The persistence of phase-separation in LiFePO4 with two-dimensional Li+ transport : the Cahn-Hilliard-reaction equation and the role of defects

We examine the solution of the two-dimensional Cahn-Hilliard-reaction (CHR) equation in the xy plane as a model of Li+ intercalation into LiFePO4 material. We validate our numerical solution against the solution of the depth-averaged equation, which has been used to model intercalation in the limit of highly orthotropic diffusivity and gradient penalty tensors. We then examine the phase-change behaviour in the full CHR system as these parameters become more isotropic, and find that as the Li+ diffusivity is increased in the x direction, phase separation persists at high currents, even in small crystals with averaged coherency strain included. The resulting voltage curves decrease monotonically, which has previously been considered a hallmark of crystals that fill homogeneously.

Extracting deck trend to plan descent trajectory for safe landing of UAVs

This paper outlines a feasible scheme to extract deck trend when a rotary-wing unmanned aerial vehicle (RUAV)approaches an oscillating deck. An extended Kalman filter (EKF) is de- veloped to fuse measurements from multiple sensors for effective estimation of the unknown deck heave motion. Also, a recursive Prony Analysis (PA) procedure is proposed to implement online curve-fitting of the estimated heave mo- tion. The proposed PA constructs an appropriate model with parameters identified using the forgetting factor recursive least square (FFRLS)method. The deck trend is then extracted by separating dominant modes. Performance of the proposed procedure is evaluated using real ship motion data, and simulation results justify the suitability of the proposed method into safe landing of RUAVs operating in a maritime environment.

Family violence or woman abuse? Putting gender back into the Canadian research equation

Research on violence against women has been among the most scrutinized areas in social science. From the beginning, efforts to empirically document the prevalence, incidence, and characteristics of violence against women have been hotly debated (DeKeseredy, 2011; Dragiewicz & DeKeseredy, forthcoming; Minaker & Snider, 2006). Objections that violence against women was rare have given way to acknowledgement that it is more common than once thought. Research on the outcomes of woman abuse has documented the serious ramifications of this type of violence for individual victims and the broader community. However, violence against women was not simply “discovered” by scholars in the 1960s, leading to a progressive growth of the literature. Knowledge production around violence against women has been fiercely contested, and feminist insights in particular have always been met with backlash(Gotell, 2007; Minkaer & Snider, 2006; Randall, 1989; Sinclair, 2003)...

Pore formation during dehydration of polycrystalline gypsum observed and quantified in a time-series synchrotron radiation based X-ray micro-tomography experiment

We conducted an in-situ X-ray micro-computed tomography heating experiment at the Advanced Photon Source (USA) to dehydrate an unconfined 2.3 mm diameter cylinder of Volterra Gypsum. We used a purpose-built X-ray transparent furnace to heat the sample to 388 K for a total of 310 min to acquire a three-dimensional time-series tomography dataset comprising nine time steps. The voxel size of 2.2 μm3 proved sufficient to pinpoint reaction initiation and the organization of drainage architecture in space and time. We observed that dehydration commences across a narrow front, which propagates from the margins to the centre of the sample in more than four hours. The advance of this front can be fitted with a square-root function, implying that the initiation of the reaction in the sample can be described as a diffusion process. Novel parallelized computer codes allow quantifying the geometry of the porosity and the drainage architecture from the very large tomographic datasets (20483 voxels) in unprecedented detail. We determined position, volume, shape and orientation of each resolvable pore and tracked these properties over the duration of the experiment. We found that the pore-size distribution follows a power law. Pores tend to be anisotropic but rarely crack-shaped and have a preferred orientation, likely controlled by a pre-existing fabric in the sample. With on-going dehydration, pores coalesce into a single interconnected pore cluster that is connected to the surface of the sample cylinder and provides an effective drainage pathway. Our observations can be summarized in a model in which gypsum is stabilized by thermal expansion stresses and locally increased pore fluid pressures until the dehydration front approaches to within about 100 μm. Then, the internal stresses are released and dehydration happens efficiently, resulting in new pore space. Pressure release, the production of pores and the advance of the front are coupled in a feedback loop.

Stability and convergence of a finite volume method for the space fractional advection-dispersion equation

We consider the space fractional advection–dispersion equation, which is obtained from the classical advection–diffusion equation by replacing the spatial derivatives with a generalised derivative of fractional order. We derive a finite volume method that utilises fractionally-shifted Grünwald formulae for the discretisation of the fractional derivative, to numerically solve the equation on a finite domain with homogeneous Dirichlet boundary conditions. We prove that the method is stable and convergent when coupled with an implicit timestepping strategy. Results of numerical experiments are presented that support the theoretical analysis.

