendritic cell vaccine administered to the system and find that control of the tumour cell population is best effected via a high initial vaccine level, followed by reduced treatment and finally cessation of treatment. We also found that increasing the strength of the dendritic cell vaccine causes an increase in the number of natural killer cells and lymphocytes, which in turn reduces the growth of the tumour.

Inflow cannula design for biventricular assist devices

Cardiovascular diseases are a leading cause of death throughout the developed world. With the demand for donor hearts far exceeding the supply, a bridge-to-transplant or permanent solution is required. This is currently achieved with ventricular assist devices (VADs), which can be used to assist the left ventricle (LVAD), right ventricle (RVAD), or both ventricles simultaneously (BiVAD). Earlier generation VADs were large, volume-displacement devices designed for temporary support until a donor heart was found. The latest generation of VADs use rotary blood pump technology which improves device lifetime and the quality of life for end stage heart failure patients. VADs are connected to the heart and greater vessels of the patient through specially designed tubes called cannulae. The inflow cannulae, which supply blood to the VAD, are usually attached to the left atrium or ventricle for LVAD support, and the right atrium or ventricle for RVAD support. Few studies have characterized the haemodynamic difference between the two cannulation sites, particularly with respect to rotary RVAD support. Inflow cannulae are usually made of metal or a semi-rigid polymer to prevent collapse with negative pressures. However suction, and subsequent collapse, of the cannulated heart chamber can be a frequent occurrence, particularly with the relatively preload insensitive rotary blood pumps. Suction events may be associated with endocardial damage, pump flow stoppages and ventricular arrhythmias. While several VAD control strategies are under development, these usually rely on potentially inaccurate sensors or somewhat unreliable inferred data to estimate preload. Fixation of the inflow cannula is usually achieved through suturing the cannula, often via a felt sewing ring, to the cannulated chamber. This technique extends the time on cardiopulmonary bypass which is associated with several postoperative complications. The overall objective of this thesis was to improve the placement and design of rotary LVAD and RVAD inflow cannulae to achieve enhanced haemodynamic performance, reduced incidence of suction events, reduced levels of postoperative bleeding and a faster implantation procedure. Specific objectives were: * in-vitro evaluation of LVAD and RVAD inflow cannula placement, * design and in-vitro evaluation of a passive mechanism to reduce the potential for heart chamber suction, * design and in-vitro evaluation of a novel suture-less cannula fixation device. In order to complete in-vitro evaluation of VAD inflow cannulae, a mock circulation loop (MCL) was developed to accurately replicate the haemodynamics in the human systemic and pulmonary circulations. Validation of the MCL’s haemodynamic performance, including the form and magnitude of pressure, flow and volume traces was completed through comparisons of patient data and the literature. The MCL was capable of reproducing almost any healthy or pathological condition, and provided a useful tool to evaluate VAD cannulation and other cardiovascular devices. The MCL was used to evaluate inflow cannula placement for rotary VAD support. Left and right atrial and ventricular cannulation sites were evaluated under conditions of mild and severe heart failure. With a view to long term LVAD support in the severe left heart failure condition, left ventricular inflow cannulation was preferred due to improved LVAD efficiency and reduced potential for thrombus formation. In the mild left heart failure condition, left atrial cannulation was preferred to provide an improved platform for myocardial recovery. Similar trends were observed with RVAD support, however to a lesser degree due to a smaller difference in right atrial and ventricular pressures. A compliant inflow cannula to prevent suction events was then developed and evaluated in the MCL. As rotary LVAD or RVAD preload was reduced, suction events occurred in all instances with a rigid inflow cannula. Addition of the compliant segment eliminated suction events in all instances. This was due to passive restriction of the compliant segment as preload dropped, thus increasing the VAD circuit resistance and decreasing the VAD flow rate. Therefore, the compliant inflow cannula acted as a passive flow control / anti-suction system in LVAD and RVAD support. A novel suture-less inflow cannula fixation device was then developed to reduce implantation time and postoperative bleeding. The fixation device was evaluated for LVAD and RVAD support in cadaveric animal and human hearts attached to a MCL. LVAD inflow cannulation was achieved in under two minutes with the suture-less fixation device. No leakage through the suture-less fixation device – myocardial interface was noted. Continued development and in-vivo evaluation of this device may result in an improved inflow cannulation technique with the potential for off-bypass insertion. Continued development of this research, in particular the compliant inflow cannula and suture-less inflow cannulation device, will result in improved postoperative outcomes, life span and quality of life for end-stage heart failure patients.

