Symmetries of a class of nonlinear fourth order partial differential equations

In this paper we study symmetry reductions of a class of nonlinear fourth order partial differential equations \be u_{tt} = \left(\kappa u + \gamma u^2\right)_{xx} + u u_{xxxx} +\mu u_{xxtt}+\alpha u_x u_{xxx} + \beta u_{xx}^2, \ee where $\alpha$, $\beta$, $\gamma$, $\kappa$ and $\mu$ are constants. This equation may be thought of as a fourth order analogue of a generalization of the Camassa-Holm equation, about which there has been considerable recent interest. Further equation (1) is a ``Boussinesq-type'' equation which arises as a model of vibrations of an anharmonic mass-spring chain and admits both ``compacton'' and conventional solitons. A catalogue of symmetry reductions for equation (1) is obtained using the classical Lie method and the nonclassical method due to Bluman and Cole. In particular we obtain several reductions using the nonclassical method which are no} obtainable through the classical method

Mitochondrial variation in Anopheles gambiae and Anopheles coluzzii: phylogeographic legacy and mitonuclear associations with metabolic resistance to pathogens and insecticides

Mitochondrial DNA has been a popular marker in phylogeography, phylogeny, and molecular ecology, but its complex evolution is increasingly recognized. Here, we investigated mitochondrial DNA variation in Anopheles gambiae and Anopheles coluzzii, in relation to other species in the Anopheles gambiae complex, by assembling the mitogenomes of 1,219 mosquitoes across Africa. The mitochondrial DNA phylogeny of the Anopheles gambiae complex was consistent with previously reported highly reticulated evolutionary history, revealing important discordances with the species tree. The three most widespread species (An. gambiae, An. coluzzii, and Anopheles arabiensis), known for extensive historical introgression, could not be discriminated based on mitogenomes. Furthermore, a monophyletic clustering of the three saltwater-tolerant species (Anopheles merus, Anopheles melas, and Anopheles bwambae) in the Anopheles gambiae complex also suggested that introgression and possibly selection shaped mitochondrial DNA evolution. Mitochondrial DNA variation in An. gambiae and An. coluzzii across Africa revealed significant partitioning among populations and species. A peculiar mitochondrial DNA lineage found predominantly in An. coluzzii and in the hybrid taxon of the African “far-west” exhibited divergence comparable to the interspecies divergence in the Anopheles gambiae complex, with a geographic distribution matching closely An. coluzzii's geographic range. This phylogeographic relict of the An. coluzzii and An. gambiae split was associated with population and species structure, but not with the rare Wolbachia occurrence. The lineage was significantly associated with single nucleotide polymorphisms in the nuclear genome, particularly in genes associated with pathogen and insecticide resistance. These findings underline potential mitonuclear coevolution history and the role played by mitochondria in shaping metabolic responses to pathogens and insecticides in Anopheles

Analytic and Asymptotic Methods for Nonlinear Singularity Analysis: a Review and Extensions of Tests for the Painlev\'e Property

The integrability (solvability via an associated single-valued linear problem) of a differential equation is closely related to the singularity structure of its solutions. In particular, there is strong evidence that all integrable equations have the Painlev\'e property, that is, all solutions are single-valued around all movable singularities. In this expository article, we review methods for analysing such singularity structure. In particular, we describe well known techniques of nonlinear regular-singular-type analysis, i.e. the Painlev\'e tests for ordinary and partial differential equations. Then we discuss methods of obtaining sufficiency conditions for the Painlev\'e property. Recently, extensions of \textit{irregular} singularity analysis to nonlinear equations have been achieved. Also, new asymptotic limits of differential equations preserving the Painlev\'e property have been found. We discuss these also.Comment: 40 pages in LaTeX2e. To appear in the Proceedings of the CIMPA Summer School on "Nonlinear Systems," Pondicherry, India, January 1996, (eds) B. Grammaticos and K. Tamizhman

Dietary carotenoid-rich oil supplementation improves exercise-induced anisocytosis in runners: influences of haptoglobin, MnSOD (Val9Ala), CAT (21A/T) and GPX1 (Pro198Leu) gene polymorphisms in dilutional pseudoanemia (sports anemia)

