High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations

The pioneering work of Runge and Kutta a hundred years ago has ultimately led to suites of sophisticated numerical methods suitable for solving complex systems of deterministic ordinary differential equations. However, in many modelling situations, the appropriate representation is a stochastic differential equation and here numerical methods are much less sophisticated. In this paper a very general class of stochastic Runge-Kutta methods is presented and much more efficient classes of explicit methods than previous extant methods are constructed. In particular, a method of strong order 2 with a deterministic component based on the classical Runge-Kutta method is constructed and some numerical results are presented to demonstrate the efficacy of this approach.

Visualizing the evolution of knowledge management capability in construction firms

A firm, as a dynamic, evolving, and quasi-autonomous system of knowledge production and application, develops knowledge management capability (KMC) through strategic learning in order to sustain competitive advantages in a dynamic environment. Knowledge governance mechanisms and knowledge processes connect and interact with each other forming learning mechanisms, which carry out double loop learning that drives genesis and evolution of KMC to modify operating routines that effect desired performance. This paper reports a study that was carried out within a context of construction contractors, a type of project-based firms, operating within the dynamic Hong Kong construction market. A multiple-case design was used to incorporate evidence from the literature and interviews, with the help of system dynamics modeling, to visualize the evolution of KMC. The study demonstrates the feasibility to visualize how a firm's KMC matches its operating environment over time. The findings imply that knowledge management (KM) applications can be better planned and controlled through evaluation of KM performance over time from a capability perspective.

Numerical solutions of stochastic differential equations – implementation and stability issues

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.

A variable stepsize implementation for stochastic differential equations

Stochastic differential equations (SDEs) arise from physical systems where the parameters describing the system can only be estimated or are subject to noise. Much work has been done recently on developing higher order Runge-Kutta methods for solving SDEs numerically. Fixed stepsize implementations of numerical methods have limitations when, for example, the SDE being solved is stiff as this forces the stepsize to be very small. This paper presents a completely general variable stepsize implementation of an embedded Runge Kutta pair for solving SDEs numerically; in this implementation, there is no restriction on the value used for the stepsize, and it is demonstrated that the integration remains on the correct Brownian path.

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.

A bound on the maximum strong order of stochastic Runge-Kutta methods for stochastic ordinary differential equations

In Burrage and Burrage [1] it was shown that by introducing a very general formulation for stochastic Runge-Kutta methods, the previous strong order barrier of order one could be broken without having to use higher derivative terms. In particular, methods of strong order 1.5 were developed in which a Stratonovich integral of order one and one of order two were present in the formulation. In this present paper, general order results are proven about the maximum attainable strong order of these stochastic Runge-Kutta methods (SRKs) in terms of the order of the Stratonovich integrals appearing in the Runge-Kutta formulation. In particular, it will be shown that if an s-stage SRK contains Stratonovich integrals up to order p then the strong order of the SRK cannot exceed min{(p + 1)/2, (s - 1)/2), p greater than or equal to 2, s greater than or equal to 3 or 1 if p = 1.

Smartphone malware evolution revisited : Android next target?

Smartphones started being targets for malware in June 2004 while malware count increased steadily until the introduction of a mandatory application signing mechanism for Symbian OS in 2006. From this point on, only few news could be read on this topic. Even despite of new emerging smartphone platforms, e.g. android and iPhone, malware writers seemed to lose interest in writing malware for smartphones giving users an unappropriate feeling of safety. In this paper, we revisit smartphone malware evolution for completing the appearance list until end of 2008. For contributing to smartphone malware research, we continue this list by adding descriptions on possible techniques for creating the first malware(s) for Android platform. Our approach involves usage of undocumented Android functions enabling us to execute native Linux application even on retail Android devices. This can be exploited to create malicious Linux applications and daemons using various methods to attack a device. In this manner, we also show that it is possible to bypass the Android permission system by using native Linux applications.

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.