Understanding mild acid pretreatment of sugarcane bagasse through particle scale modeling

Sugarcane bagasse is an abundant and sustainable resource, generated as a by-product of sugarcane milling. The cellulosic material within bagasse can be broken down into glucose molecules and fermented to produce ethanol, making it a promising feedstock for biofuel production. Mild acid pretreatment hydrolyses the hemicellulosic component of biomass, thus allowing enzymes greater access to the cellulosic substrate during saccharification. A particle-scale mathematical model describing the mild acid pretreatment of sugarcane bagasse has been developed, using a volume averaged framework. Discrete population-balance equations are used to characterise the polymer degradation kinetics, and diffusive effects account for mass transport within the cell wall of the bagasse. As the fibrous material hydrolyses over time, variations in the porosity of the cell wall and the downstream effects on the reaction kinetics are accounted for using conservation of volume arguments. Non-dimensionalization of the model equations reduces the number of parameters in the system to a set of four dimensionless ratios that compare the timescales of different reaction and diffusion events. Theoretical yield curves are compared to macroscopic experimental observations from the literature and inferences are made as to constraints on these “unknown” parameters. These results enable connections to be made between experimental data and the underlying thermodynamics of acid pretreatment. Consequently, the results suggest that data-fitting techniques used to obtain kinetic parameters should be carefully applied, with prudent consideration given to the chemical and physiological processes being modeled.

Study of the underlying electrochemistry of polycrystalline gold electrodes in aqueous solution and electrocatalysis by large amplitude Fourier transformed alternating current voltammetry

Polycrystalline gold electrodes of the kind that are routinely used in analysis and catalysis in aqueous media are often regarded as exhibiting relatively simple double-layer charging/discharging and monolayer oxide formation/ removal in the positive potential region. Application of the large amplitude Fourier transformed alternating current (FT-ac) voltammetric technique that allows the faradaic current contribution of fast electron-transfer processes to be emphasized in the higher harmonic components has revealed the presence of well-defined faradaic (premonolayer oxidation) processes at positive potentials in the double-layer region in acidic and basic media which are enhanced by electrochemical activation. These underlying quasi-reversible interfacial electron-transfer processes may mediate the course of electrocatalytic oxidation reactions of hydrazine, ethylene glycol, and glucose on gold electrodes in aqueous media. The observed responses support key assumptions associated with the incipient hydrous oxide adatom mediator (IHOAM) model of electrocatalysis.

Auto-inhibition of hydrogen gas evolution on gold in aqueous acid solution

It was demonstrated recently that dramatic changes in the redox behaviour of gold/aqueous solution interfaces may be observed following either cathodic or thermal electrode pretreatment. Further work on the cathodic pretreatment of gold in acid solution revealed that as the activity of the gold surface was increased, its performance as a substrate for hydrogen gas evolution under constant potential conditions deteriorated. The change in activity of the gold atoms at the interface, which was attributed to a hydrogen embrittlement process (the occurrence of the latter was subsequently checked by surface microscopy), was confirmed, as in earlier work, by the appearance of a substantial anodic peak at ca. 0.5 V (RHE) in a post-activation positive sweep. Changes in the catalytic activity of a metal surface reflect the fact that the structure (or topography), thermodynamic activity and electronic properties of a surface are dependent not only on pretreatment but also, in the case of the hydrogen evolution reaction, vary with time during the course of reaction. As will be reported shortly, similar (and often more dramatic) time-dependent behaviour was observed for hydrogen gas evolution on other metal electrodes.

The role of defects, or active states, in surface electrochemistry with particular reference to gold in neutral solution

Metastable, active, or nonequilibrium states due to the presence of abnormal structures and various types of defects are well known in metallurgy. The role of such states at gold surfaces in neutral aqueous media (an important electrode system in the microsensor area) was explored using cyclic voltammetry. It was demonstrated that, as postulated in earlier work from this laboratory, there is a close relationship between premonolayer oxidation, multilayer hydrous oxide reduction and electrocatalytic behaviour in the case of this and other metal electrode systems. Some of the most active, and therefore most important, entities at surfaces (e.g., metal adatoms) are not readily imageable or detectable by high resolution surface microscopy techniques. Cyclic voltammetry, however, provides significant, though not highly specific, information about such species. The main conclusion is that further practical and theoretical work on active states of metal surfaces is highly desirable as their behaviour is not simple and is of major importance in many electrocatalytic processes.

The formation of gold nanoparticles using hydroquinone as a reducing agent through a localized pH change upon addition of NaOH to a solution of HAuCl4

We demonstrate a rapid synthesis of gold nanoparticles using hydroquinone as a reducing agent under acidic conditions without the need for precursor seed particles. The nanoparticle formation process is facilitated by the addition of NaOH to a solution containing HAuCl4 and hydroquinone to locally change the pH; this enhances the reducing capability of hydroquinone to form gold nucleation centres, after which further growth of gold can take place through an autocatalytic mechanism. The stability of the nanoparticles is highly dependent on the initial solution pH, and both the concentration of added NaOH and hydroquinone present in solution. The gold nanoparticles were characterized by UV–visible spectroscopy, transmission electron microscopy, Fourier transform infrared spectroscopy, atomic force microscopy, dynamic light scattering, and zeta potential measurements. It was found that under optimal conditions that stable aqueous suspensions of 20 nm diameter nanoparticles can be achieved where benzoquinone, the oxidized product of hydroquinone, acts as a capping agent preventing nanoparticles aggregation.

