Upconversion assisted self-pulsing in a high-concentration erbium doped fiber laser

We report results on experimental and theoretical characterisation of self-pulsing in high concentration erbium doped fibre laser which is free from erbium clusters. Unlike previous models of self-pulsing accounting for pair-induced quenching (PIQ) on the clustered erbium ions, new model has been developed with accounting for statistical nature of the excitation migration and upconversion and resonance-like pumpto-signal intensity noise transfer. The obtained results are in a good agreement with the experimental data.

A novel concentration dependent amino acid ion pair strategy to mediate drug permeation using indomethacin as a model insoluble drug

Assessment of oral drug bioavailability is an important parameter for new chemical entities (NCEs) in drug development cycle. After evaluating the pharmacological response of these new molecules, the following critical stage is to investigate their in vitro permeability. Despite the great success achieved by prodrugs, covalent linking the drug molecule with a hydrophobic moiety might result in a new entity that might be toxic or ineffective. Therefore, an alternative that would improve the drug uptake without affecting the efficacy of the drug molecule would be advantageous. The aim of the current study is to investigate the effect of ion-pairing on the permeability profile of a model drug: indomethacin (IND) to understand the mechanism behind the permeability improvement across Caco-2 monolayers. Arginine and lysine formed ion-pairs with IND at various molar ratios 1:1, 1:2, 1:4 and 1:8 as reflected by the double reciprocal graphs. The partitioning capacities of the IND were evaluated using octanol/water partitioning studies and the apparent permeabilities (P app) were measured across Caco-2 monolayers for the different formulations. Partitioning studies reflected the high hydrophobicity of IND (Log P = 3) which dropped upon increasing the concentrations of arginine/lysine in the ion pairs. Nevertheless, the prepared ion pairs improved IND permeability especially after 60 min of the start of the experiment. Coupling partitioning and permeability results suggest a decrease in the passive transcellular uptake due to the drop in IND portioning capacities and a possible involvement of active carriers. Future work will investigate which transport gene might be involved in the absorption of the ion paired formulations using molecular biology technologies. © 2014 Elsevier B.V. All rights reserved.

Velocity and Concentration field of discharge from a boat propeller

Two-stroke outboard boat engines using total loss lubrication deposit a significant proportion of their lubricant and fuel directly into the water. The purpose of this work is to document the velocity and concentration field characteristics of a submerged swirling water jet emanating from a propeller in order to provide information on its fundamental characteristics. Measurements of the velocity and concentration field were performed in a turbulent jet generated by a model boat propeller (0.02 m diameter) operating at 1500 rpm and 3000 rpm. The measurements were carried out in the Zone of Established Flow up to 50 propeller diameters downstream of the propeller. Both the mean axial velocity profile and the mean concentration profile showed self-similarity. Further, the stand deviation growth curve was linear. The effects of propeller speed and dye release location were also investigated.

Image synthesis based on a model of human vision

Modern computer graphics systems are able to construct renderings of such high quality that viewers are deceived into regarding the images as coming from a photographic source. Large amounts of computing resources are expended in this rendering process, using complex mathematical models of lighting and shading. However, psychophysical experiments have revealed that viewers only regard certain informative regions within a presented image. Furthermore, it has been shown that these visually important regions contain low-level visual feature differences that attract the attention of the viewer. This thesis will present a new approach to image synthesis that exploits these experimental findings by modulating the spatial quality of image regions by their visual importance. Efficiency gains are therefore reaped, without sacrificing much of the perceived quality of the image. Two tasks must be undertaken to achieve this goal. Firstly, the design of an appropriate region-based model of visual importance, and secondly, the modification of progressive rendering techniques to effect an importance-based rendering approach. A rule-based fuzzy logic model is presented that computes, using spatial feature differences, the relative visual importance of regions in an image. This model improves upon previous work by incorporating threshold effects induced by global feature difference distributions and by using texture concentration measures. A modified approach to progressive ray-tracing is also presented. This new approach uses the visual importance model to guide the progressive refinement of an image. In addition, this concept of visual importance has been incorporated into supersampling, texture mapping and computer animation techniques. Experimental results are presented, illustrating the efficiency gains reaped from using this method of progressive rendering. This visual importance-based rendering approach is expected to have applications in the entertainment industry, where image fidelity may be sacrificed for efficiency purposes, as long as the overall visual impression of the scene is maintained. Different aspects of the approach should find many other applications in image compression, image retrieval, progressive data transmission and active robotic vision.

