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.

Jacobian-free Newton-Krylov methods with GPU acceleration for computing nonlinear ship wave patterns

The nonlinear problem of steady free-surface flow past a submerged source is considered as a case study for three-dimensional ship wave problems. Of particular interest is the distinctive wedge-shaped wave pattern that forms on the surface of the fluid. By reformulating the governing equations with a standard boundary-integral method, we derive a system of nonlinear algebraic equations that enforce a singular integro-differential equation at each midpoint on a two-dimensional mesh. Our contribution is to solve the system of equations with a Jacobian-free Newton-Krylov method together with a banded preconditioner that is carefully constructed with entries taken from the Jacobian of the linearised problem. Further, we are able to utilise graphics processing unit acceleration to significantly increase the grid refinement and decrease the run-time of our solutions in comparison to schemes that are presently employed in the literature. Our approach provides opportunities to explore the nonlinear features of three-dimensional ship wave patterns, such as the shape of steep waves close to their limiting configuration, in a manner that has been possible in the two-dimensional analogue for some time.

A preconditioned numerical solver for stiff nonlinear reaction-diffusion equations with fractional Laplacians that avoids dense matrices

The numerical solution of fractional partial differential equations poses significant computational challenges in regard to efficiency as a result of the spatial nonlocality of the fractional differential operators. The dense coefficient matrices that arise from spatial discretisation of these operators mean that even one-dimensional problems can be difficult to solve using standard methods on grids comprising thousands of nodes or more. In this work we address this issue of efficiency for one-dimensional, nonlinear space-fractional reaction–diffusion equations with fractional Laplacian operators. We apply variable-order, variable-stepsize backward differentiation formulas in a Jacobian-free Newton–Krylov framework to advance the solution in time. A key advantage of this approach is the elimination of any requirement to form the dense matrix representation of the fractional Laplacian operator. We show how a banded approximation to this matrix, which can be formed and factorised efficiently, can be used as part of an effective preconditioner that accelerates convergence of the Krylov subspace iterative solver. Our approach also captures the full contribution from the nonlinear reaction term in the preconditioner, which is crucial for problems that exhibit stiff reactions. Numerical examples are presented to illustrate the overall effectiveness of the solver.

The severity of chorioamnionitis in pregnant sheep is associated with in vivo variation of the surface-exposed multiple-banded antigen/gene of ureaplasma parvum

Ureaplasma species are the bacteria most frequently isolated from human amniotic fluid in asymptomatic pregnancies and placental infections. Ureaplasma parvum serovars 3 and 6 are the most prevalent serovars isolated from men and women. We hypothesized that the effects on the fetus and chorioamnion of chronic ureaplasma infection in amniotic fluid are dependent on the serovar, dose, and variation of the ureaplasma multiple banded antigen (MBA) and mba gene. We injected high- or low dose U. parvum serovar 3, serovar 6, or vehicle intra-amniotically into pregnant ewes at 55 days of gestation (term = 150 days) and examined the chorioamnion, amniotic fluid, and fetal lung tissue of animals delivered by cesarean section at 125 days of gestation. Variation of the multiple banded antigen/mba generated by serovar 3 and serovar 6 ureaplasmas in vivo were compared by PCR assay and Western blot. Ureaplasma inoculums demonstrated only one (serovar 3) or two (serovar 6) MBA variants in vitro, but numerous antigenic variants were generated in vivo: serovar 6 passage 1 amniotic fluid cultures contained more MBA size variants than serovar 3 (P = 0.005),and ureaplasma titers were inversely related to the number of variants (P = 0.025). The severity of chorioamnionitis varied between animals. Low numbers of mba size variants (five or fewer) within amniotic fluid were associated with severe inflammation, whereas the chorioamnion from animals with nine or more mba variants showed little or no inflammation. These differences in chorioamnion inflammation may explain why not all women with in utero Ureaplasma spp. experience adverse pregnancy outcomes.

The role of the multiple banded antigen of ureaplasma parvum in intra-amniotic infection : major virulence factor or decoy?

