A novel approach to rigid spheroid models in viscous flows using operator splitting methods

Calculating cost-effective solutions to particle dynamics in viscous flows is an important problem in many areas of industry and nature. We implement a second-order symmetric splitting method on the governing equations for a rigid spheroidal particle model with torques, drag and gravity. The method splits the operators into a vector field that is conservative and one that takes into account the forces of the fluid. Error analysis and numerical tests are performed on perturbed and stiff particle-fluid systems. For the perturbed case, the splitting method greatly improves the solution accuracy, when compared to a conventional multi-step method, and the global error behaves as $\mathcal{O}(\varepsilon h^2)$ for roughly equal computational cost. For stiff systems, we show that the splitting method retains stability in regimes where conventional methods blow up. In addition, we show through numerical experiments that the global order is reduced from $\mathcal{O}(h^2/\varepsilon)$ in the non-stiff regime to $\mathcal{O}(h)$ in the stiff regime.Comment: 24 pages, 6 figures (13 if you count sub figs), all figures are in colou

Detecting and determining preserved measures and integrals of rational maps

In this paper we use the method of discrete Darboux polynomials to calculate preserved measures and integrals of rational maps. The approach is based on the use of cofactors and Darboux polynomials and relies on the use of symbolic algebra tools. Given sufficient computing power, most, if not all, rational preserved integrals can be found (and even some non-rational ones). We show, in a number of examples, how it is possible to use this method to both determine and detect preserved measures and integrals of the considered rational maps. Many of the examples arise from the Kahan-Hirota-Kimura discretization of completely integrable systems of ordinary differential equations

Adopting a Holistic Approach to Amphibian Conservation

Amphibians are significant components of healthy ecosystems and provide important ecosystem services. Amphibians are disproportionately threatened by a variety of anthropogenic threats and their current rates of extinction may be hundreds of times greater than background extinction rates. Whilst amphibians are overall highly threatened, there is an ongoing need to identify the most at-risk species and prioritise species for subsequent conservation. However, many amphibian species are poorly known, and new species are discovered on a weekly basis. Our lack of knowledge of amphibians may undermine our ability to use limited conservation resources to conserve the most imperilled species or assemblages. Conservation practitioners must decide when they know enough about a species or a threat to have some degree of certainty that conservation interventions will be effective against the backdrop of ongoing species decline and a need for imminent action. We show that we currently lack a robust understanding of the extinction risk in assessed amphibians, largely due to high rates of species discovery and financial constraints of undertaking extinction risk assessments. We demonstrate how integrative taxonomy, and the use of both traditional and non-traditional monitoring techniques may identify and robustly delimit cryptic species and aid timely extinction risk assessments by providing important data on their range, extent of available habitat and threats posted to amphibians. These data are often sufficient to inform conservation prioritisation schemes and identify candidate species for resource intensive conservation action such as ex situ conservation breeding programmes. However, some ex situ programmes have been established with insufficient data on species biology and natural history. Conversely, research on captive amphibian populations may elucidate aspects of species biology that were previously unknown and potentially difficult, time-consuming and costly to acquire. The knowledge gained through ex situ research may inform conservation management decisions in nature and represents an important contribution in efforts to combat global amphibian declines. Amphibians are an extremely diverse group of animals and even congeneric species may have dramatically different natural histories, differing susceptibilities to threats and differences with regard to the effectiveness of different conservation actions or interventions. Generalised Class-focused approaches to conserve amphibians that do not consider species-specific factors risk missing the subtle, yet potentially critical nuances that may be pivotal in the success of conservation programmes. Whilst there are knowledge gaps that currently impede conservation these could be overcome with the adoption of new methods, refined processes and by everyone working on amphibians taking a collective responsibility to conserve them

A field method for sampling blood of male anurans with hypertrophied limbs

A field method for sampling blood of male anurans with hypertrophied limbs is presented here

Distribution and habitat associations of the Critically Endangered frog Walkerana phrynoderma (Anura: Ranixalidae), with an assessment of potential threats, abundance, and morphology

