The Nonlinear Asymptotic Stage of the Rayleigh-Taylor Instability with Wide Bubbles and Narrowing Spikes

The potential flow of an incompressible inviscid heavy fluid over a light one is considered. The integral version of the method of matched asymptotic expansion is applied to the construction of the solution over long intervals of time. The asymptotic solution describes the flow in which a bubble rises with constant speed and the "tongue" is in free fall. The outer expansion is stationary, but the inner one depends on time. It is shown that the solution exists within the same range of Froude number obtained previously by Vanden-Broeck (1984a,b). The Froude number and the solution depend on the initial energy of the disturbance. At the top of the bubble, the derivative of the free-surface curvature has a discontinuity when the Froude number is not equal to 0.23. This makes it possible to identify the choice of the solution obtained in a number of studies with the presence of an artificial numerical surface tension. The first correction term in the neighborhood of the tongue is obtained when large surface tension is included

Exponential asymptotics and gravity waves

The problem of irrotational inviscid incompressible free-surface flow is examined in the limit of small Froude number. Since this is a singular perturbation, singularities in the flow field (or its analytic continuation) such as stagnation points, or corners in submerged objects or on rough beds, lead to a divergent asymptotic expansion, with associated Stokes lines. Recent techniques in exponential asymptotics are employed to observe the switching on of exponentially small gravity waves across these Stokes lines. As a concrete example, the flow over a step is considered. It is found that there are three possible parameter regimes, depending on whether the dimensionless step height is small, of the same order, or large compared to the square of the Froude number. Asymptotic results are derived in each case, and compared with numerical simulations of the full nonlinear problem. The agreement is remarkably good, even at relatively large Froude number. This is in contrast to the alternative analytical theory of small step height, which is accurate only for very small steps

Large-amplitude capillary waves in electrified fluid sheets

Large-amplitude capillary waves on fluid sheets are computed in the presence of a uniform electric field acting in a direction parallel to the undisturbed configuration. The fluid is taken to be inviscid, incompressible and non-conducting. Travelling waves of arbitrary amplitudes and wavelengths are calculated and the effect of the electric field is studied. The solutions found generalize the exact symmetric solutions of Kinnersley (1976) to include electric fields, for which no exact solutions have been found. Long-wave nonlinear waves are also constructed using asymptotic methods. The asymptotic solutions are compared with the full computations as the wavelength increases, and agreement is found to be excellent

Trapped waves between submerged obstacles

Free-surface flows past submerged obstacles in a channel are considered. The fluid is assumed to be inviscid and incompressible and the flow to be irrotational. In previous work involving a single obstacle (Dias & Vanden-Broeck 2002), new solutions called ‘generalized hydraulic falls’ were found. These solutions are characterized by a supercritical flow on one side of the obstacle and a train of waves on the other. However, in the case of a single submerged object, the generalized hydraulic falls are unphysical because the waves do not satisfy the radiation condition. In this paper new solutions for the flow past two obstacles of arbitrary shape are computed. These solutions are characterized by a train of waves ‘trapped’ between the obstacles. The generalized hydraulic falls are shown to describe locally the flow over one of the two obstacles when the distance between the two obstacles is large

Bulky-yet-flexible carbene ligands and their use in palladium cross-coupling

In recent years, several classes of new N-heterocyclic carbene (NHC) ligands were developed around the concept of flexible steric bulk. The steric hindrance of these ligands brings stability to the active species, while ligand flexibility still allows for the approach of the substrate. In this review, the synthesis of several types of new classes, such as IBiox, cyclic alkyl amino carbenes (CAAC), ITent, and IPr* are discussed, as well as how they move the state-of-the-art in palladium catalyzed cross-coupling forward

Supercritical two-fluid interactions with surface tension and gravity

Gravity and surface-tension effects are examined for inviscid–inviscid interactions between two fluids close to a wall. The ratios of density and viscosity of the two fluids are taken to be small. A nonlinear integro–differential equation is found to govern the near-wall flow velocity, interface shape and pressure; analysis, computation and comparisons are then applied. Travelling-state solutions are of particular interest

Distribution of human papillomaviruses and bacterial vaginosis in HIV positive women with abnormal cytology in Mombasa, Kenya

Background: HPV is the major etiological factor in the causal pathway for cervical cancer, which is the leading cancer among women in sub-Saharan Africa. HIV is associated with a higher prevalence and a broader range of high-risk HPV genotypes. Studies have shown a positive association between Bacterial vaginosis (BV) and HPV and HIV. Also, in African women, BV was found to be significantly associated with vaginal inflammation. The high prevalence of BV, HIV and HPV infections in the African continent makes elucidation of the interactions with one another of utmost public health interest. The aims of the current study are to examine the frequency of HPV genotypes and BV as well as their respective risk factors within an HIV infected population with abnormal cytology in the resource-constrained setting of Mombasa, Kenya and, secondly, highlight issues to consider for triple co-infection clinical management. Method: Cross-sectional analysis with a sample drawn from an ongoing cohort study. All consenting, non-pregnant HIV infected women, between 18 and 50 years of age, without a history of cervical cancer or hysterectomy, between November 2005 and April 2006 were screened for HR HPV DNA in Mombasa, Kenya. 1 out of 4 HIV positive women fulfilled the criteria by having SIL (24.9 %). 600 HIV infected women were tested to reach a cohort of 74 HIV women with abnormal cytology. To assess which factors were associated with HR HPV, crude statistical analysis was performed through logistic regression. Results: Bacterial vaginosis (BV) was found in 46 women out of 74 (62.2 %). Cervicitis was diagnosed in 15 % of women (n = 11), of which 8 had BV. The most prevalent HPV genotypes were HPV 16 (33.8), HPV 53 (24.3) and HPV 18 (17.6 %), while 65 % of the participants had multiple genotype infection. Statistically significant associations between CD4 counts = 350 mu l and HPV 16 adjusted for age (OR = 2.9; 95 % CI: 1.0-8.3; p = 0.05). A borderline statistically significant association was observed between BV and HPV58 (crude OR = 4.1, 95 % CI: 0.8-21.0; p = 0.07). Conclusion: The most prevalent HPV genotypes observed were HPV 16, HPV 53, and HPV 18, which have a combined prevalence of 76 %. Our results show that a triage based on CD4 count should start at CD4 count >= 350 mu l as our study suggests that HPV 16 are more prevalent when women are moderately immunosuppressed. Given the high prevalence of HPV 53 in a HIV infected population with abnormal cytology, its cervical carcinoma genesis potential as a stand-alone genotype and as well as its synergism with multiple infections should be investigated. The new WHO guideline in resource-poor settings to rescreen women for HPV within ten years may be more effective if BV and cervicitis management become a major component for HIV-HPV management

A study of the effects of electric field on two-dimensional inviscid nonlinear free surface flows generated by moving disturbances

Two-dimensional free surface flows generated by a moving disturbance are considered. The flows are assumed to be potential. The effects of electric field, gravity and surface tension are included in the dynamic boundary condition. The disturbance is chosen to be a distribution of pressure moving at a constant velocity. Both linear and nonlinear results are presented. For some values of the parameters, the linear theory predicts unbounded displacements of the free surface. It is shown that this nonuniformity is removed by developing a weakly nonlinear theory. There are then solutions which are perturbations of a uniform stream and others which are perturbations of solitary waves with decaying tails