A novel method for the synthesis of monodisperse gold-coated silica nanoparticles

Monodisperse silica nanoparticles were synthesised by the well-known Stober protocol, then dispersed in acetonitrile (ACN) and subsequently added to a bisacetonitrile gold(I) coordination complex ([Au(MeCN)2]?) in ACN. The silica hydroxyl groups were deprotonated in the presence of ACN, generating a formal negative charge on the siloxy groups. This allowed the [Au(MeCN)2]? complex to undergo ligand exchange with the silica nanoparticles and form a surface coordination complex with reduction to metallic gold (Au0) proceeding by an inner sphere mechanism. The residual [Au(MeCN)2]? complex was allowed to react with water, disproportionating into Au0 and Au(III), respectively, with the Au0 adding to the reduced gold already bound on the silica surface. The so-formed metallic gold seed surface was found to be suitable for the conventional reduction of Au(III) to Au0 by ascorbic acid (ASC). This process generated a thin and uniform gold coating on the silica nanoparticles. The silica NPs batches synthesised were in a size range from 45 to 460 nm. Of these silica NP batches, the size range from 400 to 480 nm were used for the gold-coating experiments.

Efficient preconditioning of the method of lines for solving nonlinear two-sided space-fractional diffusion equations

A standard method for the numerical solution of partial differential equations (PDEs) is the method of lines. In this approach the PDE is discretised in space using �finite di�fferences or similar techniques, and the resulting semidiscrete problem in time is integrated using an initial value problem solver. A significant challenge when applying the method of lines to fractional PDEs is that the non-local nature of the fractional derivatives results in a discretised system where each equation involves contributions from many (possibly every) spatial node(s). This has important consequences for the effi�ciency of the numerical solver. First, since the cost of evaluating the discrete equations is high, it is essential to minimise the number of evaluations required to advance the solution in time. Second, since the Jacobian matrix of the system is dense (partially or fully), methods that avoid the need to form and factorise this matrix are preferred. In this paper, we consider a nonlinear two-sided space-fractional di�ffusion equation in one spatial dimension. A key contribution of this paper is to demonstrate how an eff�ective preconditioner is crucial for improving the effi�ciency of the method of lines for solving this equation. In particular, we show how to construct suitable banded approximations to the system Jacobian for preconditioning purposes that permit high orders and large stepsizes to be used in the temporal integration, without requiring dense matrices to be formed. The results of numerical experiments are presented that demonstrate the effectiveness of this approach.

Multi-method, multi-theoretical, multi-level research in the learning sciences

We examine methodologies and methods that apply to multi-level research in the learning sciences. In so doing we describe how multiple theoretical frameworks informs the use of different methods that apply to social levels involving space-time relationships that are not accessible consciously as social life is enacted. Most of the methods involve analyses of video and audio files. Within a framework of interpretive research we present a methodology of event-oriented social science, which employs video ethnography, narrative, conversation analysis, prosody analysis, and facial expression analysis. We illustrate multi-method research in an examination of the role of emotions in teaching and learning. Conversation and prosody analyses augment facial expression analysis and ethnography. We conclude with an exploration of ways in which multi-level studies can be complemented with neural level analyses.

Modeling ion channel dynamics through reflected stochastic differential equations

Ion channels are membrane proteins that open and close at random and play a vital role in the electrical dynamics of excitable cells. The stochastic nature of the conformational changes these proteins undergo can be significant, however current stochastic modeling methodologies limit the ability to study such systems. Discrete-state Markov chain models are seen as the "gold standard," but are computationally intensive, restricting investigation of stochastic effects to the single-cell level. Continuous stochastic methods that use stochastic differential equations (SDEs) to model the system are more efficient but can lead to simulations that have no biological meaning. In this paper we show that modeling the behavior of ion channel dynamics by a reflected SDE ensures biologically realistic simulations, and we argue that this model follows from the continuous approximation of the discrete-state Markov chain model. Open channel and action potential statistics from simulations of ion channel dynamics using the reflected SDE are compared with those of a discrete-state Markov chain method. Results show that the reflected SDE simulations are in good agreement with the discrete-state approach. The reflected SDE model therefore provides a computationally efficient method to simulate ion channel dynamics while preserving the distributional properties of the discrete-state Markov chain model and also ensuring biologically realistic solutions. This framework could easily be extended to other biochemical reaction networks. © 2012 American Physical Society.