The multiple banded antigen (MBA) is a predicted virulence factor of Ureaplasma species. Antigenic variation of the MBA is a potential mechanism by which ureaplasmas avoid immune recognition and cause chronic infections of the upper genital tract of pregnant women. We tested whether the MBA is involved in the pathogenesis of intra-amniotic infection and chorioamnionitis by injecting virulent or avirulent-derived ureaplasma clones (expressing single MBA variants) into the amniotic fluid of pregnant sheep. At 55 days of gestation pregnant ewes (n = 20) received intra-amniotic injections of virulent-derived or avirulent-derived U. parvum serovar 6 strains (2×104 CFU), or 10B medium (n = 5). Amniotic fluid was collected every two weeks post-infection and fetal tissues were collected at the time of surgical delivery of the fetus (140 days of gestation). Whilst chronic colonisation was established in the amniotic fluid of animals infected with avirulent-derived and virulent-derived ureaplasmas, the severity of chorioamnionitis and fetal inflammation was not different between these groups (p>0.05). MBA size variants (32–170 kDa) were generated in vivo in amniotic fluid samples from both the avirulent and virulent groups, whereas in vitro antibody selection experiments led to the emergence of MBA-negative escape variants in both strains. Anti-ureaplasma IgG antibodies were detected in the maternal serum of animals from the avirulent (40%) and virulent (55%) groups, and these antibodies correlated with increased IL-1β, IL-6 and IL-8 expression in chorioamnion tissue (p<0.05). We demonstrate that ureaplasmas are capable of MBA phase variation in vitro; however, ureaplasmas undergo MBA size variation in vivo, to potentially prevent eradication by the immune response. Size variation of the MBA did not correlate with the severity of chorioamnionitis. Nonetheless, the correlation between a maternal humoral response and the expression of chorioamnion cytokines is a novel finding. This host response may be important in the pathogenesis of inflammation-mediated adverse pregnancy outcomes.

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.

Ureaplasma parvum multiple banded antigen (MBA) size variation - association with fetal inflammation in a sheep model (Published abstract)

Background: Ureaplasma species are the most prevalent isolates from women who deliver preterm. The MBA, a surface exposed lipoprotein, is a key virulence factor of ureaplasmas. We investigated MBA variation after chronic and acute intra-amniotic (IA) ureaplasma infections. Method: U. parvum serovar 3 (2x104 colony-forming-units) was injected IA into pregnant ewes at: 55 days gestation (d, term = 145d) (n=8); 117d (n=8) and 121d (n=8). Fetuses were delivered surgically (124d) and ureaplasmas cultured from amniotic fluid (AF), chorioamnion, fetal lung (FL) and umbilical cord were tested by western blot and PCR assays to demonstrate MBA and mba gene variation respectively. Tissue sections were sectioned and stained by haemotoxylin and eosin and inflammatory cell counts and pathology were reported (blinded to outcome). Results: Numerous MBA/mba variants were generated in vivo after chronic exposure to ureaplasma infection but after acute infection no variants (3d) or very few variants (7d) were generated. Identical MBA variants were detected within the AF and FL but different ureaplasma variants were detected within chorioamnion specimens. The severity of inflammation within chronically infected tissues varied between animals ranging from no inflammation to severe inflammation with/without fibrosis. Chorioamnion, FL and cord from the same animal demonstrated the same degree of inflammation. Conclusions: MBA/mba variation in vivo occurred after the initiation of the host immune response and we propose that ureaplasmas vary the MBA antigen to evade the host immune response. In some animals there was no inflammation despite colonisation with high numbers of ureaplasmas.

Ureaplasma parvum serovar 3 multiple banded antigen size variation after chronic intra-amniotic infection/colonization

Ureaplasma species are the microorganisms most frequently associated with adverse pregnancy outcomes. The multiple banded antigen (MBA), a surface-exposed lipoprotein, is a key virulence factor of ureaplasmas. The MBA demonstrates size variation, which we have shown previously to be correlated with the severity of chorioamnion inflammation. We aimed to investigate U. parvum serovar 3 pathogenesis in vivo, using a sheep model, by investigating: MBA variation after long term (chronic) and short term (acute) durations of in utero ureaplasma infections, and the severity of chorioamnionitis and inflammation in other fetal tissues. Inocula of 2x107 colony-forming-units (CFU) of U. parvum serovar 3 (Up) or media controls (C) were injected intra-amniotically into pregnant ewes at one of three time points: day 55 (69d Up, n=8; C69, n=4); day 117 (7d Up, n=8; C7, n=2); and day 121 (3d Up, n=8; C3, n=2) of gestation (term=145-150d). At day 124, preterm fetuses were delivered surgically. Samples of chorioamnion, fetal lung, and umbilical cord were: (i) snap frozen for subsequent ureaplasma culture, and (ii) fixed, embedded, sectioned and stained by haematoxylin and eosin stain for histological analysis. Selected fetal lung clinical ureaplasma isolates were cloned and filtered to obtain cultures from a single CFU. Passage 1 and clone 2 ureaplasma cultures were tested by western blot to demonstrate MBA variation. In acute durations of ureaplasma infection no MBA variants (3d Up) or very few MBA variants (7d Up) were present when compared to the original inoculum. However, numerous MBA size variants were generated in vivo (alike within contiguous tissues, amniotic fluid and fetal lung, but different variants were present within chorioamnion), during chronic, 69d exposure to ureaplasma infection. For the first time we have shown that the degree of ureaplasma MBA variation in vivo increased with the duration of gestation.

