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.

Advanced Bioactive Inorganic Materials for Bone Regeneration and Drug Delivery

Bioceramics play an important role in repairing and regenerating bone defects. Annually, more than 500,000 bone graft procedures are performed in the United states and approximately 2.2 million are conducted worldwide. The estimated cost of these procedures approaches $2.5billion per year. Around 60% of the bone graft substitutes available on the market involve bioceramics. It is reported that bioceramics in the world market increase by 9% per year. For this reason, the research of bioceramics has been one of the most active areas during, the past several years. Considering the significant importance of bioceramics, our goal was to compile this book to review the latest research advances in the field of bioceramics. The text also summarizes our work during the past 10 years in an effort to share innovative concepts, design of bioceramisc, and methods for material synthesis and drug delivery. We anticipate that this text will provide some useful information and guidance in the bioceramics field for biomedical engineering researchers and material scientists. Information on novel mesoporous bioactive glasses and silicate-based ceramics for bone regeneration and drug delivery are presented. Mesoporous bioactive glasses have shown multifunctional characteristics of bone regeneration and drug delivery due to their special mesopore structures,whereas silicated-based bioceramics, as typical third-generation biomaterials,possess significant osteostimulation properties. Silica nanospheres with a core-shell structure and specific properties for controllable drug delivery have been carefully reviewed-a variety of advanced synthetic strategies have been developed to construct functional mesoporous silica nanoparticles with a core-shell structure, including hollow, magnetic, or luminescent, and other multifunctional core-shell mesoporous silica nanoparticles. In addition, multifunctional drug delivery systems based on these nanoparticles have been designed and optimized to deliver the drugs into the targeted organs or cells,with a controllable release fashioned by virtue of various internal and external triggers. The novel 3D-printing technique to prepare advanced bioceramic scaffolds for bone tissue engineering applications has been highlighted, including the preparation, mechanical strength, and biological properties of 3D-printed porous scaffolds of calcium phosphate cement and silicate bioceramics. Three-dimensional printing techniques offer improved large-pore structure and mechanical strength. In addition , biomimetic preparation and controllable crystal growth as well as biomineralization of bioceramics are summarized, showing the latest research progress in this area. Finally, inorganic and organic composite materials are reviewed for bone regeneration and gene delivery. Bioactive inorganic and organic composite materials offer unique biological, electrical, and mechanical properties for designing excellent bone regeneration or gene delivery systems. It is our sincere hope that this book will updated the reader as to the research progress of bioceramics and their applications in bone repair and regeneration. It will be the best reward to all the contributors of this book if their efforts herein in some way help reader in any part of their study, research, and career development.

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.

Controlled synthesis of inorganic semiconductor nanocrystals and their applications

This thesis is a comprehensive study of the synthesis of nanomaterials. It explores the synthetic methods on the control of the size, shape and phase of semiconductor nanocrystals. A number of important conclusions, including the mechanism behind crystal growth and the structure-relationship, have been drawn through the experimental and theoretical investigation. The synthesized nanocrystals have been tested for applications in gas sensing, photocatalysis and solar cells, which exhibit considerable commercialization potential.

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.

Electrochemically-induced TCNQ/Mn TCNQ 2 (H2O) 2 (TCNQ= 7, 7, 8, 8-Tetracyanoquinodimethane) solid-solid interconversion : two voltammetrically distinct processes that allow selective generation of nanofiber or nanorod network morphologies

