Technical note : modelling a complex micro-multileaf collimator using the standard BEAMnrc distribution

Purpose: The component modules in the standard BEAMnrc distribution may appear to be insufficient to model micro-multileaf collimators that have tri-faceted leaf ends and complex leaf profiles. This note indicates, however, that accurate Monte Carlo simulations of radiotherapy beams defined by a complex collimation device can be completed using BEAMnrc's standard VARMLC component module.---------- Methods: That this simple collimator model can produce spatially and dosimetrically accurate micro-collimated fields is illustrated using comparisons with ion chamber and film measurements of the dose deposited by square and irregular fields incident on planar, homogeneous water phantoms.---------- Results: Monte Carlo dose calculations for on- and off-axis fields are shown to produce good agreement with experimental values, even upon close examination of the penumbrae.--------- Conclusions: The use of a VARMLC model of the micro-multileaf collimator, along with a commissioned model of the associated linear accelerator, is therefore recommended as an alternative to the development or use of in-house or third-party component modules for simulating stereotactic radiotherapy and radiosurgery treatments. Simulation parameters for the VARMLC model are provided which should allow other researchers to adapt and use this model to study clinical stereotactic radiotherapy treatments.

Biologically inspired joint control for a humanoid robot

The GuRoo is a 1.2 m tall, 23 degree of freedom humanoid constructed at the University of Queensland for research into humanoid robotics. The key challenge being addressed by the GuRoo project is the development of appropriate learning strategies for control and coordination of the robot's many joints. The development of learning strategies is seen as a way to side-step the inherent intricacy of modeling a multi-DOF biped robot. This paper outlines the approach taken to generate an appropriate control scheme for the joints of the GuRoo. The paper demonstrates the determination of local feedback control parameters using a genetic algorithm. The feedback loop is then augmented by a predictive modulator that learns a form of feed-forward control to overcome the irregular loads experienced at each joint during the gait cycle. The predictive modulator is based on the CMAC architecture. Results from tests on the GuRoo platform show that both systems provide improvements in stability and tracking of joint control.

Recent advances in dermal wound healing : biomedical device approaches

Successful repair of wounds and tissues remains a major healthcare and biomedical challenge in the 21st Century. In particular, chronic wounds often lead to loss of functional ability, increased pain and decreased quality of life, and can be a burden on carers and health-system resources. Advanced healing therapies employing biological dressings, skin substitutes, growth factor-based therapies and synthetic a cellular matrices, all of which aim to correct irregular and dysfunctional cellular pathways present in chronic wounds, are becoming more popular. This review focuses on recent advances in biologically inspired devices for would healing and includes a commentary on the challenges facing the regulatory governance of such products.

Numerical modelling of industrial microwave heating

The numerical modelling of electromagnetic waves has been the focus of many research areas in the past. Some specific applications of electromagnetic wave scattering are in the fields of Microwave Heating and Radar Communication Systems. The equations that govern the fundamental behaviour of electromagnetic wave propagation in waveguides and cavities are the Maxwell's equations. In the literature, a number of methods have been employed to solve these equations. Of these methods, the classical Finite-Difference Time-Domain scheme, which uses a staggered time and space discretisation, is the most well known and widely used. However, it is complicated to implement this method on an irregular computational domain using an unstructured mesh. In this work, a coupled method is introduced for the solution of Maxwell's equations. It is proposed that the free-space component of the solution is computed in the time domain, whilst the load is resolved using the frequency dependent electric field Helmholtz equation. This methodology results in a timefrequency domain hybrid scheme. For the Helmholtz equation, boundary conditions are generated from the time dependent free-space solutions. The boundary information is mapped into the frequency domain using the Discrete Fourier Transform. The solution for the electric field components is obtained by solving a sparse-complex system of linear equations. The hybrid method has been tested for both waveguide and cavity configurations. Numerical tests performed on waveguides and cavities for inhomogeneous lossy materials highlight the accuracy and computational efficiency of the newly proposed hybrid computational electromagnetic strategy.