Distribuição e associações de habitat do anuro Criticamente Ameaçado Walkerana phrynoderma (Anura: Ranixalidae), com uma avaliação das ameaças potenciais, abundância e morfologia. Pouco se sabe sobre Walkerana phrynoderma, um anuro endêmico dos Montes Anamalai dos Ghats Ocidentais da Índia. Com o objetivo de aumentar nosso conhecimento do status da espécie na natureza, fornecemos informações básicas (i.e., distribuição, ameaças, características do habitat, padrões de atividade e abundância relativa). Foram feitas investigações por encontro visual, transectos e orçamento temporal no interior e entorno dos Montes Anamalai dos Ghats Ocidentais. A secreção da pele dos animais foi amostrada para determinar a presença/ausência de Batrachochytrium dendrobatidis, e foram registradas as características do habitat e do ambiente nos locais onde W. phrynoderma foi encontrada. Esses dados foram comparados com os dos locais em que a espécie estava aparentemente ausente. Walkerana phrynoderma está restrita às forestas perenifolias situadas entre 1300 e 1700 m a.s.l. na Reserva Anamalai Tiger e em Munnar; dessa forma, sua distribuição foi extendida do estado de Tamil Nadu para o estado vizinho de Kerala. As ameaças mais severas a essa espécia são o uso de pesticidas e perturbações antrópicas; B. dendrobatidis não foi detectado. Esse anuro norturno prefere bordas forestais e está associado com chãos de forestas bem sombreadas em áreas frescas próximo a riachos. Walkerana phrynoderma é raramente encontrada, enquanto sua congênere, W. leptodactyla, é mais comum. O impacto de perturbações antropogênicas, especialmente deposição de lixo e desenvolvimento de infraestrutura turística, deveria ser avaliado. A área de propriedade do Departamento de Florestas na periferia das áreas protegidas poderia ser designada como locais ecossensíveis para prevenir mudanças no uso da terra que pudessem ter um efeito adverso sobre W. phrynoderma.Distribution and habitat associations of the Critically Endangered frog Walkerana phrynoderma (Anura: Ranixalidae), with an assessment of potential threats, abundance, and morphology. Little is known about Walkerana phrynoderma, a frog endemic to the Anamalai Hills of the Western Ghats of India. Baseline information (i.e., distribution, threats, habitat characteristics, activity patterns, and relative abundance) is provided for this species, with the aim of improving our understanding of the status of the species in the wild. Visual-encounter, transect, and time-activity budget surveys were conducted in and around the Anamalai Hills of the Western Ghats. The frog skin was swabbed to determine the presence/absence of Batrachochytrium dendrobatidis, and habitat and environmental characteristics were recorded at sites where W. phrynoderma was found. These data were compared with those of sites apparently lacking this species that had suitable habitat. Walkerana phrynoderma is restricted to evergreen forests between 1300 and 1700 m a.s.l. in the Anamalai Tiger Reserve and at Munnar; thus, its range was extended from the state of Tamil Nadu to the adjoining state of Kerala. Pesticide runoff and human disturbance are the most severe threats to the species; B. dendrobatidis was not detected. This nocturnal anuran prefers forest edges and is associated with well-shaded forest foors in cool areas near freshwater streams. Walkerana phrynoderma is rarely encountered whereas its congener, W. leptodactyla, is more common. The impact of anthropogenic disturbances, especially waste disposal and development of tourism infrastructure, should be evaluated. The land that is owned by the Forest Department peripheral to the protected areas could be designated as eco-sensitive sites to prevent changes in land use that could have an adverse effect on W. phrynoderma

An integral model based on slender body theory, with applications to curved rigid fibers

We propose a novel integral model describing the motion of curved slender fibers in viscous flow, and develop a numerical method for simulating dynamics of rigid fibers. The model is derived from nonlocal slender body theory (SBT), which approximates flow near the fiber using singular solutions of the Stokes equations integrated along the fiber centerline. In contrast to other models based on (singular) SBT, our model yields a smooth integral kernel which incorporates the (possibly varying) fiber radius naturally. The integral operator is provably negative definite in a non-physical idealized geometry, as expected from PDE theory. This is numerically verified in physically relevant geometries. We propose a convergent numerical method for solving the integral equation and discuss its convergence and stability. The accuracy of the model and method is verified against known models for ellipsoids. Finally, a fast algorithm for computing dynamics of rigid fibers with complex geometries is developed

Linear Darboux polynomials for Lotka-Volterra systems, trees and superintegrable families

We present a method to construct superintegrable $n$-component Lotka-Volterra systems with $3n-2$ parameters. We apply the method to Lotka-Volterra systems with $n$ components for $1 < n < 6$, and present several $n$-dimensional superintegrable families. The Lotka-Volterra systems are in one-to-one correspondence with trees on $n$ vertices.Comment: 14 pages, 4 figure