GameFlow : a model for evaluating player enjoyment in games

Although player enjoyment is central to computer games, there is currently no accepted model of player enjoyment in games. There are many heuristics in the literature, based on elements such as the game interface, mechanics, gameplay, and narrative. However, there is a need to integrate these heuristics into a validated model that can be used to design, evaluate, and understand enjoyment in games. We have drawn together the various heuristics into a concise model of enjoyment in games that is structured by flow. Flow, a widely accepted model of enjoyment, includes eight elements that, we found, encompass the various heuristics from the literature. Our new model, GameFlow, consists of eight elements -- concentration, challenge, skills, control, clear goals, feedback, immersion, and social interaction. Each element includes a set of criteria for achieving enjoyment in games. An initial investigation and validation of the GameFlow model was carried out by conducting expert reviews of two real-time strategy games, one high-rating and one low-rating, using the GameFlow criteria. The result was a deeper understanding of enjoyment in real-time strategy games and the identification of the strengths and weaknesses of the GameFlow model as an evaluation tool. The GameFlow criteria were able to successfully distinguish between the high-rated and low-rated games and identify why one succeeded and the other failed. We concluded that the GameFlow model can be used in its current form to review games; further work will provide tools for designing and evaluating enjoyment in games.

Experimental study of the concentration field of discharge from a boat propeller

Two-stroke outboard boat engines using total loss lubrication deposit a significant proportion of their lubricant and fuel directly into the water. The purpose of this work is to document the velocity and concentration field characteristics of a submerged swirling water jet emanating from a propeller in order to provide information on its fundamental characteristics. The properties of the jet were examined far enough downstream to be relevant to the eventual modelling of the mixing problem. Measurements of the velocity and concentration field were performed in a turbulent jet generated by a model boat propeller (0.02 m diameter) operating at 1500 rpm and 3000 rpm in a weak co-flow of 0.04 m/s. The measurements were carried out in the Zone of Established Flow up to 50 propeller diameters downstream of the propeller, which was placed in a glass-walled flume 0.4 m wide with a free surface depth of 0.15 m. The jet and scalar plume development were compared to that of a classical free round jet. Further, results pertaining to radial distribution, self similarity, standard deviation growth, maximum value decay and integral fluxes of velocity and concentration were presented and fitted with empirical correlations. Furthermore, propeller induced mixing and pollutant source concentration from a two-stroke engine were estimated.

Prediction model of the buildup of volatile organic compounds on urban roads

A model to predict the buildup of mainly traffic-generated volatile organic compounds or VOCs (toluene, ethylbenzene, ortho-xylene, meta-xylene, and para-xylene) on urban road surfaces is presented. The model required three traffic parameters, namely average daily traffic (ADT), volume to capacity ratio (V/C), and surface texture depth (STD), and two chemical parameters, namely total suspended solid (TSS) and total organic carbon (TOC), as predictor variables. Principal component analysis and two phase factor analysis were performed to characterize the model calibration parameters. Traffic congestion was found to be the underlying cause of traffic-related VOC buildup on urban roads. The model calibration was optimized using orthogonal experimental design. Partial least squares regression was used for model prediction. It was found that a better optimized orthogonal design could be achieved by including the latent factors of the data matrix into the design. The model performed fairly accurately for three different land uses as well as five different particle size fractions. The relative prediction errors were 10–40% for the different size fractions and 28–40% for the different land uses while the coefficients of variation of the predicted intersite VOC concentrations were in the range of 25–45% for the different size fractions. Considering the sizes of the data matrices, these coefficients of variation were within the acceptable interlaboratory range for analytes at ppb concentration levels.