Physical training induces beneficial adaptation, whereas exhaustive exercises increase reactive oxygen-species generation, thereby causing oxidative damage in plasma and erythrocytes, fractions susceptible to lipid peroxidation. Pequi (Caryocar brasiliense Camb.) is a Brazilian Cerrado fruit containing a carotenoid-rich oil. The aim was to investigate the effects of pequi-oil on exercise-induced oxidative damage in plasma and erythrocytes, after running in the same environment and undergoing weekly training under the same conditions as to type, intensity and length. Evaluations were accomplished after outdoor running on flat land before and after ingestion of 400 mg pequi-oil capsules for 14 days. Blood samples were taken after running and submitted to TBARS assay and erythrogram analysis. Haptoglobin, MnSOD (Val9Ala), CAT (21A/T) and GPX1 (Pro198Leu) gene polymorphisms were priorly investigated, so as to estimate genetic influence The reduction in erythrocytes, hemoglobin and hematocrit after pequi-oil treatment was notably associated with higher plasma expansion. Except for MCHC (mean corpuscular hemoglobin concentration) and RDW (red cell distribution width), the results were influenced by the polymorphisms studied. The best response to pequi-oil was presented by MnSOD Val/Val, CAT AA or AT genotypes and the GPX1 Pro allele. The significantly lower RDW and higher MHCH values were related to pequi-oil protective effects. Pequi oil, besides possessing other nutritional properties, showed protective blood effects

Optical coherence tomography in the 2µm wavelength regime for paint and other high opacity materials

An optical coherence tomography system using a compact fiber source emitting amplified spontaneous emission at central wavelength of 1960nm with bandwidth of 40nm is developed to enhance the probing depth in a highly scattering material with low water content. Examples of application to paint are used to demonstrate significantly improved penetration depth in high opacity materials in the 2µm wavelength regime

Estimation of fracture height growth in layered tight/shale gas reservoirs using flowback gas rates and compositions–Part II: Field application in a liquid-rich tight reservoir

While hydraulic fracturing is the key to unlocking the potential of unconventional low-permeability hydrocarbon resources, challenges remain in the monitoring of subsurface propagation of fractures and the determination of which geologic intervals have been contacted. This is particularly challenging for wells that are completed in multiple hydraulic fracture stages (multi-fractured horizontal wells or MFHWs) where fracture spacing may be very close and fracture geometry complex. Understanding the fracture extent is important not only for assisting with hydraulic fracture design, but also for mitigating unwanted fracture growth into non-target geologic intervals that do not contain hydrocarbons (e.g. zones with high water saturation). Popular current technologies used for hydraulic fracture surveillance include microseismic (surface and subsurface monitoring) and tiltmeter surveys. While these methods have proven useful for characterizing the extent of created hydraulic fractures, they do not necessarily lead to an understanding of what portions of the geologic section (bounding and target intervals for MFHWs, for example) are in direct hydraulic communication with the well. A solution for establishing the extent of hydraulic fracture growth from target to bounding zones is to first obtain a fluid composition fingerprint of those intervals while drilling through them, and then compare these data with fluid compositions obtained from flowback after hydraulic fracturing. In the current work, a MFHW completed in a liquid-rich tight reservoir is used to test this novel concept. Gas samples extracted from the headspace of isojars® containing cuttings samples, obtained during drilling of the MFHW well, were used to geochemically fingerprint geologic intervals through which the well was drilled. The cuttings samples were collected at high frequency in the vertical, bend and lateral sections of the well over a measured depth range of 4725 ft (1440 m). A compositional marker was identified in the bend of the horizontal well above which the average methane to ethane (C1/C2) ratio was 15.7, versus 2.6 below it. The flowback gas compositions were observed to be intermediate (average C1/C2 = 7.4) between the reservoir above and below the marker, suggesting fracture height grew above the compositional marker. In order to estimate fracture height growth from the geologic interval and flowback compositions, a compositional numerical simulation study was performed. An innovative approach was used to estimate recombined in-situ fluid compositions, on a layer-by-layer basis, by combining the cuttings gas compositional data with separator oil compositions. The resulting numerical simulation model, initialized through use of the layered fluid model and a detailed geological model developed for the subject well and offset drilling locations, was used to history match flowback rates, pressures and gas compositions. The gas compositions of the fingerprinted geologic intervals were therefore employed as a constraint on fracture height growth, estimated in the model to be 175 ft (53 m, propped height). However, because of the uncertainty in model input parameters, a stochastic approach was required to derive a range in hydraulic fracture properties. The current study demonstrates for the first time that it is possible to constrain fracture height growth estimates from flowback data, combined with gas compositional data obtained from cuttings data, provided that the geochemical fingerprints are distinct