Multi loop soliton solutions and their interactions in the Degasperis-Procesi equation

In this article, we construct loop soliton solutions and mixed soliton - loop soliton solution for the Degasperis-Procesi equation. To explore these solutions we adopt the procedure given by Matsuno. By appropriately modifying the $\tau$-function given in the above paper we derive these solutions. We present the explicit form of one and two loop soliton solutions and mixed soliton - loop soliton solutions and investigate the interaction between (i) two loop soliton solutions in different parametric regimes and (ii) a loop soliton with a conventional soliton in detail.Comment: Published in Physica Scripta (2012

A class of Poisson-Nijenhuis structures on a tangent bundle

Equipping the tangent bundle TQ of a manifold with a symplectic form coming from a regular Lagrangian L, we explore how to obtain a Poisson-Nijenhuis structure from a given type (1,1) tensor field J on Q. It is argued that the complete lift of J is not the natural candidate for a Nijenhuis tensor on TQ, but plays a crucial role in the construction of a different tensor R, which appears to be the pullback under the Legendre transform of the lift of J to co-tangent manifold of Q. We show how this tangent bundle view brings new insights and is capable also of producing all important results which are known from previous studies on the cotangent bundle, in the case that Q is equipped with a Riemannian metric. The present approach further paves the way for future generalizations.Comment: 22 page

Biodiversity Loss and the Taxonomic Bottleneck: Emerging Biodiversity Science

Human domination of the Earth has resulted in dramatic changes to global and local patterns of biodiversity. Biodiversity is critical to human sustainability because it drives the ecosystem services that provide the core of our life-support system. As we, the human species, are the primary factor leading to the decline in biodiversity, we need detailed information about the biodiversity and species composition of specific locations in order to understand how different species contribute to ecosystem services and how humans can sustainably conserve and manage biodiversity. Taxonomy and ecology, two fundamental sciences that generate the knowledge about biodiversity, are associated with a number of limitations that prevent them from providing the information needed to fully understand the relevance of biodiversity in its entirety for human sustainability: (1) biodiversity conservation strategies that tend to be overly focused on research and policy on a global scale with little impact on local biodiversity; (2) the small knowledge base of extant global biodiversity; (3) a lack of much-needed site-specific data on the species composition of communities in human-dominated landscapes, which hinders ecosystem management and biodiversity conservation; (4) biodiversity studies with a lack of taxonomic precision; (5) a lack of taxonomic expertise and trained taxonomists; (6) a taxonomic bottleneck in biodiversity inventory and assessment; and (7) neglect of taxonomic resources and a lack of taxonomic service infrastructure for biodiversity science. These limitations are directly related to contemporary trends in research, conservation strategies, environmental stewardship, environmental education, sustainable development, and local site-specific conservation. Today’s biological knowledge is built on the known global biodiversity, which represents barely 20% of what is currently extant (commonly accepted estimate of 10 million species) on planet Earth. Much remains unexplored and unknown, particularly in hotspots regions of Africa, South Eastern Asia, and South and Central America, including many developing or underdeveloped countries, where localized biodiversity is scarcely studied or described. ‘‘Backyard biodiversity’’, defined as local biodiversity near human habitation, refers to the natural resources and capital for ecosystem services at the grassroots level, which urgently needs to be explored, documented, and conserved as it is the backbone of sustainable economic development in these countries. Beginning with early identification and documentation of local flora and fauna, taxonomy has documented global biodiversity and natural history based on the collection of ‘‘backyard biodiversity’’ specimens worldwide. However, this branch of science suffered a continuous decline in the latter half of the twentieth century, and has now reached a point of potential demise. At present there are very few professional taxonomists and trained local parataxonomists worldwide, while the need for, and demands on, taxonomic services by conservation and resource management communities are rapidly increasing. Systematic collections, the material basis of biodiversity information, have been neglected and abandoned, particularly at institutions of higher learning. Considering the rapid increase in the human population and urbanization, human sustainability requires new conceptual and practical approaches to refocusing and energizing the study of the biodiversity that is the core of natural resources for sustainable development and biotic capital for sustaining our life-support system. In this paper we aim to document and extrapolate the essence of biodiversity, discuss the state and nature of taxonomic demise, the trends of recent biodiversity studies, and suggest reasonable approaches to a biodiversity science to facilitate the expansion of global biodiversity knowledge and to create useful data on backyard biodiversity worldwide towards human sustainability