Asymptotic and numerical results for a model of solvent-dependent drug diffusion through polymeric spheres

A model for drug diffusion from a spherical polymeric drug delivery device is considered. The model contains two key features. The first is that solvent diffuses into the polymer, which then transitions from a glassy to a rubbery state. The interface between the two states of polymer is modelled as a moving boundary, whose speed is governed by a kinetic law; the same moving boundary problem arises in the one-phase limit of a Stefan problem with kinetic undercooling. The second feature is that drug diffuses only through the rubbery region, with a nonlinear diffusion coefficient that depends on the concentration of solvent. We analyse the model using both formal asymptotics and numerical computation, the latter by applying a front-fixing scheme with a finite volume method. Previous results are extended and comparisons are made with linear models that work well under certain parameter regimes. Finally, a model for a multi-layered drug delivery device is suggested, which allows for more flexible control of drug release.

Model selection and error estimation

We study model selection strategies based on penalized empirical loss minimization. We point out a tight relationship between error estimation and data-based complexity penalization: any good error estimate may be converted into a data-based penalty function and the performance of the estimate is governed by the quality of the error estimate. We consider several penalty functions, involving error estimates on independent test data, empirical VC dimension, empirical VC entropy, and margin-based quantities. We also consider the maximal difference between the error on the first half of the training data and the second half, and the expected maximal discrepancy, a closely related capacity estimate that can be calculated by Monte Carlo integration. Maximal discrepancy penalty functions are appealing for pattern classification problems, since their computation is equivalent to empirical risk minimization over the training data with some labels flipped.

A Bayesian model predicts the response of axons to molecular gradients

Axon guidance by molecular gradients plays a crucial role in wiring up the nervous system. However, the mechanisms axons use to detect gradients are largely unknown. We first develop a Bayesian “ideal observer” analysis of gradient detection by axons, based on the hypothesis that a principal constraint on gradient detection is intrinsic receptor binding noise. Second, from this model, we derive an equation predicting how the degree of response of an axon to a gradient should vary with gradient steepness and absolute concentration. Third, we confirm this prediction quantitatively by performing the first systematic experimental analysis of how axonal response varies with both these quantities. These experiments demonstrate a degree of sensitivity much higher than previously reported for any chemotacting system. Together, these results reveal both the quantitative constraints that must be satisfied for effective axonal guidance and the computational principles that may be used by the underlying signal transduction pathways, and allow predictions for the degree of response of axons to gradients in a wide variety of in vivo and in vitro settings.

Quantification of particle emission characteristics and development of an emission model for use in transport microenvironments affected by traffic emissions