A preconditioned Lanczos method for space-fractional reaction-diffusion equations on two-dimensional unstructured meshes

We consider a two-dimensional space-fractional reaction diffusion equation with a fractional Laplacian operator and homogeneous Neumann boundary conditions. The finite volume method is used with the matrix transfer technique of Ilić et al. (2006) to discretise in space, yielding a system of equations that requires the action of a matrix function to solve at each timestep. Rather than form this matrix function explicitly, we use Krylov subspace techniques to approximate the action of this matrix function. Specifically, we apply the Lanczos method, after a suitable transformation of the problem to recover symmetry. To improve the convergence of this method, we utilise a preconditioner that deflates the smallest eigenvalues from the spectrum. We demonstrate the efficiency of our approach for a fractional Fisher’s equation on the unit disk.

Early-mid Cretaceous tectonic evolution of eastern Gondwana : from silicic LIP magmatism to continental rupture

The Early–mid Cretaceous marks the confluence of three major continental-scale events in eastern Gondwana: (1) the emplacement of a Silicic Large Igneous Province (LIP) near the continental margin; (2) the volcaniclastic fill, transgression and regression of a major epicontinental seaway developed over at least a quarter of the Australian continent; and (3) epeirogenic uplift, exhumation and continental rupturing culminating in the opening of the Tasman Basin c. 84 Ma. The Whitsunday Silicic LIP event had widespread impact, producing both substantial extrusive volumes of dominantly silicic pyroclastic material and coeval first-cycle volcanogenic sediment that accumulated within many eastern Australian sedimentary basins, and principally in the Great Australian Basin system (>2 Mkm3 combined volume). The final pulse of volcanism and volcanogenic sedimentation at c. 105–95 Ma coincided with epicontinental seaway regression, which shows a lack of correspondence with the global sea-level curve, and alternatively records a wider, continental-scale effect of volcanism and rift tectonism. Widespread igneous underplating related to this LIP event is evident from high paleogeothermal gradients and regional hydrothermal fluid flow detectable in the shallow crust and over a broad region. Enhanced CO2 fluxing through sedimentary basins also records indirectly, large-scale, LIP-related mafic underplating. A discrete episode of rapid crustal cooling and exhumation began c. 100–90 Ma along the length of the eastern Australian margin, related to an enhanced phase of continental rifting that was largely amagmatic, and probably a switch from wide–more narrow rift modes. Along-margin variations in detachment fault architecture produced narrow (SE Australia) and wide continental margins with marginal, submerged continental plateaux (NE Australia). Long-lived NE-trending cross-orogen lineaments controlled the switch from narrow to wide continental margin geometries.

New insights into magmatism and changing rift styles in the evolution of the Gulf of California

The Gulf of California (GoC) has been an important focus site for understanding the spatial and temporal evolution of rifts, with recent studies concluding: 1) rapid crustal rupturing within 10 Myrs; 2) surprisingly abrupt variations in rifting style and magmatism with apparently wide magma-poor and narrow, magmatic rift segments; and 3) that high sedimentation rates may promote switching from wide to narrow rift modes or thermally blanket the crust to enhance rift magmatism. Critical to these conclusions is the onset of rifting at~12 Ma following the cessation of subduction. New field-based volcanostratigraphic and geochronologic studies along the southeastern GoC margin reveal Early Miocene (~25-18 Ma) bimodal volcanism in wide rifting mode (~400 km width), followed by a mid-Miocene (~18-12 Ma) phase of dominantly intermediate composition magmatism in and around the nascent GoC with lavas/domes often emplaced into actively subsiding basins, but contemporaneous with bimodal volcanism regionally. Flat-lying intraplate basaltic lava fields emplaced ~12-10 Ma along the GoC east coast abut tilted blocks of ~20 Ma ignimbrites onshore, and also occur offshore. The reduction in crustal thickness from ~55 to 20 km along the eastern GoC edge must have been largely achieved by 12 Ma. Extension has demonstrably began earlier than previously thought, downplaying rapid rifting and any thermal effects from <6 Ma sedimentation. New age data from onshore indicate significant structurally controlled corridors of magmatism during 18-12 Ma extension in apparently magma-poor rift segments, and this magmatism temporally coincides with the switch from wide to narrow rifting.

