Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain

Multi-term time-fractional differential equations have been used for describing important physical phenomena. However, studies of the multi-term time-fractional partial differential equations with three kinds of nonhomogeneous boundary conditions are still limited. In this paper, a method of separating variables is used to solve the multi-term time-fractional diffusion-wave equation and the multi-term time-fractional diffusion equation in a finite domain. In the two equations, the time-fractional derivative is defined in the Caputo sense. We discuss and derive the analytical solutions of the two equations with three kinds of nonhomogeneous boundary conditions, namely, Dirichlet, Neumann and Robin conditions, respectively.

A Combined Renormalization Group-Multiple Scale Method for Singularly Perturbed Problems

This paper introduces a straightforward method to asymptotically solve a variety of initial and boundary value problems for singularly perturbed ordinary differential equations whose solution structure can be anticipated. The approach is simpler than conventional methods, including those based on asymptotic matching or on eliminating secular terms. © 2010 by the Massachusetts Institute of Technology.

Self-organized quantum dot arrays : kinetic mapping of adatom capture

Deterministic synthesis of self-organized quantum dot arrays for renewable energy, biomedical, and optoelectronic applications requires control over adatom capture zones, which are presently mapped using unphysical geometric tessellation. In contrast, the proposed kinetic mapping is based on simulated two-dimensional adatom fluxes in the array and includes the effects of nucleation, dissolution, coalescence, and process parameters such as surface temperature and deposition rate. This approach is generic and can be used to control the nanoarray development in various practical applications. © 2009 American Institute of Physics.

Spectral approximations to the fractional integral and derivative

In this paper, the spectral approximations are used to compute the fractional integral and the Caputo derivative. The effective recursive formulae based on the Legendre, Chebyshev and Jacobi polynomials are developed to approximate the fractional integral. And the succinct scheme for approximating the Caputo derivative is also derived. The collocation method is proposed to solve the fractional initial value problems and boundary value problems. Numerical examples are also provided to illustrate the effectiveness of the derived methods.

A simplified approach for calculating the moments of action for linear reaction-diffusion equations

The mean action time is the mean of a probability density function that can be interpreted as a critical time, which is a finite estimate of the time taken for the transient solution of a reaction-diffusion equation to effectively reach steady state. For high-variance distributions, the mean action time under-approximates the critical time since it neglects to account for the spread about the mean. We can improve our estimate of the critical time by calculating the higher moments of the probability density function, called the moments of action, which provide additional information regarding the spread about the mean. Existing methods for calculating the nth moment of action require the solution of n nonhomogeneous boundary value problems which can be difficult and tedious to solve exactly. Here we present a simplified approach using Laplace transforms which allows us to calculate the nth moment of action without solving this family of boundary value problems and also without solving for the transient solution of the underlying reaction-diffusion problem. We demonstrate the generality of our method by calculating exact expressions for the moments of action for three problems from the biophysics literature. While the first problem we consider can be solved using existing methods, the second problem, which is readily solved using our approach, is intractable using previous techniques. The third problem illustrates how the Laplace transform approach can be used to study coupled linear reaction-diffusion equations.

Analysis of steel structures for first- and second-order element (displacement and force) solutions

Finite element method (FEM) relies on an approximate function to fit into a governing equation and minimizes the residual error in the integral sense in order to generate solutions for the boundary value problems (nodal solutions). Because of this FEM does not show simultaneous capacities for accurate displacement and force solutions at node and along an element, especially when under the element loads, which is of much ubiquity. If the displacement and force solutions are strictly confined to an element’s or member’s ends (nodal response), the structural safety along an element (member) is inevitably ignored, which can definitely hinder the design of a structure for both serviceability and ultimate limit states. Although the continuous element deflection and force solutions can be transformed into the discrete nodal solutions by mesh refinement of an element (member), this setback can also hinder the effective and efficient structural assessment as well as the whole-domain accuracy for structural safety of a structure. To this end, this paper presents an effective, robust, applicable and innovative approach to generate accurate nodal and element solutions in both fields of displacement and force, in which the salient and unique features embodies its versatility in applications for the structures to account for the accurate linear and second-order elastic displacement and force solutions along an element continuously as well as at its nodes. The significance of this paper is on shifting the nodal responses (robust global system analysis) into both nodal and element responses (sophisticated element formulation).

Some solutions for a compressible isotropic elastic material

In this article we obtain closed-form solutions for the combined inflation and axial shear of an elastic tube in respect of the compressible Isotropic elastic material introduced by Levinson and Burgess. Several other boundary-value problems are also examined, including the bending of a rectangular block and straightening of a cylindrical sector, both coupled with stretching and shearing, and an axially varying twist deformation. Some of the solutions appear in closed form, others are expressible in terms of elliptic functions.