Vehicle emitted particles are of significant concern based on their potential to influence local air quality and human health. Transport microenvironments usually contain higher vehicle emission concentrations compared to other environments, and people spend a substantial amount of time in these microenvironments when commuting. Currently there is limited scientific knowledge on particle concentration, passenger exposure and the distribution of vehicle emissions in transport microenvironments, partially due to the fact that the instrumentation required to conduct such measurements is not available in many research centres. Information on passenger waiting time and location in such microenvironments has also not been investigated, which makes it difficult to evaluate a passenger’s spatial-temporal exposure to vehicle emissions. Furthermore, current emission models are incapable of rapidly predicting emission distribution, given the complexity of variations in emission rates that result from changes in driving conditions, as well as the time spent in driving condition within the transport microenvironment. In order to address these scientific gaps in knowledge, this work conducted, for the first time, a comprehensive statistical analysis of experimental data, along with multi-parameter assessment, exposure evaluation and comparison, and emission model development and application, in relation to traffic interrupted transport microenvironments. The work aimed to quantify and characterise particle emissions and human exposure in the transport microenvironments, with bus stations and a pedestrian crossing identified as suitable research locations representing a typical transport microenvironment. Firstly, two bus stations in Brisbane, Australia, with different designs, were selected to conduct measurements of particle number size distributions, particle number and PM2.5 concentrations during two different seasons. Simultaneous traffic and meteorological parameters were also monitored, aiming to quantify particle characteristics and investigate the impact of bus flow rate, station design and meteorological conditions on particle characteristics at stations. The results showed higher concentrations of PN20-30 at the station situated in an open area (open station), which is likely to be attributed to the lower average daily temperature compared to the station with a canyon structure (canyon station). During precipitation events, it was found that particle number concentration in the size range 25-250 nm decreased greatly, and that the average daily reduction in PM2.5 concentration on rainy days compared to fine days was 44.2 % and 22.6 % at the open and canyon station, respectively. The effect of ambient wind speeds on particle number concentrations was also examined, and no relationship was found between particle number concentration and wind speed for the entire measurement period. In addition, 33 pairs of average half-hourly PN7-3000 concentrations were calculated and identified at the two stations, during the same time of a day, and with the same ambient wind speeds and precipitation conditions. The results of a paired t-test showed that the average half-hourly PN7-3000 concentrations at the two stations were not significantly different at the 5% confidence level (t = 0.06, p = 0.96), which indicates that the different station designs were not a crucial factor for influencing PN7-3000 concentrations. A further assessment of passenger exposure to bus emissions on a platform was evaluated at another bus station in Brisbane, Australia. The sampling was conducted over seven weekdays to investigate spatial-temporal variations in size-fractionated particle number and PM2.5 concentrations, as well as human exposure on the platform. For the whole day, the average PN13-800 concentration was 1.3 x 104 and 1.0 x 104 particle/cm3 at the centre and end of the platform, respectively, of which PN50-100 accounted for the largest proportion to the total count. Furthermore, the contribution of exposure at the bus station to the overall daily exposure was assessed using two assumed scenarios of a school student and an office worker. It was found that, although the daily time fraction (the percentage of time spend at a location in a whole day) at the station was only 0.8 %, the daily exposure fractions (the percentage of exposures at a location accounting for the daily exposure) at the station were 2.7% and 2.8 % for exposure to PN13-800 and 2.7% and 3.5% for exposure to PM2.5 for the school student and the office worker, respectively. A new parameter, “exposure intensity” (the ratio of daily exposure fraction and the daily time fraction) was also defined and calculated at the station, with values of 3.3 and 3.4 for exposure to PN13-880, and 3.3 and 4.2 for exposure to PM2.5, for the school student and the office worker, respectively. In order to quantify the enhanced emissions at critical locations and define the emission distribution in further dispersion models for traffic interrupted transport microenvironments, a composite line source emission (CLSE) model was developed to specifically quantify exposure levels and describe the spatial variability of vehicle emissions in traffic interrupted microenvironments. This model took into account the complexity of vehicle movements in the queue, as well as different emission rates relevant to various driving conditions (cruise, decelerate, idle and accelerate), and it utilised multi-representative segments to capture the accurate emission distribution for real vehicle flow. This model does not only helped to quantify the enhanced emissions at critical locations, but it also helped to define the emission source distribution of the disrupted steady flow for further dispersion modelling. The model then was applied to estimate particle number emissions at a bidirectional bus station used by diesel and compressed natural gas fuelled buses. It was found that the acceleration distance was of critical importance when estimating particle number emission, since the highest emissions occurred in sections where most of the buses were accelerating and no significant increases were observed at locations where they idled. It was also shown that emissions at the front end of the platform were 43 times greater than at the rear of the platform. The CLSE model was also applied at a signalled pedestrian crossing, in order to assess increased particle number emissions from motor vehicles when forced to stop and accelerate from rest. The CLSE model was used to calculate the total emissions produced by a specific number and mix of light petrol cars and diesel passenger buses including 1 car travelling in 1 direction (/1 direction), 14 cars / 1 direction, 1 bus / 1 direction, 28 cars / 2 directions, 24 cars and 2 buses / 2 directions, and 20 cars and 4 buses / 2 directions. It was found that the total emissions produced during stopping on a red signal were significantly higher than when the traffic moved at a steady speed. Overall, total emissions due to the interruption of the traffic increased by a factor of 13, 11, 45, 11, 41, and 43 for the above 6 cases, respectively. In summary, this PhD thesis presents the results of a comprehensive study on particle number and mass concentration, together with particle size distribution, in a bus station transport microenvironment, influenced by bus flow rates, meteorological conditions and station design. Passenger spatial-temporal exposure to bus emitted particles was also assessed according to waiting time and location along the platform, as well as the contribution of exposure at the bus station to overall daily exposure. Due to the complexity of the interrupted traffic flow within the transport microenvironments, a unique CLSE model was also developed, which is capable of quantifying emission levels at critical locations within the transport microenvironment, for the purpose of evaluating passenger exposure and conducting simulations of vehicle emission dispersion. The application of the CLSE model at a pedestrian crossing also proved its applicability and simplicity for use in a real-world transport microenvironment.