Unlike the case with other divalent transition metal M\[TCNQ](2)(H(2)O)(2) (M = Fe, Co, Ni) analogues, the electrochemically induced solid-solid phase interconversion of TCNQ microcrystals (TCNQ = 7,7,8,8-tetracyanoquinodimethane) to Mn\[TCNQ](2)(H(2)O)(2) occurs via two voltammetrically distinct, time dependent processes that generate the coordination polymer in nanofiber or rod-like morphologies. Careful manipulation of the voltammetric scan rate, electrolysis time, Mn(2+)((aq)) concentration, and the method of electrode modification with solid TCNQ allows selective generation of either morphology. Detailed ex situ spectroscopic (IR, Raman), scanning electron microscopy (SEM), and X-ray powder diffraction (XRD) characterization clearly establish that differences in the electrochemically synthesized Mn-TCNQ material are confined to morphology. Generation of the nanofiber form is proposed to take place rapidly via formation and reduction of a Mn-stabilized anionic dimer intermediate, \[(Mn(2+))(TCNQ-TCNQ)(2)(*-)], formed as a result of radical-substrate coupling between TCNQ(*-) and neutral TCNQ, accompanied by ingress of Mn(2+) ions from the aqueous solution at the triple phase TCNQ/electrode/electrolyte boundary. In contrast, formation of the nanorod form is much slower and is postulated to arise from disproportionation of the \[(Mn(2+))(TCNQ-TCNQ)(*-)(2)] intermediate. Thus, identification of the time dependent pathways via the solid-solid state electrochemical approach allows the crystal size of the Mn\[TCNQ](2)(H(2)O)(2) material to be tuned and provides new mechanistic insights into the formation of different morphologies.

Synthesis of CuTCNQ/Au microrods by galvanic replacement of semiconducting phase I CuTCNQ with KAuBr4 in aqueous medium

The spontaneous reaction between microrods of an organic semiconductor molecule, copper 7,7,8,8-tetracyanoquinodimethane (CuTCNQ) with [AuBr4]− ions in an aqueous environment is reported. The reaction is found to be redox in nature which proceeds via a complex galvanic replacement mechanism, wherein the surface of the CuTCNQ microrods is replaced with metallic gold nanoparticles. Unlike previous reactions reported in acetonitrile, the galvanic replacement reaction in aqueous solution proceeds via an entirely different reaction mechanism, wherein a cyclical reaction mechanism involving continuous regeneration of CuTCNQ consumed during the galvanic replacement reaction occurs in parallel with the galvanic replacement reaction. This results in the driving force of the galvanic replacement reaction in aqueous medium being largely dependent on the availability of [AuBr4]− ions during the reaction. Therefore, this study highlights the importance of the choice of an appropriate solvent during galvanic replacement reactions, which can significantly impact upon the reaction mechanism. The reaction progress with respect to different gold salt concentration was monitored using Fourier transform infrared (FT-IR), Raman, and X-ray photoelectron spectroscopy (XPS), as well as XRD and EDX analysis, and SEM imaging. The CuTCNQ/Au nanocomposites were also investigated for their potential photocatalytic properties, wherein the destruction of the organic dye, Congo red, in a simulated solar light environment was found to be largely dependent on the degree of gold nanoparticle surface coverage. The approach reported here opens up new possibilities of decorating metal–organic charge transfer complexes with a host of metals, leading to potentially novel applications in catalysis and sensing.

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.

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.

Observation of solution-induced corneal staining with fluorescein, rose bengal and lissamine green

Ever since sodium fluorescein (‘fluorescein’ [FL]) was first used to investigate the ocular surface over a century ago, the term ‘staining’ has been taken to mean the presence of ocular surface fluorescence [1]. This term has not been necessarily taken to infer any particular mechanism of causation, and indeed, can be attributed to a variety of possible aetiologies [2]. In recent times, there has been considerable interest in a form of ocular surface fluorescence seen in association with the use of certain combinations of soft contact lenses and multipurpose solutions. The first clinical account of this phenomenon was reported by Jones et al. [3], which was followed by a more formal investigation by the same author in 2002 [4]. Jones et al described this appearance as a ‘classic solution-based toxicity reaction’. Subsequently, this appearance has come to be known as ‘solution-induced corneal staining’ or more recently by the acronym ‘SICS’ [5]. The term SICS is potentially problematic in that from a cell biology point of view, there is an inference that ‘staining’ means the entry of a dye into corneal epithelial cells. Morgan and Maldonado-Codina [2] noted there was no foundation of solid scientific literature underpinning our understanding of the true basic causative mechanisms of this phenomenon; since that time, further work has been published in this field [6] and [7] but questions still remain about the precise aetiology of this phenomenon...