Algebraic attacks on clock-controlled stream ciphers

Stream ciphers are encryption algorithms used for ensuring the privacy of digital telecommunications. They have been widely used for encrypting military communications, satellite communications, pay TV encryption and for voice encryption of both fixed lined and wireless networks. The current multi year European project eSTREAM, which aims to select stream ciphers suitable for widespread adoptation, reflects the importance of this area of research. Stream ciphers consist of a keystream generator and an output function. Keystream generators produce a sequence that appears to be random, which is combined with the plaintext message using the output function. Most commonly, the output function is binary addition modulo two. Cryptanalysis of these ciphers focuses largely on analysis of the keystream generators and of relationships between the generator and the keystream it produces. Linear feedback shift registers are widely used components in building keystream generators, as the sequences they produce are well understood. Many types of attack have been proposed for breaking various LFSR based stream ciphers. A recent attack type is known as an algebraic attack. Algebraic attacks transform the problem of recovering the key into a problem of solving multivariate system of equations, which eventually recover the internal state bits or the key bits. This type of attack has been shown to be effective on a number of regularly clocked LFSR based stream ciphers. In this thesis, algebraic attacks are extended to a number of well known stream ciphers where at least one LFSR in the system is irregularly clocked. Applying algebriac attacks to these ciphers has only been discussed previously in the open literature for LILI-128. In this thesis, algebraic attacks are first applied to keystream generators using stop-and go clocking. Four ciphers belonging to this group are investigated: the Beth-Piper stop-and-go generator, the alternating step generator, the Gollmann cascade generator and the eSTREAM candidate: the Pomaranch cipher. It is shown that algebraic attacks are very effective on the first three of these ciphers. Although no effective algebraic attack was found for Pomaranch, the algebraic analysis lead to some interesting findings including weaknesses that may be exploited in future attacks. Algebraic attacks are then applied to keystream generators using (p; q) clocking. Two well known examples of such ciphers, the step1/step2 generator and the self decimated generator are investigated. Algebraic attacks are shown to be very powerful attack in recovering the internal state of these generators. A more complex clocking mechanism than either stop-and-go or the (p; q) clocking keystream generators is known as mutual clock control. In mutual clock control generators, the LFSRs control the clocking of each other. Four well known stream ciphers belonging to this group are investigated with respect to algebraic attacks: the Bilateral-stop-and-go generator, A5/1 stream cipher, Alpha 1 stream cipher, and the more recent eSTREAM proposal, the MICKEY stream ciphers. Some theoretical results with regards to the complexity of algebraic attacks on these ciphers are presented. The algebraic analysis of these ciphers showed that generally, it is hard to generate the system of equations required for an algebraic attack on these ciphers. As the algebraic attack could not be applied directly on these ciphers, a different approach was used, namely guessing some bits of the internal state, in order to reduce the degree of the equations. Finally, an algebraic attack on Alpha 1 that requires only 128 bits of keystream to recover the 128 internal state bits is presented. An essential process associated with stream cipher proposals is key initialization. Many recently proposed stream ciphers use an algorithm to initialize the large internal state with a smaller key and possibly publicly known initialization vectors. The effect of key initialization on the performance of algebraic attacks is also investigated in this thesis. The relationships between the two have not been investigated before in the open literature. The investigation is conducted on Trivium and Grain-128, two eSTREAM ciphers. It is shown that the key initialization process has an effect on the success of algebraic attacks, unlike other conventional attacks. In particular, the key initialization process allows an attacker to firstly generate a small number of equations of low degree and then perform an algebraic attack using multiple keystreams. The effect of the number of iterations performed during key initialization is investigated. It is shown that both the number of iterations and the maximum number of initialization vectors to be used with one key should be carefully chosen. Some experimental results on Trivium and Grain-128 are then presented. Finally, the security with respect to algebraic attacks of the well known LILI family of stream ciphers, including the unbroken LILI-II, is investigated. These are irregularly clock- controlled nonlinear filtered generators. While the structure is defined for the LILI family, a particular paramater choice defines a specific instance. Two well known such instances are LILI-128 and LILI-II. The security of these and other instances is investigated to identify which instances are vulnerable to algebraic attacks. The feasibility of recovering the key bits using algebraic attacks is then investigated for both LILI- 128 and LILI-II. Algebraic attacks which recover the internal state with less effort than exhaustive key search are possible for LILI-128 but not for LILI-II. Given the internal state at some point in time, the feasibility of recovering the key bits is also investigated, showing that the parameters used in the key initialization process, if poorly chosen, can lead to a key recovery using algebraic attacks.

Australasian horror

This Australasian horror special issue is an important step forward in putting Australian and New Zealand horror movies on the map of film and cinema studies as a subject worthy of intellectual debate. The journal issue is the first devoted solely to the academic discussion of Australasian horror movies. While an Australian horror movie tradition has produced numerous titles since the 1970s achieving commercial success and cult popularity worldwide, the horror genre is largely missing from Australian film history. While there have been occasional essays on standout titles such as Wolf Creek (Mclean, 2005), an increasing number of articles on ‘Ozploitation’ movies, and irregular discussion about Australian Gothic, overall the nature of Australian horror as a genre remains poorly understood. In terms of New Zealand, debate has tended to revolve around ‘Kiwi Gothic’ and of course Peter Jackon’s early splatter films, rather than Kiwi horror as a specific filmmaking tradition.