Clinical strategies for the alleviation of contractures from a predictive mathematical model of dermal repair

Hypertrophic scars arise when there is an overproduction of collagen during wound healing. These are often associated with poor regulation of the rate of programmed cell death(apoptosis) of the cells synthesizing the collagen or by an exuberant inflammatory response that prolongs collagen production and increases wound contraction. Severe contractures that occur, for example, after a deep burn can cause loss of function especially if the wound is over a joint such as the elbow or knee. Recently, we have developed a morphoelastic mathematical model for dermal repair that incorporates the chemical, cellular and mechanical aspects of dermal wound healing. Using this model, we examine pathological scarring in dermal repair by first assuming a smaller than usual apoptotic rate for myofibroblasts, and then considering a prolonged inflammatory response, in an attempt to determine a possible optimal intervention strategy to promote normal repair, or terminate the fibrotic scarring response. Our model predicts that in both cases it is best to apply the intervention strategy early in the wound healing response. Further, the earlier an intervention is made, the less aggressive the intervention required. Finally, if intervention is conducted at a late time during healing, a significant intervention is required; however, there is a threshold concentration of the drug or therapy applied, above which minimal further improvement to wound repair is obtained.

Ureaplasma parvum : understanding the complexities of intra-amniotic infection in an ovine model

The human Ureaplasma species are the most frequently isolated bacteria from the upper genital tract of pregnant women and can cause clinically asymptomatic, intra-uterine infections, which are difficult to treat with antimicrobials. Ureaplasma infection of the upper genital tract during pregnancy has been associated with numerous adverse outcomes including preterm birth, chorioamnionitis and neonatal respiratory diseases. The mechanisms by which ureaplasmas are able to chronically colonise the amniotic fluid and avoid eradication by (i) the host immune response and (ii) maternally-administered antimicrobials, remain virtually unexplored. To address this gap within the literature, this study investigated potential mechanisms by which ureaplasmas are able to cause chronic, intra-amniotic infections in an established ovine model. In this PhD program of research the effectiveness of standard, maternal erythromycin for the treatment of chronic, intra-amniotic ureaplasma infections was evaluated. At 55 days of gestation pregnant ewes received an intra-amniotic injection of either: a clinical Ureaplasma parvum serovar 3 isolate that was sensitive to macrolide antibiotics (n = 16); or 10B medium (n = 16). At 100 days of gestation, ewes were then randomised to receive either maternal erythromycin treatment (30 mg/kg/day for four days) or no treatment. Ureaplasmas were isolated from amniotic fluid, chorioamnion, umbilical cord and fetal lung specimens, which were collected at the time of preterm delivery of the fetus (125 days of gestation). Surprisingly, the numbers of ureaplasmas colonising the amniotic fluid and fetal tissues were not different between experimentally-infected animals that received erythromycin treatment or infected animals that did not receive treatment (p > 0.05), nor were there any differences in fetal inflammation and histological chorioamnionitis between these groups (p > 0.05). These data demonstrate the inability of maternal erythromycin to eradicate intra-uterine ureaplasma infections. Erythromycin was detected in the amniotic fluid of animals that received antimicrobial treatment (but not in those that did not receive treatment) by liquid chromatography-mass spectrometry; however, the concentrations were below therapeutic levels (<10 – 76 ng/mL). These findings indicate that the ineffectiveness of standard, maternal erythromycin treatment of intra-amniotic ureaplasma infections may be due to the poor placental transfer of this drug. Subsequently, the phenotypic and genotypic characteristics of ureaplasmas isolated from the amniotic fluid and chorioamnion of pregnant sheep after chronic, intra-amniotic infection and low-level exposure to erythromycin were investigated. At 55 days of gestation twelve pregnant ewes received an intra-amniotic injection of a clinical U. parvum serovar 3 isolate, which was sensitive to macrolide antibiotics. At 100 days of gestation, ewes received standard maternal erythromycin treatment (30 mg/kg/day for four days, n = 6) or saline (n = 6). Preterm fetuses were surgically delivered