Projective dynamics and classical gravitation

Given a real vector space V of finite dimension, together with a particular homogeneous field of bivectors that we call a "field of projective forces", we define a law of dynamics such that the position of the particle is a "ray" i.e. a half-line drawn from the origin of V. The impulsion is a bivector whose support is a 2-plane containing the ray. Throwing the particle with a given initial impulsion defines a projective trajectory. It is a curve in the space of rays S(V), together with an impulsion attached to each ray. In the simplest example where the force is identically zero, the curve is a straight line and the impulsion a constant bivector. A striking feature of projective dynamics appears: the trajectories are not parameterized. Among the projective force fields corresponding to a central force, the one defining the Kepler problem is simpler than those corresponding to other homogeneities. Here the thrown ray describes a quadratic cone whose section by a hyperplane corresponds to a Keplerian conic. An original point of view on the hidden symmetries of the Kepler problem emerges, and clarifies some remarks due to Halphen and Appell. We also get the unexpected conclusion that there exists a notion of divergence-free field of projective forces if and only if dim V=4. No metric is involved in the axioms of projective dynamics.Comment: 20 pages, 4 figure

Tunneling Theory for Tunable Open Quantum Systems of Ultracold Atoms in One-Dimensional Traps

The creation of tunable open quantum systems is becoming feasible in current experiments with ultracold atoms in low-dimensional traps. In particular, the high degree of experimental control over these systems allows detailed studies of tunneling dynamics, e.g., as a function of the trapping geometry and the interparticle interaction strength. In order to address this exciting opportunity we present a theoretical framework for two-body tunneling based on the rigged Hilbert space formulation. In this approach, bound, resonant and scattering states are included on an equal footing, and we argue that the coupling of all these components is vital for a correct description of the relevant threshold phenomena. In particular, we study the tunneling mechanism for two-body systems in one-dimensional traps and different interaction regimes. We find a strong dominance of sequential tunneling of single particles for repulsive and weakly attractive systems, while there is a signature of correlated pair tunneling in the calculated many-particle flux for strongly attractive interparticle interaction.Comment: To be published in Phys. Rev. A (Rapid Communication

Quantitative cross-species extrapolation between humans and fish: The case of the anti-depressant fluoxetine

This article has been made available through the Brunel Open Access Publishing Fund.Fish are an important model for the pharmacological and toxicological characterization of human pharmaceuticals in drug discovery, drug safety assessment and environmental toxicology. However, do fish respond to pharmaceuticals as humans do? To address this question, we provide a novel quantitative cross-species extrapolation approach (qCSE) based on the hypothesis that similar plasma concentrations of pharmaceuticals cause comparable target-mediated effects in both humans and fish at similar level of biological organization (Read-Across Hypothesis). To validate this hypothesis, the behavioural effects of the anti-depressant drug fluoxetine on the fish model fathead minnow (Pimephales promelas) were used as test case. Fish were exposed for 28 days to a range of measured water concentrations of fluoxetine (0.1, 1.0, 8.0, 16, 32, 64 μg/L) to produce plasma concentrations below, equal and above the range of Human Therapeutic Plasma Concentrations (HTPCs). Fluoxetine and its metabolite, norfluoxetine, were quantified in the plasma of individual fish and linked to behavioural anxiety-related endpoints. The minimum drug plasma concentrations that elicited anxiolytic responses in fish were above the upper value of the HTPC range, whereas no effects were observed at plasma concentrations below the HTPCs. In vivo metabolism of fluoxetine in humans and fish was similar, and displayed bi-phasic concentration-dependent kinetics driven by the auto-inhibitory dynamics and saturation of the enzymes that convert fluoxetine into norfluoxetine. The sensitivity of fish to fluoxetine was not so dissimilar from that of patients affected by general anxiety disorders. These results represent the first direct evidence of measured internal dose response effect of a pharmaceutical in fish, hence validating the Read-Across hypothesis applied to fluoxetine. Overall, this study demonstrates that the qCSE approach, anchored to internal drug concentrations, is a powerful tool to guide the assessment of the sensitivity of fish to pharmaceuticals, and strengthens the translational power of the cross-species extrapolation

Involving Citizen Scientists in Biodiversity Observation

The involvement of non-professionals in scientific research and environmental monitoring, termed Citizen Science (CS), has now become a mainstream approach for collecting data on earth processes, ecosystems and biodiversity. This chapter examines how CS might contribute to ongoing efforts in biodiversity monitoring, enhancing observation and recording of key species and systems in a standardised manner, thereby supporting data relevant to the Essential Biodiversity Variables (EBVs), as well as reaching key constituencies who would benefit Biodiversity Observation Networks (BONs). The design of successful monitoring or observation networks that rely on citizen observers requires a careful balancing of the two primary user groups, namely data users and data contributors (i.e., citizen scientists). To this end, this chapter identifies examples of successful CS programs as well as considering practical issues such as the reliability of the data, participant recruitment and motivation, and the use of emerging technologies