Pre-eruptive uplift in the Emeishan? [Correspondence]

In their correspondence, He and colleagues question our conclusion of little or no uplift preceding Emeishan volcanism that we reported in our letter1. Debate concerns the nature of the contact between the Maokou limestone and Emeishan volcanics, the depositional environment and volumetric significance of mafic hydromagmatic deposits (MHDs), and evidence for symmetrical domal thinning. MHDs in the Daqiao section are separated from the Maokou limestone by 100 m of subaerial basaltic lavas, but elsewhere MHDs — previously interpreted as basal conglomerates2, 3 — directly overlie the Maokou2, 3. MHDs thus feature strongly in basal sections of the Emeishan lava succession, as also recently shown4 elsewhere in the Emeishan. An irregular surface at the top of the Maokou limestone has been interpreted as an erosional unconformity2, 3, but clastic deposits presented as evidence of this erosion2, 3 are MHDs produced by explosive magma–water interaction1. A clear demonstration that this irregular top surface is an erosional truncation of limestone reef facies (slope/rim, flat, lagoonal) is currently lacking, but is critical because reefs and carbonate platforms show considerable natural relief of tens of metres. The persistent hot, wet climate since the Oligocene has produced well-developed weathering profiles on exposed Palaeozoic marine sedimentary sequences5, but weathering and karst relief of the uppermost Maokou limestone underlying the flood basalts have not been properly documented, nor shown to be of middle Permian age and immediately preceding emplacement of the large igneous province.

Computed success rates of various carrier phase integer estimation solutions and their comparison with statistical success rates

The success rate of carrier phase ambiguity resolution (AR) is the probability that the ambiguities are successfully fixed to their correct integer values. In existing works, an exact success rate formula for integer bootstrapping estimator has been used as a sharp lower bound for the integer least squares (ILS) success rate. Rigorous computation of success rate for the more general ILS solutions has been considered difficult, because of complexity of the ILS ambiguity pull-in region and computational load of the integration of the multivariate probability density function. Contributions of this work are twofold. First, the pull-in region mathematically expressed as the vertices of a polyhedron is represented by a multi-dimensional grid, at which the cumulative probability can be integrated with the multivariate normal cumulative density function (mvncdf) available in Matlab. The bivariate case is studied where the pull-region is usually defined as a hexagon and the probability is easily obtained using mvncdf at all the grid points within the convex polygon. Second, the paper compares the computed integer rounding and integer bootstrapping success rates, lower and upper bounds of the ILS success rates to the actual ILS AR success rates obtained from a 24 h GPS data set for a 21 km baseline. The results demonstrate that the upper bound probability of the ILS AR probability given in the existing literatures agrees with the actual ILS success rate well, although the success rate computed with integer bootstrapping method is a quite sharp approximation to the actual ILS success rate. The results also show that variations or uncertainty of the unit–weight variance estimates from epoch to epoch will affect the computed success rates from different methods significantly, thus deserving more attentions in order to obtain useful success probability predictions.

Minority activism : trends informing political participation across Australian communities

In the late 1990’s, intense and vigorous debate surrounded the impact of minority communities on Australia’s mainstream society. The rise of far-right populism took the stage with the introduction to the political landscape of Pauline Hanson and her One Nation party, whilst John Howard’s Liberal-National Coalition Government took the fore on debate over immigration issues corresponding with an influx of irregular arrivals. In 2001, following the September 11 terrorist attacks in the United States of America and subsequent attacks on western targets globally, many of these issues continued to be debated through the security posturing that followed. In recent years, much effort has been afforded to countering the threat of terrorism from home grown assailants. The Government has introduced stringent legislative responses whilst researchers have studied social movements and trends within Australian communities, particularly with respect to minorities. In 2008, the Scanlon Foundation, in association with Monash University and various government entities, released its findings into its survey approach to mapping social cohesion in Australia. It identified a number of spheres of exploration which it believed were essential to measuring cohesiveness of Australian communities generally including, economic, political and socio-cultural factors (Markus and Dharmalingam, 2008). This doctoral project report will explore the political sphere as identified in the Mapping Social Cohesion project and apply it to identified minority ethnic communities. The Scanlon Foundation project identified political participation as one of a number of true indicators of social cohesion. This project acknowledges that democracy in Australia is represented predominantly by two political entities representing a vast majority of constituents under a compulsory voting regime. This essay will identify the levels of political activism achieved by minority ethnic communities and access to democratic participation within the Australian political structure. It will define a ten year period from 1999 to 2009, identifying trends and issues within minority communities that have proactively and reactively promoted engagement in achieving a political voice, framed within a mainstream-dominated political system. It will research social movements and other influential factors over that period to enrich existing knowledge in relation to political participation rates across Australian communities.