Simplified method for including spatial correlations in mean-field approximations

Biological systems involving proliferation, migration and death are observed across all scales. For example, they govern cellular processes such as wound-healing, as well as the population dynamics of groups of organisms. In this paper, we provide a simplified method for correcting mean-field approximations of volume-excluding birth-death-movement processes on a regular lattice. An initially uniform distribution of agents on the lattice may give rise to spatial heterogeneity, depending on the relative rates of proliferation, migration and death. Many frameworks chosen to model these systems neglect spatial correlations, which can lead to inaccurate predictions of their behaviour. For example, the logistic model is frequently chosen, which is the mean-field approximation in this case. This mean-field description can be corrected by including a system of ordinary differential equations for pair-wise correlations between lattice site occupancies at various lattice distances. In this work we discuss difficulties with this method and provide a simplication, in the form of a partial differential equation description for the evolution of pair-wise spatial correlations over time. We test our simplified model against the more complex corrected mean-field model, finding excellent agreement. We show how our model successfully predicts system behaviour in regions where the mean-field approximation shows large discrepancies. Additionally, we investigate regions of parameter space where migration is reduced relative to proliferation, which has not been examined in detail before, and our method is successful at correcting the deviations observed in the mean-field model in these parameter regimes.

Cometary evolution : clues on physical properties from chondritic interplanetary dust particles

The degree of diversity or similarity detected in comets depends primarily on the lifetimes of the individual cometary nuclei at the time of analysis. It is inherent in our understanding of cometary orbital dynamics and the seminal model of comet origins that cometary evolution is the natural order of events in our Solar System. Thus, predictions of cometary behaviour in terms of bulk physical, mineralogical or chemical parameters should contain an appreciation of temporal variation(s). Previously, Rietmeijer and Mackinnon [1987] developed mineralogical bases for the chemical evolution of cometary nuclei primarily with regard to the predominantly silicate fraction of comet nuclei. We suggested that alteration of solids in cometary nuclei should be expected and that indications of likely reactants and products can be derived from judicious comparison with terrestrial diagenetic environments which include hydrocryogenic and low-temperature aqueous alterations. In a further development of this concept, Rietmeijer [1988] provides indirect evidence for the formation of sulfides and oxides in comet nuclei. Furthermore, Rietmeijer [1988] noted that timescales for hydrocryogenic and low-temperature reactions involving liquid water are probably adequate for relatively mature comets, e.g. P/comet Halley. In this paper, we will address the evolution of comet nuclei physical parameters such as solid particle grain size, porosity and density. In natural environments, chemical evolution (e.g. mineral reactions) is often accompanied by changes in physical properties. These concurrent changes are well-documented in the terrestrial geological literature, especially in studies of sediment diagenesis and we suggest that similar basic principles apply within the upper few meters of active comet nuclei. The database for prediction of comet nuclei physical parameters is, in principle, the same as used for the proposition of chemical evolution. We use detailed mineralogical studies of chondritic interplanetary dust particles (IDPS) as a guide to the likely constitution of mature comets traversing the inner Solar System. While there is, as yet, no direct proof that a specific sub-group or type of chondritic IDP is derived from a specific comet, it is clear that these particles are extraterrestrial in origin and that a certain portion of the interplanetary flux received by the Earth is cometary in origin. Two chondritic porous (CP) IDPS, sample numbers W701OA2 and W7029CI, from the Johnson Space Center Cosmic Dust Collection have been selected for this study of putative cometary physical parameters. This particular type of particle is considered a likely candidate for a cometary origin on the basis of mineralogy, bulk composition and morphology. While many IDPs have been subjected to intensive study over the past decade, we can develop a physical parameter model on only these two CP IDPs because few others have been studied in sufficient detail.

Evolution and innovation in guardianship laws: Assisted decision-making

Guardianship laws in most Western societies provide decision-making mechanisms for adults with impaired capacity. Since the inception of these laws, the principle of autonomy and recognition of human rights for those coming within guardianship regimes has gained prominence. A new legal model has emerged, which seeks to incorporate ‘assisted decision-making’ models into guardianship laws. Such models legally recognise that an adult’s capacity may be maintained through assistance or support provided by another person, and provide formal recognition of the person in that ‘assisting’ role. This article situates this latest legal innovation within a historical context, examining the social and legal evolution of guardianship laws and determining whether modern assisted decision-making models remain consistent with guardianship reform thus far. It identifies and critically analyses the different assisted decision-making models which exist internationally. Finally, it discusses a number of conceptual, legal and practical concerns that remain unresolved. These issues require serious consideration before assisted decisionmaking models are adopted in guardianship regimes in Australia.