Ureaplasma species multiple banded antigen (MBA) variation is associated with the severity of chorioamnionitis in late preterm placentas

Background: Intra-amniotic infection accounts for 30% of all preterm births (PTB), with the human Ureaplasma species being the most frequently identified microorganism from the placentas of women who deliver preterm. The highest prevalence of PTB occurs late preterm (32-36 weeks) but no studies have investigated the role of infectious aetiologies associated with late preterm birth. Method: Placentas from women with late PTB were dissected aseptically and samples of chorioamnion tissue and membrane swabs were collected. These were tested for Ureaplasma spp. and aerobic/anaerobic bacteria by culture and real-time PCR. Western blot was used to assess MBA variation in ureaplasma clinical isolates. The presence of microorganisms was correlated with histological chorioamnionitis. Results: Ureaplasma spp. were isolated from 33/466 (7%) of placentas by culture or PCR. The presence of ureaplasmas, but not other microorganisms, was associated with histological chorioamnionitis (21/33 ureaplasma-positive vs. 8/42 other bacteria; p= 0.001). Ureaplasma clinical isolates demonstrating no MBA variation were associated with histological chorioamnionitis. By contrast, ureaplasmas displaying MBA variation were isolated from placentas with no significant histological chorioamnionitis (p= 0.001). Conclusion: Ureaplasma spp. within placentas delivered late preterm (7%) is associated with histological chorioamnionitis (p = 0.001). Decreased inflammation within chorioamnion was observed when the clinical ureaplasma isolates demonstrated variation of their surface-exposed lipoproteins (MBA). This variation may be a mechanism by which ureaplasmas modulate and evade the host immune response. So whilst ureaplasmas are present intra-amniotically they are not suspected because of the normal macroscopic appearance of the placentas and the amniotic fluid.

A compliant, banded outflow cannula for decreased afterload sensitivity of rotary right ventricular assist devices

Biventricular support with dual rotary ventricular assist devices (VADs) has been implemented clinically with restriction of the right VAD (RVAD) outflow cannula to artificially increase afterload and, therefore, operate within recommended design speed ranges. However, the low preload and high afterload sensitivity of these devices increase the susceptibility of suction events. Active control systems are prone to sensor drift or inaccurate inferred (sensor-less) data, therefore an alternative solution may be of benefit. This study presents the in vitro evaluation of a compliant outflow cannula designed to passively decrease the afterload sensitivity of rotary RVADs and minimize left-sided suction events. A one-way fluid-structure interaction model was initially used to produce a design with suitable flow dynamics and radial deformation. The resultant geometry was cast with different initial cross-sectional restrictions and concentrations of a softening diluent before evaluation in a mock circulation loop. Pulmonary vascular resistance (PVR) was increased from 50 dyne s/cm5 until left-sided suction events occurred with each compliant cannula and a rigid, 4.5 mm diameter outflow cannula for comparison. Early suction events (PVR ∼ 300 dyne s/cm5) were observed with the rigid outflow cannula. Addition of the compliant section with an initial 3 mm diameter restriction and 10% diluent expanded the outflow restriction as PVR increased, thus increasing RVAD flow rate and preventing left-sided suction events at PVR levels beyond 1000 dyne s/cm5. Therefore, the compliant, restricted outflow cannula provided a passive control system to assist in the prevention of suction events with rotary biventricular support while maintaining pump speeds within normal ranges of operation.