In situ preparation and protein delivery of silicate/alginate composite microspheres with core-shell structure

It is predicted that with increased life expectancy in the developed world, there will be a greater demand for synthetic materials to repair or regenerate lost, injured or diseased bone (Hench & Thompson 2010). There are still few synthetic materials having true bone inductivity, which limits their application for bone regeneration, especially in large-size bone defects. To solve this problem, growth factors, such as bone morphogenetic proteins (BMPs), have been incorporated into synthetic materials in order to stimulate de novo bone formation in the center of large-size bone defects. The greatest obstacle with this approach is that the rapid diffusion of the protein from the carrier material, leading to a precipitous loss of bioactivity; the result is often insufficient local induction or failure of bone regeneration (Wei et al. 2007). It is critical that the protein is loaded in the carrier material in conditions which maintains its bioactivity (van de Manakker et al. 2009). For this reason, the efficient loading and controlled release of a protein from a synthetic material has remained a significant challenge. The use of microspheres as protein/drug carriers has received considerable attention in recent years (Lee et al. 2010; Pareta & Edirisinghe 2006; Wu & Zreiqat 2010). Compared to macroporous block scaffolds, the chief advantage of microspheres is their superior protein-delivery properties and ability to fill bone defects with irregular and complex shapes and sizes. Upon implantation, the microspheres are easily conformed to the irregular implant site, and the interstices between the particles provide space for both tissue and vascular ingrowth, which are important for effective and functional bone regeneration (Hsu et al. 1999). Alginates are natural polysaccharides and their production does not have the implicit risk of contamination with allo or xeno-proteins or viruses (Xie et al. 2010). Because alginate is generally cytocompatible, it has been used extensively in medicine, including cell therapy and tissue engineering applications (Tampieri et al. 2005; Xie et al. 2010; Xu et al. 2007). Calcium cross-linked alginate hydrogel is considered a promising material as a delivery matrix for drugs and proteins, since its gel microspheres form readily in aqueous solutions at room temperature, eliminating the need for harsh organic solvents, thereby maintaining the bioactivity of proteins in the process of loading into the microspheres (Jay & Saltzman 2009; Kikuchi et al. 1999). In addition, calcium cross-linked alginate hydrogel is degradable under physiological conditions (Kibat PG et al. 1990; Park K et al. 1993), which makes alginate stand out as an attractive candidate material for the protein carrier and bone regeneration (Hosoya et al. 2004; Matsuno et al. 2008; Turco et al. 2009). However, the major disadvantages of alginate microspheres is their low loading efficiency and also rapid release of proteins due to the mesh-like networks of the gel (Halder et al. 2005). Previous studies have shown that a core-shell structure in drug/protein carriers can overcome the issues of limited loading efficiencies and rapid release of drug or protein (Chang et al. 2010; Molvinger et al. 2004; Soppimath et al. 2007). We therefore hypothesized that introducing a core-shell structure into the alginate microspheres could solve the shortcomings of the pure alginate. Calcium silicate (CS) has been tested as a biodegradable biomaterial for bone tissue regeneration. CS is capable of inducing bone-like apatite formation in simulated body fluid (SBF) and its apatite-formation rate in SBF is faster than that of Bioglass® and A-W glass-ceramics (De Aza et al. 2000; Siriphannon et al. 2002). Titanium alloys plasma-spray coated with CS have excellent in vivo bioactivity (Xue et al. 2005) and porous CS scaffolds have enhanced in vivo bone formation ability compared to porous β-tricalcium phosphate ceramics (Xu et al. 2008). In light of the many advantages of this material, we decided to prepare CS/alginate composite microspheres by combining a CS shell with an alginate core to improve their protein delivery and mineralization for potential protein delivery and bone repair applications