Exponential integrators and a dual-scale model for wood drying

For the timber industry, the ability to simulate the drying of wood is invaluable for manufacturing high quality wood products. Mathematically, however, modelling the drying of a wet porous material, such as wood, is a diffcult task due to its heterogeneous and anisotropic nature, and the complex geometry of the underlying pore structure. The well{ developed macroscopic modelling approach involves writing down classical conservation equations at a length scale where physical quantities (e.g., porosity) can be interpreted as averaged values over a small volume (typically containing hundreds or thousands of pores). This averaging procedure produces balance equations that resemble those of a continuum with the exception that effective coeffcients appear in their deffnitions. Exponential integrators are numerical schemes for initial value problems involving a system of ordinary differential equations. These methods differ from popular Newton{Krylov implicit methods (i.e., those based on the backward differentiation formulae (BDF)) in that they do not require the solution of a system of nonlinear equations at each time step but rather they require computation of matrix{vector products involving the exponential of the Jacobian matrix. Although originally appearing in the 1960s, exponential integrators have recently experienced a resurgence in interest due to a greater undertaking of research in Krylov subspace methods for matrix function approximation. One of the simplest examples of an exponential integrator is the exponential Euler method (EEM), which requires, at each time step, approximation of φ(A)b, where φ(z) = (ez - 1)/z, A E Rnxn and b E Rn. For drying in porous media, the most comprehensive macroscopic formulation is TransPore [Perre and Turner, Chem. Eng. J., 86: 117-131, 2002], which features three coupled, nonlinear partial differential equations. The focus of the first part of this thesis is the use of the exponential Euler method (EEM) for performing the time integration of the macroscopic set of equations featured in TransPore. In particular, a new variable{ stepsize algorithm for EEM is presented within a Krylov subspace framework, which allows control of the error during the integration process. The performance of the new algorithm highlights the great potential of exponential integrators not only for drying applications but across all disciplines of transport phenomena. For example, when applied to well{ known benchmark problems involving single{phase liquid ow in heterogeneous soils, the proposed algorithm requires half the number of function evaluations than that required for an equivalent (sophisticated) Newton{Krylov BDF implementation. Furthermore for all drying configurations tested, the new algorithm always produces, in less computational time, a solution of higher accuracy than the existing backward Euler module featured in TransPore. Some new results relating to Krylov subspace approximation of '(A)b are also developed in this thesis. Most notably, an alternative derivation of the approximation error estimate of Hochbruck, Lubich and Selhofer [SIAM J. Sci. Comput., 19(5): 1552{1574, 1998] is provided, which reveals why it performs well in the error control procedure. Two of the main drawbacks of the macroscopic approach outlined above include the effective coefficients must be supplied to the model, and it fails for some drying configurations, where typical dual{scale mechanisms occur. In the second part of this thesis, a new dual{scale approach for simulating wood drying is proposed that couples the porous medium (macroscale) with the underlying pore structure (microscale). The proposed model is applied to the convective drying of softwood at low temperatures and is valid in the so{called hygroscopic range, where hygroscopically held liquid water is present in the solid phase and water exits only as vapour in the pores. Coupling between scales is achieved by imposing the macroscopic gradient on the microscopic field using suitably defined periodic boundary conditions, which allows the macroscopic ux to be defined as an average of the microscopic ux over the unit cell. This formulation provides a first step for moving from the macroscopic formulation featured in TransPore to a comprehensive dual{scale formulation capable of addressing any drying configuration. Simulation results reported for a sample of spruce highlight the potential and flexibility of the new dual{scale approach. In particular, for a given unit cell configuration it is not necessary to supply the effective coefficients prior to each simulation.

Joint identification of infinite-frequency added mass and fluid-memory models of marine structures

This paper addresses the problem of joint identification of infinite-frequency added mass and fluid memory models of marine structures from finite frequency data. This problem is relevant for cases where the code used to compute the hydrodynamic coefficients of the marine structure does not give the infinite-frequency added mass. This case is typical of codes based on 2D-potential theory since most 3D-potential-theory codes solve the boundary value associated with the infinite frequency. The method proposed in this paper presents a simpler alternative approach to other methods previously presented in the literature. The advantage of the proposed method is that the same identification procedure can be used to identify the fluid-memory models with or without having access to the infinite-frequency added mass coefficient. Therefore, it provides an extension that puts the two identification problems into the same framework. The method also exploits the constraints related to relative degree and low-frequency asymptotic values of the hydrodynamic coefficients derived from the physics of the problem, which are used as prior information to refine the obtained models.

