Generalized helical vortex pairs

International audienceNew solutions describing the interaction of helical pairs of counter-rotating vortices are obtained using a vortex filament approach. The vortices are assumed to have a small core size allowing the calculation of the self-induced velocities from the Biot-Savart law using the cutoff theory. These new vortex structures do not possess any helical symmetry but they exhibit a spatial periodicity and are stationary in a rotating and translating frame. Their properties, such as radial deformation, frame velocity and induced flow, are provided as a function of the four geometric parameters characterizing each solution. Approximate solutions are also obtained when the mutual interaction is weak. This allows us to provide explicit expressions for the rotation and translation velocities of the structure in this limit. First-order corrections describing helix deformation are also calculated and used for comparison with the numerical results. The variation of the vortex core size induced by the helix deformation is also analysed. We show that these variations have a weak effect on the shape and characteristics of the solutions, for the range of parameters that we have considered. The results are finally applied to rotor wakes. It is explained how these solutions could possibly describe the far wake of an helicopter rotor in vertical flight

A strongly-coupled model for flexible rotors

International audienceA fluid-structure model describing the equilibrium state of a flexible blade rotor with its own wake is derived for various external axial flow conditions. The model is based on three building blocks. The two-dimensional lifting-line theory is first used to compute the local aerodynamic loads and the blade circulation profile. The blade deformation is then obtained by solving the nonlinear equations for bending and twisting angles deduced from a one-dimensional beam model. Finally, the wake is obtained using a Joukowski model. In this wake model, the wake of each blade is modeled by two small-core-size counter-rotating vortices emitted from the rotor axis and blade tip. The velocity field induced by these vortices is computed using the Biot-Savart law. We show that, in the rotor frame, we can obtain a stationary vortex structure for almost any vertical flight regimes. This wake solution can then be used to compute the induced velocity in the rotor plane and apply the two-dimensional lifting-line theory again. By iterating a few times this loop, we converge toward a nonlinear solution of the problem for which the aerodynamics loads, blade deformation and wake structure are compatible. As illustration, this newly-developed model is applied to two rotors. We analyze the effects of the external wind conditions, geometry and material properties of the blades on the blade deformation and wake characteristics. We show that we can describe slow descending regimes for which the classical momentum theory does not apply

A coupled model for flexible rotors

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Catena-(bis((1,10-Phenanthroline-N,N')-copper(II)) hydroxy-bis( phosphato)-tris(dioxo-vanadium(v))): a polymorphic phase driven by disorder.

International audienceIn the present paper a copper(II) phosphovanadate is presented and formulated as [Cu6(phen)6(VVO2)6(PO4)6(VVO2HO)3] (1a). This compound was obtained by hydrothermal synthesis and crystallizes in the triclinic group P-1, with a = 10.6290(5), b = 17.4275(8), c = 23.6151(11) Å; α = 92.888(4)°, β = 98.910(4)° and γ = 91.995(4)°. The leitmotif in (1a) is almost identical to some previously reported ones, viz. [Cu(phen)(VVO2)(PO4)]2[VVO2(OH)] (2); [Cu(phen)(VVO2)(PO4)]2[VIVO2(H2O)] (3) except for the fact that the small cells found in (2)-(3) are tripled in (1a). The reasons driving to these differences are subtle, and reside in the way in which the disorder in some vanadate groups takes place, viz., completely at random in (2)-(3) thus leading to a small "average" cell, while keeping some systematics in (1a) thus needing for a larger motif to take account of its repetition scheme in the crystal. The magnetic unit in the structure of (1a) is defined by a dinuclear system of CuII bonded by a μ2,η1-PO4 bridge. A fit of the corresponding magnetic data of (1a) was done, using the van Vleck equation for two S = ½ centres View the MathML source. The parameters obtained by the fit of the experimental data were g = 2.1 and J = −3.5 cm−1

A New Web-stepwise Solver for Ordinary Differential Equations

In this paper we introduce SODES (Step-wise Ordinary Differential Equations Solver) which is a new solver for Ordinary Dfferential Equations (ODE). SODES can be used not only as a solver but also as a tutorial for the teaching and learning process of ODE, since it provides the solution displaying all the the steps needed to obtain it. In [1] we introduced SFOPDES (Step-wise First Order Partial Differential Equations Solver) developed in Derive, a Computer Algebra System (CAS). Two of the future works related considered in [1] were the development of new step-wise solvers for different math topics and the use of other CAS and programming with Python. This way, it is possible to develop web applications, freely available, providing different step-wise solvers. In this sense, SODES is the first work related with both ideas. Therefore, SODES is a web solver for ODE, developed in Python (using its CAS module SymPy). SODES increases the types of ODE that SFOPDES can deal with. Specifically, it provides, step by step, the solution of the following types of ODE: 1. First-order ODE: separable equations and equations reducible to them, homogeneous equations and equations reducible to them, exact differential equations and equations reducible to them (integrating factor technique), linear equations, the Bernoulli equation, the Riccati equation, First-order differential equations and nth degree in y', Generic programs to solve first order differential equations. 2. Higher-order ODE: higher order linear equations with constant coefficients. As a final remark, actually, SODES can be used in English, French or Spanish, but it can be easily extendable to other languages.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