Non-invasive method for detecting changes in soil moisture using wireless sensor networks

There are several popular soil moisture measurement methods today such as time domain reflectometry, electromagnetic (EM) wave, electrical and acoustic methods. Significant studies have been dedicated in developing method of measurements using those concepts, especially to achieve the characteristics of noninvasiveness. EM wave method provides an advantage because it is non-invasive to the soil and does not need to utilise probes to penetrate or bury in the soil. But some EM methods are also too complex, expensive, and not portable for the application of Wireless Sensor Networks; for example satellites or UAV (Unmanned Aerial Vehicle) based sensors. This research proposes a method in detecting changes in soil moisture using soil-reflected electromagnetic (SREM) wave from Wireless Sensor Networks (WSNs). Studies have shown that different levels of soil moisture will affects soil’s dielectric properties, such as relative permittivity and conductivity, and in turns change its reflection coefficients. The SREM wave method uses a transmitter adjacent to a WSNs node with purpose exclusively to transmit wireless signals that will be reflected by the soil. The strength from the reflected signal that is determined by the soil’s reflection coefficients is used to differentiate the level of soil moisture. The novel nature of this method comes from using WSNs communication signals to perform soil moisture estimation without the need of external sensors or invasive equipment. This innovative method is non-invasive, low cost and simple to set up. There are three locations at Brisbane, Australia chosen as the experiment’s location. The soil type in these locations contains 10–20% clay according to the Australian Soil Resource Information System. Six approximate levels of soil moisture (8, 10, 13, 15, 18 and 20%) are measured at each location; with each measurement consisting of 200 data. In total 3600 measurements are completed in this research, which is sufficient to achieve the research objective, assessing and proving the concept of SREM wave method. These results are compared with reference data from similar soil type to prove the concept. A fourth degree polynomial analysis is used to generate an equation to estimate soil moisture from received signal strength as recorded by using the SREM wave method.

A boundary preserving numerical algorithm for the Wright-Fisher model with mutation

The Wright-Fisher model is an Itô stochastic differential equation that was originally introduced to model genetic drift within finite populations and has recently been used as an approximation to ion channel dynamics within cardiac and neuronal cells. While analytic solutions to this equation remain within the interval [0,1], current numerical methods are unable to preserve such boundaries in the approximation. We present a new numerical method that guarantees approximations to a form of Wright-Fisher model, which includes mutation, remain within [0,1] for all time with probability one. Strong convergence of the method is proved and numerical experiments suggest that this new scheme converges with strong order 1/2. Extending this method to a multidimensional case, numerical tests suggest that the algorithm still converges strongly with order 1/2. Finally, numerical solutions obtained using this new method are compared to those obtained using the Euler-Maruyama method where the Wiener increment is resampled to ensure solutions remain within [0,1].

RCA method for fault diagnosis in digital substations of power systems

The authors present a Cause-Effect fault diagnosis model, which utilises the Root Cause Analysis approach and takes into account the technical features of a digital substation. The Dempster/Shafer evidence theory is used to integrate different types of fault information in the diagnosis model so as to implement a hierarchical, systematic and comprehensive diagnosis based on the logic relationship between the parent and child nodes such as transformer/circuit-breaker/transmission-line, and between the root and child causes. A real fault scenario is investigated in the case study to demonstrate the developed approach in diagnosing malfunction of protective relays and/or circuit breakers, miss or false alarms, and other commonly encountered faults at a modern digital substation.