(Z)-11-Hexadecenal and (3Z,6Z,9Z)-Tricosatriene: Sex Pheromone Components of the Red Banded Mango Caterpillar Deanolis sublimbalis

The sex pheromone of the red banded mango caterpillar, Deanolis sublimbalis (Lepidoptera: Crambidae), a serious pest of the mango Mangifera indica (Anacardiaceae) in India and Southeast Asia and a recent invader into northern Australia, has been identified. Three candidate compounds were identified from pheromone gland extracts of female moths, using gas chromatography (GC), GC-electroantennographic detection and GC-mass spectrometric analyses, in conjunction with dimethyldisulfide derivatization. Field bioassays established that both (Z)-11-hexadecenal (Z11-16:Ald) and (3Z,6Z,9Z)-tricosatriene (3Z,6Z,9Z-23:Hy) were required for attraction of male D. sublimbalis moths, and 1,000 μg of a 1:1 mix of Z11-16:Ald and 3Z,6Z,9Z-23:Hy was more attractive to male moths than caged virgin females. However, the binary blend was only attractive when the isomeric purity of the monounsaturated aldehyde was >99%, suggesting that the (E)-isomer was inhibitory. Although (Z)-11-hexadecen-1-ol (Z11-16:OH) was tentatively identified in gland extracts, the addition of this compound to the binary blend did not increase the numbers of moths captured. The pheromone can now be used in integrated pest management strategies.

Reducing the risk of herbicide runoff in sugarcane farming through controlled traffic and early-banded application

The off-site transport of agricultural chemicals, such as herbicides, into freshwater and marine ecosystems is a world-wide concern. The adoption of farm management practices that minimise herbicide transport in rainfall-runoff is a priority for the Australian sugarcane industry, particularly in the coastal catchments draining into the World Heritage listed Great Barrier Reef (GBR) lagoon. In this study, residual herbicide runoff and infiltration were measured using a rainfall simulator in a replicated trial on a brown Chromosol with 90–100% cane trash blanket cover in the Mackay Whitsunday region, Queensland. Management treatments included conventional 1.5 m spaced sugarcane beds with a single row of sugarcane (CONV) and 2 m spaced, controlled traffic sugarcane beds with dual sugarcane rows (0.8 m apart) (2mCT). The aim was to simulate the first rainfall event after the application of the photosynthesis inhibiting (PSII) herbicides ametryn, atrazine, diuron and hexazinone, by broadcast (100% coverage, on bed and furrow) and banding (50–60% coverage, on bed only) methods. These events included heavy rainfall 1 day after herbicide application, considered a worst case scenario, or rainfall 21 days after application. The 2mCT rows had significantly (P < 0.05) less runoff (38%) and lower peak runoff rates (43%) than CONV rows for a rainfall average of 93 mm at 100 mm h−1 (1:20 yr Average Return Interval). Additionally, final infiltration rates were higher in 2mCT rows than CONV rows, with 72 and 52 mm h−1 respectively. This resulted in load reductions of 60, 55, 47, and 48% for ametryn, atrazine, diuron and hexazinone from 2mCT rows, respectively. Herbicide losses in runoff were also reduced by 32–42% when applications were banded rather than broadcast. When rainfall was experienced 1 day after application, a large percentage of herbicides were washed off the cane trash. However, by day 21, concentrations of herbicide residues on cane trash were lower and more resistant to washoff, resulting in lower losses in runoff. Consequently, ametryn and atrazine event mean concentrations in runoff were approximately 8 fold lower at day 21 compared with day 1, whilst diuron and hexazinone were only 1.6–1.9 fold lower, suggesting longer persistence of these chemicals. Runoff collected at the end of the paddock in natural rainfall events indicated consistent though smaller treatment differences to the rainfall simulation study. Overall, it was the combination of early application, banding and controlled traffic that was most effective in reducing herbicide losses in runoff. Crown copyright © 2012

Banded spatiotemporal chaos in sheared nematogenic fluids

We present the results of a numerical study of a model of the hydrodynamics of a sheared nematogenic fluid, taking into account the effects of order-parameter stresses on the velocity profile but allowing spatial variations only in the gradient direction. When parameter values are such that the stress from orientational distortions is comparable to the bare viscous stress, the system exhibits steady states with the characteristics of shear banding. In addition, nonlinearity in the coupling of extensional flow to orientation leads to the appearance of a new steady state in which the features of both spatiotemporal chaos and shear banding are present.

The study of banded spherulite patterns by coupled logistic map lattice model

Banded spherulite patterns are simulated in two dimensions by means of a coupled logistic map lattice model. Both target pattern and spiral pattern which have been proved to be existent experimentally in banded spherulite are obtained by choosing suitable parameters in the model. The simulation results also indicate that the band spacing is decreased with the increase of parameter mu in the logistic map and increased with the increase of the coupling parameter epsilon, which is quite similar to the results in some experiments. Moreover, the relationship between the parameters and the corresponding patterns is obtained, and the target patterns and spiral patterns are distinguished for a given group of initial values, which may guide the study of banded spherulite.