A review of elliptical and disc galaxy structure, and modern scaling laws

A century ago, in 1911 and 1913, Plummer and then Reynolds introduced their models to describe the radial distribution of stars in `nebulae'. This article reviews the progress since then, providing both an historical perspective and a contemporary review of the stellar structure of bulges, discs and elliptical galaxies. The quantification of galaxy nuclei, such as central mass deficits and excess nuclear light, plus the structure of dark matter halos and cD galaxy envelopes, are discussed. Issues pertaining to spiral galaxies including dust, bulge-to-disc ratios, bulgeless galaxies, bars and the identification of pseudobulges are also reviewed. An array of modern scaling relations involving sizes, luminosities, surface brightnesses and stellar concentrations are presented, many of which are shown to be curved. These 'redshift zero' relations not only quantify the behavior and nature of galaxies in the Universe today, but are the modern benchmark for evolutionary studies of galaxies, whether based on observations, N-body-simulations or semi-analytical modelling. For example, it is shown that some of the recently discovered compact elliptical galaxies at 1.5 < z < 2.5 may be the bulges of modern disc galaxies.Comment: Condensed version (due to Contract) of an invited review article to appear in "Planets, Stars and Stellar Systems"(www.springer.com/astronomy/book/978-90-481-8818-5). 500+ references incl. many somewhat forgotten, pioneer papers. Original submission to Springer: 07-June-201

‘Medusa head ataxia’: the expanding spectrum of Purkinje cell antibodies in autoimmune cerebellar ataxia. Part 3: Anti-Yo/CDR2, anti-Nb/AP3B2, PCA-2, anti-Tr/DNER, other antibodies, diagnostic pitfalls, summary and outlook

Serological testing for anti-neural autoantibodies is important in patients presenting with idiopathic cerebellar ataxia, since these autoantibodies may indicate cancer, determine treatment and predict prognosis. While some of them target nuclear antigens present in all or most CNS neurons (e.g. anti-Hu, anti-Ri), others more specifically target antigens present in the cytoplasm or plasma membrane of Purkinje cells (PC). In this series of articles, we provide a detailed review of the clinical and paraclinical features, oncological, therapeutic and prognostic implications, pathogenetic relevance, and differential laboratory diagnosis of the 12 most common PC autoantibodies (often referred to as ‘Medusa head antibodies’ due to their characteristic somatodendritic binding pattern when tested by immunohistochemistry). To assist immunologists and neurologists in diagnosing these disorders, typical high-resolution immunohistochemical images of all 12 reactivities are presented, diagnostic pitfalls discussed and all currently available assays reviewed. Of note, most of these antibodies target antigens involved in the mGluR1/calcium pathway essential for PC function and survival. Many of the antigens also play a role in spinocerebellar ataxia. Part 1 focuses on anti-metabotropic glutamate receptor 1-, anti-Homer protein homolog 3-, anti-Sj/inositol 1,4,5-trisphosphate receptor- and anti-carbonic anhydrase-related protein VIII-associated autoimmune cerebellar ataxia (ACA); part 2 covers anti-protein kinase C gamma-, anti-glutamate receptor delta-2-, anti-Ca/RhoGTPase-activating protein 26- and anti-voltage-gated calcium channel-associated ACA; and part 3 reviews the current knowledge on anti-Tr/delta notch-like epidermal growth factor-related receptor-, anti-Nb/AP3B2-, anti-Yo/cerebellar degeneration-related protein 2- and Purkinje cell antibody 2-associated ACA, discusses differential diagnostic aspects and provides a summary and outlook

Thermal capability of electric vehicle PMSM with different slot areas via thermal network analysis

In this paper, the effect that a varied stator slot size has on the efficiency and thermal capability of a permanent magnet synchronous machine for an electric vehicle, is evaluated and quantified. A machine with four differently sized slot areas was electromagnetically evaluated with finite element analysis, and thermally with a lumped parameter network model. By decreasing the slot size while keeping other dimensions fixed, the core losses reduce due to the wider magnetic path, whereas the winding losses increase. Additionally, a higher maximum torque is reached due to reduced saturation. Results are compared in the machine\u27s torque-speed operating area regarding machine-part and total losses, continuous torque and transient overload capability, as well as during 19 low, middle and high-speed drive cycles regarding energy losses and peak winding temperature. The largest slot showed the lowest winding losses and thus the highest thermally limited torque capability. In contrast, the energy losses with the largest slot were the highest in 13 of the drive cycles, and the lowest in 11 of them with the smallest slot due to its lower part load (i.e. core) losses. The smallest slot would also result in the lowest material cost since it has the least copper