Investigating the potential value of individual parameters of histological grading systems in a sheep model of cartilage damage : the modified Mankin method

A total histological grade does not necessarily distinguish between different manifestations of cartilage damage or degeneration. An accurate and reliable histological assessment method is required to separate normal and pathological tissue within a joint during treatment of degenerative joint conditions and to sub-classify the latter in meaningful ways. The Modified Mankin method may be adaptable for this purpose. We investigated how much detail may be lost by assigning one composite score/grade to represent different degenerative components of the osteoarthritic condition. We used four ovine injury models (sham surgery, anterior cruciate ligament/medial collateral ligament instability, simulated anatomic anterior cruciate ligament reconstruction and meniscal removal) to induce different degrees and potentially 'types' (mechanisms) of osteoarthritis. Articular cartilage was systematically harvested, prepared for histological examination and graded in a blinded fashion using a Modified Mankin grading method. Results showed that the possible permutations of cartilage damage were significant and far more varied than the current intended use that histological grading systems allow. Of 1352 cartilage specimens graded, 234 different manifestations of potential histological damage were observed across 23 potential individual grades of the Modified Mankin grading method. The results presented here show that current composite histological grading may contain additional information that could potentially discern different stages or mechanisms of cartilage damage and degeneration in a sheep model. This approach may be applicable to other grading systems.

Alternating direction implicit numerical method for the space and time fractional Bloch-Torrey equation in 3-D

Recently, some authors have considered a new diffusion model–space and time fractional Bloch-Torrey equation (ST-FBTE). Magin et al. (2008) have derived analytical solutions with fractional order dynamics in space (i.e., _ = 1, β an arbitrary real number, 1 < β ≤ 2) and time (i.e., 0 < α < 1, and β = 2), respectively. Yu et al. (2011) have derived an analytical solution and an effective implicit numerical method for solving ST-FBTEs, and also discussed the stability and convergence of the implicit numerical method. However, due to the computational overheads necessary to perform the simulations for nuclear magnetic resonance (NMR) in three dimensions, they present a study based on a two-dimensional example to confirm their theoretical analysis. Alternating direction implicit (ADI) schemes have been proposed for the numerical simulations of classic differential equations. The ADI schemes will reduce a multidimensional problem to a series of independent one-dimensional problems and are thus computationally efficient. In this paper, we consider the numerical solution of a ST-FBTE on a finite domain. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. A fractional alternating direction implicit scheme (FADIS) for the ST-FBTE in 3-D is proposed. Stability and convergence properties of the FADIS are discussed. Finally, some numerical results for ST-FBTE are given.

A new implicit numerical method for the space and time fractional Bloch-Torrey equation

In recent years, it has been found that many phenomena in engineering, physics, chemistry and other sciences can be described very successfully by models using mathematical tools from fractional calculus. Recently, noted a new space and time fractional Bloch-Torrey equation (ST-FBTE) has been proposed (see Magin et al. (2008)), and successfully applied to analyse diffusion images of human brain tissues to provide new insights for further investigations of tissue structures. In this paper, we consider the ST-FBTE on a finite domain. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. Firstly, we propose a new effective implicit numerical method (INM) for the STFBTE whereby we discretize the Riesz fractional derivative using a fractional centered difference. Secondly, we prove that the implicit numerical method for the ST-FBTE is unconditionally stable and convergent, and the order of convergence of the implicit numerical method is ( T2 - α + h2 x + h2 y + h2 z ). Finally, some numerical results are presented to support our theoretical analysis.

The Galerkin finite element approximation of the fractional cable equation

The cable equation is one of the most fundamental equations for modeling neuronal dynamics. Cable equations with a fractional order temporal derivative have been introduced to model electrotonic properties of spiny neuronal dendrites. In this paper, the fractional cable equation involving two integro-differential operators is considered. The Galerkin finite element approximations of the fractional cable equation are proposed. The main contribution of this work is outlined as follow: • A semi-discrete finite difference approximation in time is proposed. We prove that the scheme is unconditionally stable, and the numerical solution converges to the exact solution with order O(Δt). • A semi-discrete difference scheme for improving the order of convergence for solving the fractional cable equation is proposed, and the numerical solution converges to the exact solution with order O((Δt)2). • Based on the above semi-discrete difference approximations, Galerkin finite element approximations in space for a full discretization are also investigated. • Finally, some numerical results are given to demonstrate the theoretical analysis.