Validation of the Edinburgh Postnatal Depression Scale for men, and comparison of item endorsement with their partners

BACKGROUND: The Edinburgh Postnatal Depression Scale (EPDS) has been validated and used extensively in screening for depression in new mothers, both in English speaking and non-English speaking communities. While some studies have reported the use of the EPDS with fathers, none have validated it for this group, and thus the appropriate cut-off score for screening for depression or anxiety caseness for this population is not known. METHODS: Couples were recruited antenatally and interviewed at six weeks postpartum. EPDS scores and distress caseness (depression or anxiety disorders) for 208 fathers and 230 mothers were determined using the Diagnostic Interview Schedule. RESULTS: Analyses of the EPDS for fathers using distress caseness (depression or anxiety disorders) as the criterion shows that a cut-off of 5/6 has optimum receiver operating characteristics. Furthermore acceptable reliability (split-half and internal consistency) and validity (concurrent) coefficients were obtained. For mothers the optimum cut-off screening value to detect distress caseness was 7/8. Item analysis revealed that fathers endorsed seven of the ten items at lower rates to mothers, with the most significant being that referring to crying. CONCLUSIONS: The EPDS is a reliable and valid measure of mood in fathers. Screening for depression or anxiety disorders in fathers requires a two point lower cut-off than screening for depression or anxiety in mothers, and we recommend this cut-off to be 5/6

Antisocial behaviour orders : Unanticipated directions in social network site development

Abstract: Social network technologies, as we know them today have become a popular feature of everyday life for many people. As their name suggests, their underlying premise is to enable people to connect with each other for a variety of purposes. These purposes however, are generally thought of in a positive fashion. Based on a multi-method study of two online environments, Habbo Hotel and Second Life, which incorporate social networking functionality, we she light on forms of what can be conceptualized as antisocial behaviours and the rationales for these. Such behaviours included: scamming, racist/homophobic attacks, sim attacks, avatar attacks, non-conformance to contextual norms, counterfeiting and unneighbourly behaviour. The rationales for sub behaviours included: profit, fun, status building, network disruption, accidental acts and prejudice. Through our analysis we are able to comment upon the difficulties of defining antisocial behaviour in such environments, particularly when such environments are subject to interpretation vis their use and expected norms. We also point to the problems we face in conducting our public and private lives given the role ICTs are playing in the convergence of these two spaces and also the convergence of ICTs themselves.

A study of green product industries in Taiwan

Based on the model of ‘The Smile of Value Creation' (Mudambi 2007) and the theory of concept marketing, this study aims to examine the top 20 Taiwanese environmental marks companies, and explore their circumstances, innovation patterns and value chain system in Taiwan. It found out all of them are information technology product and household appliances companies. In addition, they make special efforts in two parts of value creation: product (including basic and applied ‘R and D' (Research and Design), design, commercialization) and marketing (including advertising and brand management, specialized logistics, after-sales services). They also locate their branches depending on different stages of the value chain, and expand them globally.

An integrated information management model for ecologically sustainable development

Ecologically sustainable development has become a major feature of legal systems at the international, national and local levels throughout the world. In Australia, governments have responded to environmental crises by enacting legislation imposing obligations and restrictions over privately-owned land. Whilst these obligations and restrictions may well be necessary to achieve sustainability, the approach to management of information concerning these instruments is problematic. For example, management of information concerning obligations and restrictions in Queensland is fragmented, with some instruments registered or recorded on the land title register, some on external registers, and some information only available in the legislation itself. This approach is used in most Australian jurisdictions. This fragmented approach has led to two separate but interconnected problems. First, the Torrens system is no longer meeting its goal of providing a complete and accurate picture of title. Second, this uncoordinated approach to the management of land titles, and obligations and restrictions on land use, has created a barrier to sustainable management of natural resources. This is because compliance with environmental laws is impaired in the absence of easily accessible and accurate information. These problems demonstrate a clear need for reform in this area. To determine how information concerning these obligations and restrictions may be most effectively managed, this thesis will apply a comparative methodology and consider three case studies, which each utilise different models for management of this information. These jurisdictions will be assessed according to a set of guidelines for comparison to identify which features of their systems provide for effective management of information concerning obligations and restrictions on title and use. Based on this comparison, this thesis will devise a series of recommendations for an effective system for the management of information concerning obligations and restrictions on land title and use, taking into account any potential legal issues and barriers to implementation. This series of recommendations for reform will be supplemented by suggested draft legislative provisions.

hSSB1 interacts directly with the MRN complex stimulating its recruitment to DNA double-strand breaks and its endo-nuclease activity

hSSB1 is a recently discovered single-stranded DNA binding protein that is essential for efficient repair of DNA double-strand breaks (DSBs) by the homologous recombination pathway. hSSB1 is required for the efficient recruitment of the MRN complex to sites of DSBs and for the efficient initiation of ATM dependent signalling. Here we explore the interplay between hSSB1 and MRN. We demonstrate that hSSB1 binds directly to NBS1, a component of the MRN complex, in a DNA damage independent manner. Consistent with the direct interaction, we observe that hSSB1 greatly stimulates the endo-nuclease activity of the MRN complex, a process that requires the C-terminal tail of hSSB1. Interestingly, analysis of two point mutations in NBS1, associated with Nijmegen breakage syndrome, revealed weaker binding to hSSB1, suggesting a possible disease mechanism.