Non-invasive assessment of tear film surface quality

The tear film plays an important role preserving the health of the ocular surface and maintaining the optimal refractive power of the cornea. Moreover dry eye syndrome is one of the most commonly reported eye health problems. This syndrome is caused by abnormalities in the properties of the tear film. Current clinical tools to assess the tear film properties have shown certain limitations. The traditional invasive methods for the assessment of tear film quality, which are used by most clinicians, have been criticized for the lack of reliability and/or repeatability. A range of non-invasive methods of tear assessment have been investigated, but also present limitations. Hence no “gold standard” test is currently available to assess the tear film integrity. Therefore, improving techniques for the assessment of the tear film quality is of clinical significance and the main motivation for the work described in this thesis. In this study the tear film surface quality (TFSQ) changes were investigated by means of high-speed videokeratoscopy (HSV). In this technique, a set of concentric rings formed in an illuminated cone or a bowl is projected on the anterior cornea and their reflection from the ocular surface imaged on a charge-coupled device (CCD). The reflection of the light is produced in the outer most layer of the cornea, the tear film. Hence, when the tear film is smooth the reflected image presents a well structure pattern. In contrast, when the tear film surface presents irregularities, the pattern also becomes irregular due to the light scatter and deviation of the reflected light. The videokeratoscope provides an estimate of the corneal topography associated with each Placido disk image. Topographical estimates, which have been used in the past to quantify tear film changes, may not always be suitable for the evaluation of all the dynamic phases of the tear film. However the Placido disk image itself, which contains the reflected pattern, may be more appropriate to assess the tear film dynamics. A set of novel routines have been purposely developed to quantify the changes of the reflected pattern and to extract a time series estimate of the TFSQ from the video recording. The routine extracts from each frame of the video recording a maximized area of analysis. In this area a metric of the TFSQ is calculated. Initially two metrics based on the Gabor filter and Gaussian gradient-based techniques, were used to quantify the consistency of the pattern’s local orientation as a metric of TFSQ. These metrics have helped to demonstrate the applicability of HSV to assess the tear film, and the influence of contact lens wear on TFSQ. The results suggest that the dynamic-area analysis method of HSV was able to distinguish and quantify the subtle, but systematic degradation of tear film surface quality in the inter-blink interval in contact lens wear. It was also able to clearly show a difference between bare eye and contact lens wearing conditions. Thus, the HSV method appears to be a useful technique for quantitatively investigating the effects of contact lens wear on the TFSQ. Subsequently a larger clinical study was conducted to perform a comparison between HSV and two other non-invasive techniques, lateral shearing interferometry (LSI) and dynamic wavefront sensing (DWS). Of these non-invasive techniques, the HSV appeared to be the most precise method for measuring TFSQ, by virtue of its lower coefficient of variation. While the LSI appears to be the most sensitive method for analyzing the tear build-up time (TBUT). The capability of each of the non-invasive methods to discriminate dry eye from normal subjects was also investigated. The receiver operating characteristic (ROC) curves were calculated to assess the ability of each method to predict dry eye syndrome. The LSI technique gave the best results under both natural blinking conditions and in suppressed blinking conditions, which was closely followed by HSV. The DWS did not perform as well as LSI or HSV. The main limitation of the HSV technique, which was identified during the former clinical study, was the lack of the sensitivity to quantify the build-up/formation phase of the tear film cycle. For that reason an extra metric based on image transformation and block processing was proposed. In this metric, the area of analysis was transformed from Cartesian to Polar coordinates, converting the concentric circles pattern into a quasi-straight lines image in which a block statistics value was extracted. This metric has shown better sensitivity under low pattern disturbance as well as has improved the performance of the ROC curves. Additionally a theoretical study, based on ray-tracing techniques and topographical models of the tear film, was proposed to fully comprehend the HSV measurement and the instrument’s potential limitations. Of special interested was the assessment of the instrument’s sensitivity under subtle topographic changes. The theoretical simulations have helped to provide some understanding on the tear film dynamics, for instance the model extracted for the build-up phase has helped to provide some insight into the dynamics during this initial phase. Finally some aspects of the mathematical modeling of TFSQ time series have been reported in this thesis. Over the years, different functions have been used to model the time series as well as to extract the key clinical parameters (i.e., timing). Unfortunately those techniques to model the tear film time series do not simultaneously consider the underlying physiological mechanism and the parameter extraction methods. A set of guidelines are proposed to meet both criteria. Special attention was given to a commonly used fit, the polynomial function, and considerations to select the appropriate model order to ensure the true derivative of the signal is accurately represented. The work described in this thesis has shown the potential of using high-speed videokeratoscopy to assess tear film surface quality. A set of novel image and signal processing techniques have been proposed to quantify different aspects of the tear film assessment, analysis and modeling. The dynamic-area HSV has shown good performance in a broad range of conditions (i.e., contact lens, normal and dry eye subjects). As a result, this technique could be a useful clinical tool to assess tear film surface quality in the future.