A finite volume method for solving the two-sided time-space fractional advection-dispersion equation

The field of fractional differential equations provides a means for modelling transport processes within complex media which are governed by anomalous transport. Indeed, the application to anomalous transport has been a significant driving force behind the rapid growth and expansion of the literature in the field of fractional calculus. In this paper, we present a finite volume method to solve the time-space two-sided fractional advection dispersion equation on a one-dimensional domain. Such an equation allows modelling different flow regime impacts from either side. The finite volume formulation provides a natural way to handle fractional advection-dispersion equations written in conservative form. The novel spatial discretisation employs fractionally-shifted Gr¨unwald formulas to discretise the Riemann-Liouville fractional derivatives at control volume faces in terms of function values at the nodes, while the L1-algorithm is used to discretise the Caputo time fractional derivative. Results of numerical experiments are presented to demonstrate the effectiveness of the approach.

An implicit RBF meshless method for a fractal mobile/immobile transport model

Fractional differential equation is used to describe a fractal model of mobile/immobile transport with a power law memory function. This equation is the limiting equation that governs continuous time random walks with heavy tailed random waiting times. In this paper, we firstly propose a finite difference method to discretize the time variable and obtain a semi-discrete scheme. Then we discuss its stability and convergence. Secondly we consider a meshless method based on radial basis functions (RBF) to discretize the space variable. By contrast to conventional FDM and FEM, the meshless method is demonstrated to have distinct advantages: calculations can be performed independent of a mesh, it is more accurate and it can be used to solve complex problems. Finally the convergence order is verified from a numerical example is presented to describe the fractal model of mobile/immobile transport process with different problem domains. The numerical results indicate that the present meshless approach is very effective for modeling and simulating of fractional differential equations, and it has good potential in development of a robust simulation tool for problems in engineering and science that are governed by various types of fractional differential equations.

A second-order accurate numerical approximation for the Riesz space fractional advection-dispersion equation

In this paper, we consider a space Riesz fractional advection-dispersion equation. The equation is obtained from the standard advection-diffusion equation by replacing the ¯rst-order and second-order space derivatives by the Riesz fractional derivatives of order β 1 Є (0; 1) and β2 Є(1; 2], respectively. Riesz fractional advection and dispersion terms are approximated by using two fractional centered difference schemes, respectively. A new weighted Riesz fractional ¯nite difference approximation scheme is proposed. When the weighting factor Ѳ = 1/2, a second- order accurate numerical approximation scheme for the Riesz fractional advection-dispersion equation is obtained. Stability, consistency and convergence of the numerical approximation scheme are discussed. A numerical example is given to show that the numerical results are in good agreement with our theoretical analysis.

Numerical simulation of a fractional mathematical model for epidermal wound healing

A number of mathematical models investigating certain aspects of the complicated process of wound healing are reported in the literature in recent years. However, effective numerical methods and supporting error analysis for the fractional equations which describe the process of wound healing are still limited. In this paper, we consider numerical simulation of fractional model based on the coupled advection-diffusion equations for cell and chemical concentration in a polar coordinate system. The space fractional derivatives are defined in the Left and Right Riemann-Liouville sense. Fractional orders in advection and diffusion terms belong to the intervals (0; 1) or (1; 2], respectively. Some numerical techniques will be used. Firstly, the coupled advection-diffusion equations are decoupled to a single space fractional advection-diffusion equation in a polar coordinate system. Secondly, we propose a new implicit difference method for simulating this equation by using the equivalent of the Riemann-Liouville and Gr¨unwald-Letnikov fractional derivative definitions. Thirdly, its stability and convergence are discussed, respectively. Finally, some numerical results are given to demonstrate the theoretical analysis.