The electrochemical corrosion behaviour of quaternary gold alloys when exposed to 3.5% NaCl solution

Lower carat gold alloys, specifically 9 carat gold alloys, containing less than 40 % gold, and alloying additions of silver, copper and zinc, are commonly used in many jewellery applications, to offset high costs and poor mechanical properties associated with pure gold. While gold is considered to be chemically inert, the presence of active alloying additions raises concerns about certain forms of corrosion, particularly selective dissolution of these alloys. The purpose of this study was to systematically study the corrosion behaviour of a series of quaternary gold–silver–copper–zinc alloys using dc potentiodynamic scanning in saline (3.5 % NaCl) environment. Full anodic/cathodic scans were conducted to determine the overall corrosion characteristics of the alloy, followed by selective anodic scans and subsequent morphological and compositional analysis of the alloy surface and corroding media to determine the extent of selective dissolution. Varying degrees of selective dissolution and associated corrosion rates were observed after anodic polarisation in 3.5 % NaCl, depending on the alloy composition. The corrosion behaviour of the alloys was determined by the extent of anodic reactions which induce (1) formation of oxide scales on the alloy surface and or (2) dissolution of Zn and Cu species. In general, the improved corrosion characteristics of alloy #3 was attributed to the composition of Zn/Cu in the alloy and thus favourable microstructure promoting the formation of protective oxide/chloride scales and reducing the extent of Cu and Zn dissolution.

The effect of varied test instructions on neuropsychological performance following mild traumatic brain injury : an investigation of ‘diagnosis threat’

Diagnosis threat is a psychosocial factor that has been proposed to contribute to poor outcomes following mild traumatic brain injury (mTBI). This threat is thought to impair the cognitive test performance of individuals with mTBI because of negative injury stereotypes. University students (N= 45, 62.2% female) with a history of mTBI were randomly allocated to a diagnosis threat (DT, n=15), reduced threat (DT-reduced, n=15) or neutral (n=15) group. The reduced threat condition invoked a positive stereotype (i.e., that people with mTBI can perform well on cognitive tests). All participants were given neutral instructions before they completed baseline tests of: a) objective cognitive function across a number of domains; b) psychological symptoms; and, c) PCS symptoms, including self-reported cognitive and emotional difficulties. Participants then received either neutral, DT or DT-reduced instructions, before repeating the tests. Results were analyzed using separate mixed model ANOVAs; one for each dependent measure. The only significant result was for the 2 X 3 ANOVA on an objective test of attention/working memory, Digit Span, p<.05, such that the DT-reduced group performed better than the other groups, which were not different from each other. Although not consistent with predictions or earlier DT studies, the absence of group differences on most tests fits with several recent DT findings. The results of this study suggest that it is timely to reconsider the role of DT as a unique contributor to poor mTBI outcome.

Beliefs underlying the intention to donate again among first-time blood donors who experience a mild adverse event

Using the belief basis of the theory of planned behavior (TPB), the current study explored the rate of mild reactions reported by donors in relation to their first donation and the intention and beliefs of those donors with regard to returning to donate again. A high proportion of first-time donors indicated that they had experienced a reaction to blood donation. Further, donors who reacted were less likely to intend to return to donate. Regression analyses suggested that targeting different beliefs for those donors who had and had not reacted would yield most benefit in bolstering donors’ intentions to remain donating. The findings provide insight into those messages that could be communicated via the mass media or in targeted communications to retain first-time donors who have experienced a mild vasovagal reaction.

A review of the removal of anions and oxyanions of the halogen elements from aqueous solution by layered double hydroxides

The application of layered double hydroxides (LDHs) and thermally activated LDHs for the removal of various fluorine (F-, BF-4), chlorine (Cl-,ClO-4), bromine (Br-, BrO-3) and iodine (I-, IO-3) species from aqueous solutions has been reviewed in this article. LDHs and thermally activated LDHs were able to significantly reduce the concentration of selected anions in laboratory scale experiments. The M2+:M3+ cation ratio of the LDH adsorbent was an important factor which influenced anion uptake. Though LDHs were able to remove some target anion species through anion exchange and surface adsorption thermal activation and reformation generally produced better results. The presence of competing anions including carbonate, phosphate and sulphate had a significant impact on uptake of the target anion as LDHs typically exhibit lower affinity towards monovalent anions compared to anions with multiple charges. The removal of fluoride and perchlorate from aqueous solution by a continuous flow system utilising fixed bed columns packed with LDH adsorbents has also been investigated. The adsorption capacity of the columns at breakpoint was heavily dependent on the flow rate and lower than result reported for the corresponding batch methods. There is still considerable scope for future research on numerous topics summarised in this article.