Poly[di-mu-aqua-bis(mu-2-amino-4-nitrobenzoato)dicaesium]

In the structure of title compound [Cs2(C7H5N2O4)2(H2O)2]n the asymmetric unit comprises two independent and different Cs centres, one nine-coordinate, the other seven coordinate, with both having irregular stereochemistry. The CsO9 coordination comprises oxygen donors from three bridging water molecules, one of which is doubly bridging, three from carboxylate groups, and three from nitro groups, of which two are bidentate chelate bridging. The CsO6N coordination comprises the two bridging water molecules, one amine N donor, one carboxyl O donor and four O donors from nitro groups (two from the chelate bridges). The extension of the dimeric unit gives a two-dimensional polymeric structure which is stabilized by both intra- and intermolecular amine N-H...O and water O-H...O hydrogen bonds to carboxyl O acceptors, as well as inter-ring pi-pi interactions [minimum ring centroid separation, 3.4172(15)A].

Advanced numerical study of impact forces on railway sleepers under wheel flat

Wheel-rail interaction is one of the most important research topics in railway engineering. It includes track vibration, track impact response and safety of the track. Track structure failures caused by impact forces can lead to significant economic loss for track owners through damage to rails and to the sleepers beneath. The wheel-rail impact forces occur because of imperfections on the wheels or rails such as wheel flats, irregular wheel profile, rail corrugation and differences in the height of rails connected at a welded joint. In this paper, a finite element model for the wheel flat study is developed by use of the FEA software package ANSYS. The effect of the wheel flat to impact force on sleepers is investigated. It has found that the wheel flat significantly increases impact forces and maximum Von Mises stress, and also delays the peak position of dynamic variation for impact forces on both rail and sleeper.

Extracellular matrix of the human cyclic corpus luteum

Extracellular matrix regulates many cellular processes likely to be important for development and regression of corpora lutea. Therefore, we identified the types and components of the extracellular matrix of the human corpus luteum at different stages of the menstrual cycle. Two different types of extracellular matrix were identified by electron microscopy; subendothelial basal laminas and an interstitial matrix located as aggregates at irregular intervals between the non-vascular cells. No basal laminas were associated with luteal cells. At all stages, collagen type IV α1 and laminins α5, β2 and γ1 were localized by immunohistochemistry to subendothelial basal laminas, and collagen type IV α1 and laminins α2, α5, β1 and β2 localized in the interstitial matrix. Laminin α4 and β1 chains occurred in the subendothelial basal lamina from mid-luteal stage to regression; at earlier stages, a punctate pattern of staining was observed. Therefore, human luteal subendothelial basal laminas potentially contain laminin 11 during early luteal development and, additionally, laminins 8, 9 and 10 at the mid-luteal phase. Laminin α1 and α3 chains were not detected in corpora lutea. Versican localized to the connective tissue extremities of the corpus luteum. Thus, during the formation of the human corpus luteum, remodelling of extracellular matrix does not result in basal laminas as present in the adrenal cortex or ovarian follicle. Instead, novel aggregates of interstitial matrix of collagen and laminin are deposited within the luteal parenchyma, and it remains to be seen whether this matrix is important for maintaining the luteal cell phenotype.

Time-dependent fractional advection–diffusion equations by an implicit MLS meshless method

Recently, many new applications in engineering and science are governed by a series of fractional partial differential equations (FPDEs). Unlike the normal partial differential equations (PDEs), the differential order in a FPDE is with a fractional order, which will lead to new challenges for numerical simulation, because most existing numerical simulation techniques are developed for the PDE with an integer differential order. The current dominant numerical method for FPDEs is Finite Difference Method (FDM), which is usually difficult to handle a complex problem domain, and also hard to use irregular nodal distribution. This paper aims to develop an implicit meshless approach based on the moving least squares (MLS) approximation for numerical simulation of fractional advection-diffusion equations (FADE), which is a typical FPDE. The discrete system of equations is obtained by using the MLS meshless shape functions and the meshless strong-forms. The stability and convergence related to the time discretization of this approach are then discussed and theoretically proven. Several numerical examples with different problem domains and different nodal distributions are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. It is concluded that the present meshless formulation is very effective for the modeling and simulation of the FADE.