Reliable and valid survey design for structural equation modelling

My quantitative study asks how Chinese Australians’ “Chineseness” and their various resources influence their Chinese language proficiency, using online survey and snowball sampling. ‘Operationalization’ is a challenging process which ensures that the survey design talks back to the informing theory and forwards to the analysis model. It requires the attention to two core methodological concerns, namely ‘validity’ and ‘reliability’. Construction of a high-quality questionnaire is critical to the achievement of valid and reliable operationalization. A series of strategies were chosen to ensure the quality of the questions, and thus the eventual data. These strategies enable the use of structural equation modelling to examine how well the data fits the theoretical framework, which was constructed in light of Bourdieu’s theory of habitus, capital and field.

Transmission X-ray microscopy : a new tool in clay mineral floccules characterization

Effective flocculation and dewatering of mineral processing streams containing clays are microstructure dependent in clay-water systems. Initial clay flocculation is crucial in the design and for the development of a new methodology of gas exploitation. Microstructural engineering of clay aggregates using covalent cations and Keggin macromolecules have been monitored using the new state of the art Transmission X-ray Microscope (TXM) with 60 nm tomography resolution installed in a Taiwanese synchrotron. The 3-D reconstructions from TXM images show complex aggregation structures in montmorillonite aqueous suspensions after treatment with Na+, Ca2+ and Al13 Keggin macromolecules. Na-montmorillonite displays elongated, parallel, well-orientated and closed-void cellular networks, 0.5–3 μm in diameter. After treatment by covalent cations, the coagulated structure displays much smaller, randomly orientated and openly connected cells, 300–600 nm in diameter. The average distances measured between montmorillonite sheets was around 450 nm, which is less than half of the cell dimension measured in Na-montmorillonite. The most dramatic structural changes were observed after treatment by Al13 Keggin; aggregates then became arranged in compacted domains of a 300 nm average diameter composed of thick face-to-face oriented sheets, which forms porous aggregates with larger intra-aggregate open and connected voids.

High strong order methods for non-commutative stochastic ordinary differential equation systems and the Magnus formula

In recent years considerable attention has been paid to the numerical solution of stochastic ordinary differential equations (SODEs), as SODEs are often more appropriate than their deterministic counterparts in many modelling situations. However, unlike the deterministic case numerical methods for SODEs are considerably less sophisticated due to the difficulty in representing the (possibly large number of) random variable approximations to the stochastic integrals. Although Burrage and Burrage [High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations, Applied Numerical Mathematics 22 (1996) 81-101] were able to construct strong local order 1.5 stochastic Runge-Kutta methods for certain cases, it is known that all extant stochastic Runge-Kutta methods suffer an order reduction down to strong order 0.5 if there is non-commutativity between the functions associated with the multiple Wiener processes. This order reduction down to that of the Euler-Maruyama method imposes severe difficulties in obtaining meaningful solutions in a reasonable time frame and this paper attempts to circumvent these difficulties by some new techniques. An additional difficulty in solving SODEs arises even in the Linear case since it is not possible to write the solution analytically in terms of matrix exponentials unless there is a commutativity property between the functions associated with the multiple Wiener processes. Thus in this present paper first the work of Magnus [On the exponential solution of differential equations for a linear operator, Communications on Pure and Applied Mathematics 7 (1954) 649-673] (applied to deterministic non-commutative Linear problems) will be applied to non-commutative linear SODEs and methods of strong order 1.5 for arbitrary, linear, non-commutative SODE systems will be constructed - hence giving an accurate approximation to the general linear problem. Secondly, for general nonlinear non-commutative systems with an arbitrary number (d) of Wiener processes it is shown that strong local order I Runge-Kutta methods with d + 1 stages can be constructed by evaluated a set of Lie brackets as well as the standard function evaluations. A method is then constructed which can be efficiently implemented in a parallel environment for this arbitrary number of Wiener processes. Finally some numerical results are presented which illustrate the efficacy of these approaches. (C) 1999 Elsevier Science B.V. All rights reserved.