at 125 days of gestation and ureaplasmas were cultured from the amniotic fluid and the chorioamnion. The minimum inhibitory concentrations (MICs) of erythromycin, azithromycin and roxithromycin were determined for cultured ureaplasma isolates, and antimicrobial susceptibilities were different between ureaplasmas isolated from the amniotic fluid (MIC range = 0.08 – 1.0 mg/L) and chorioamnion (MIC range = 0.06 – 5.33 mg/L). However, the increased resistance to macrolide antibiotics observed in chorioamnion ureaplasma isolates occurred independently of exposure to erythromycin in vivo. Remarkably, domain V of the 23S ribosomal RNA gene (which is the target site of macrolide antimicrobials) of chorioamnion ureaplasmas demonstrated significant variability (125 polymorphisms out of 422 sequenced nucleotides, 29.6%) when compared to the amniotic fluid ureaplasma isolates and the inoculum strain. This sequence variability did not occur as a consequence of exposure to erythromycin, as the nucleotide substitutions were identical between chorioamnion ureaplasmas isolated from different animals, including those that did not receive erythromycin treatment. We propose that these mosaic-like 23S ribosomal RNA gene sequences may represent gene fragments transferred via horizontal gene transfer. The significant differences observed in (i) susceptibility to macrolide antimicrobials and (ii) 23S ribosomal RNA sequences of ureaplasmas isolated from the amniotic fluid and chorioamnion suggests that the anatomical site from which they were isolated may exert selective pressures that alter the socio-microbiological structure of the bacterial population, by selecting for genetic changes and altered antimicrobial susceptibility profiles. The final experiment for this PhD examined antigenic size variation of the multiple banded antigen (MBA, a surface-exposed lipoprotein and predicted ureaplasmal virulence factor) in chronic, intra-amniotic ureaplasma infections. Previously defined ‘virulent-derived’ and ‘avirulent-derived’ clonal U. parvum serovar 6 isolates (each expressing a single MBA protein) were injected into the amniotic fluid of pregnant ewes (n = 20) at 55 days of gestation, and amniotic fluid was collected by amniocentesis every two weeks until the time of near-term delivery of the fetus (at 140 days of gestation). Both the avirulent and virulent clonal ureaplasma strains generated MBA size variants (ranging in size from 32 – 170 kDa) within the amniotic fluid of pregnant ewes. The mean number of MBA size variants produced within the amniotic fluid was not different between the virulent (mean = 4.2 MBA variants) and avirulent (mean = 4.6 MBA variants) ureaplasma strains (p = 0.87). Intra-amniotic infection with the virulent strain was significantly associated with the presence of meconium-stained amniotic fluid (p = 0.01), which is an indicator of fetal distress in utero. However, the severity of histological chorioamnionitis was not different between the avirulent and virulent groups. We demonstrated that ureaplasmas were able to persist within the amniotic fluid of pregnant sheep for 85 days, despite the host mounting an innate and adaptive immune response. Pro-inflammatory cytokines (interleukin (IL)-1â, IL-6 and IL-8) were elevated within the chorioamnion tissue of pregnant sheep from both the avirulent and virulent treatment groups, and this was significantly associated with the production of anti-ureaplasma IgG antibodies within maternal sera (p < 0.05). These findings suggested that the inability of the host immune response to eradicate ureaplasmas from the amniotic cavity may be due to continual size variation of MBA surface-exposed epitopes. Taken together, these data confirm that ureaplasmas are able to cause long-term in utero infections in a sheep model, despite standard antimicrobial treatment and the development of a host immune response. The overall findings of this PhD project suggest that ureaplasmas are able to cause chronic, intra-amniotic infections due to (i) the limited placental transfer of erythromycin, which prevents the accumulation of therapeutic concentrations within the amniotic fluid; (ii) the ability of ureaplasmas to undergo rapid selection and genetic variation in vivo, resulting in ureaplasma isolates with variable MICs to macrolide antimicrobials colonising the amniotic fluid and chorioamnion; and (iii) antigenic size variation of the MBA, which may prevent eradication of ureaplasmas by the host immune response and account for differences in neonatal outcomes. The outcomes of this program of study have improved our understanding of the biology and pathogenesis of this highly adapted microorganism.

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.