General order conditions for stochastic Runge-Kutta methods for both commuting and non-commuting stochastic ordinary differential equation systems

In many modeling situations in which parameter values can only be estimated or are subject to noise, the appropriate mathematical representation is a stochastic ordinary differential equation (SODE). However, unlike the deterministic case in which there are suites of sophisticated numerical methods, numerical methods for SODEs are much less sophisticated. Until a recent paper by K. Burrage and P.M. Burrage (1996), the highest strong order of a stochastic Runge-Kutta method was one. But K. Burrage and P.M. Burrage (1996) showed that by including additional random variable terms representing approximations to the higher order Stratonovich (or Ito) integrals, higher order methods could be constructed. However, this analysis applied only to the one Wiener process case. In this paper, it will be shown that in the multiple Wiener process case all known stochastic Runge-Kutta methods can suffer a severe order reduction if there is non-commutativity between the functions associated with the Wiener processes. Importantly, however, it is also suggested how this order can be repaired if certain commutator operators are included in the Runge-Kutta formulation. (C) 1998 Elsevier Science B.V. and IMACS. All rights reserved.

A banded preconditioner for the two-sided, nonlinear space-fractional diffusion equation

The method of lines is a standard method for advancing the solution of partial differential equations (PDEs) in time. In one sense, the method applies equally well to space-fractional PDEs as it does to integer-order PDEs. However, there is a significant challenge when solving space-fractional PDEs in this way, owing to the non-local nature of the fractional derivatives. Each equation in the resulting semi-discrete system involves contributions from every spatial node in the domain. This has important consequences for the efficiency of the numerical solver, especially when the system is large. First, the Jacobian matrix of the system is dense, and hence methods that avoid the need to form and factorise this matrix are preferred. Second, 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. In this paper, we show how an effective preconditioner is essential for improving the efficiency of the method of lines for solving a quite general two-sided, nonlinear space-fractional diffusion equation. A key contribution is to 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.

Vibrational spectroscopy of the borate mineral henmilite Ca2Cu[B(OH)4]2(OH)4

Henmilite is a triclinic mineral with the crystal structure consisting of isolated B(OH)4 tetrahedra, planar Cu(OH)4 groups and Ca(OH)3 polyhedra. The structure can also be viewed as having dimers of Ca polyhedra connected to each other through 2B(OH) tetrahedra to form chains parallel to the C axis. The structure of the mineral has been assessed by the combination of Raman and infrared spectra. Raman bands at 902, 922, 951, and 984 cm−1 and infrared bands at 912, 955 and 998 cm−1 are assigned to stretching vibrations of tetragonal boron. The Raman band at 758 cm−1 is assigned to the symmetric stretching mode of tetrahedral boron. The series of bands in the 400–600 cm−1 region are due to the out-of-plane bending modes of tetrahedral boron. Two very sharp Raman bands are observed at 3559 and 3609 cm−1. Two infrared bands are found at 3558 and 3607 cm−1. These bands are assigned to the OH stretching vibrations of the OH units in henmilite. A series of Raman bands are observed at 3195, 3269, 3328, 3396, 3424 and 3501 cm−1 are assigned to water stretching modes. Infrared spectroscopy also identified water and OH units in the henmilite structure. It is proposed that water is involved in the structure of henmilite. Hydrogen bond distances based upon the OH stretching vibrations using a Libowitzky equation were calculated. The number and variation of water hydrogen bond distances are important for the stability off the mineral.

Embedding human expert cognition into autonomous UAS trajectory planning

This paper presents a new approach for the inclusion of human expert cognition into autonomous trajectory planning for unmanned aerial systems (UASs) operating in low-altitude environments. During typical UAS operations, multiple objectives may exist; therefore, the use of multicriteria decision aid techniques can potentially allow for convergence to trajectory solutions which better reflect overall mission requirements. In that context, additive multiattribute value theory has been applied to optimize trajectories with respect to multiple objectives. A graphical user interface was developed to allow for knowledge capture from a human decision maker (HDM) through simulated decision scenarios. The expert decision data gathered are converted into value functions and corresponding criteria weightings using utility additive theory. The inclusion of preferences elicited from HDM data within an automated decision system allows for the generation of trajectories which more closely represent the candidate HDM decision preferences. This approach has been demonstrated in this paper through simulation using a fixed-wing UAS operating in low-altitude environments.

General trajectory prior for non-rigid reconstruction

Trajectory basis Non-Rigid Structure From Motion (NRSFM) currently faces two problems: the limit of reconstructability and the need to tune the basis size for different sequences. This paper provides a novel theoretical bound on 3D reconstruction error, arguing that the existing definition of reconstructability is fundamentally flawed in that it fails to consider system condition. This insight motivates a novel strategy whereby the trajectory's response to a set of high-pass filters is minimised. The new approach eliminates the need to tune the basis size and is more efficient for long sequences. Additionally, the truncated DCT basis is shown to have a dual interpretation as a high-pass filter. The success of trajectory filter reconstruction is demonstrated quantitatively on synthetic projections of real motion capture sequences and qualitatively on real image sequences.