SODES: Solving ordinary differential equations step by step

In this paper, we introduce SODES (Stepwise Ordinary Differential Equations Solver) a new solver for Ordinary Differential Equations (ODE). SODES can optionally provide the solution displaying all the steps needed to obtain it. This way, SODES is an important tool not only for researchers who need solving ODE but also constitutes an important tool for the teaching and learning process of ODE. SODES has been developed using programming with a Computer Algebra System (CAS). Specifically, we use the CAS Derive but it can be easily adapted to any other CAS supporting programming. SODES provides, step by step, the solution of the following types of ODE: separable, homogeneous, exact, integrating factors, linear, Bernoulli, Riccati, first order ODE of nth degree, Cauchy’s problems of first order ODE, higher order linear homogeneous equations with constant coefficients, Lagrange’s method for particular solutions of higher order linear equations with constant coefficients, higher order linear equations with constant coefficients and Cauchy’s problems of higher order linear equations with constant coefficients. SODES also deals with two generic programs which determine the type or types of a given ODE and provides the solution. In this paper we will also introduce a draft of a Graphical User Interface (GUI) for SODES in a local web application using programming in Python (using its CAS module SymPy) which is a more portable and free CAS. This draft can be used in English, French and Spanish, and can be easily extended to other languages. The code of SODES and the GUI are freely available so that it can be used by users who also will be able to adapt it to their needsFunding for open access charge: Universidad de Málaga / CBU

Quantum walks: a comprehensive review

Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a solid field of research of quantum computation full of exciting open problems for physicists, computer scientists, mathematicians and engineers. In this paper we review theoretical advances on the foundations of both discrete- and continuous-time quantum walks, together with the role that randomness plays in quantum walks, the connections between the mathematical models of coined discrete quantum walks and continuous quantum walks, the quantumness of quantum walks, a summary of papers published on discrete quantum walks and entanglement as well as a succinct review of experimental proposals and realizations of discrete-time quantum walks. Furthermore, we have reviewed several algorithms based on both discrete- and continuous-time quantum walks as well as a most important result: the computational universality of both continuous- and discrete- time quantum walks.Comment: Paper accepted for publication in Quantum Information Processing Journa

Quantifying active and passive reforestation in central Mexico from 1986-2012 : assessing the evidence of a forest transition

Unidad de excelencia María de Maeztu MdM-2015-0552Recent land cover analysis reveals significant forest recovery around the world, suggesting that some countries may be in a forest transition. However remotely sensed imagery does not reveal the driving causes of forest recovery, which may be due to active reforestation efforts or natural successional processes (passive reforestation). We aimed to distinguish these two processes in the priority temperate forests surrounding the Monarch Butterfly Biosphere Reserve (342 773 ha) in central Mexico. We combine an analysis of remotely sensed imagery with field interviews (n=43) to examine the mechanisms and drivers of observed forest recovery. Our analysis of the satellite imagery revealed a net increase of 3 798 ha of forest between 1986 and 2012, yet the rate of recovery is slowing. Our interview data revealed that the vast majority of the recovered forests are the result of natural regrowth (passive reforestation), and most of this regrowth is observed on degraded forests. We estimate that between 58 and 429 ha have been recovered from active reforestation efforts in the 1986-2012 period. We find that reduced logging and grazing pressures are important drivers of forest recovery, while agricultural abandonment may be less influential than often believed. Our results suggest that reforestation investments might be wisely spent supporting and maintaining the natural resilience of forests rather than on costly reforestation programs

The tropical Atlantic observing system

The tropical Atlantic is home to multiple coupled climate variations covering a wide range of timescales and impacting societally relevant phenomena such as continental rainfall, Atlantic hurricane activity, oceanic biological productivity, and atmospheric circulation in the equatorial Pacific. The tropical Atlantic also connects the southern and northern branches of the Atlantic meridional overturning circulation and receives freshwater input from some of the world’s largest rivers. To address these diverse, unique, and interconnected research challenges, a rich network of ocean observations has developed, building on the backbone of the Prediction and Research Moored Array in the Tropical Atlantic (PIRATA). This network has evolved naturally over time and out of necessity in order to address the most important outstanding scientific questions and to improve predictions of tropical Atlantic severe weather and global climate variability and change. The tropical Atlantic observing system is motivated by goals to understand and better predict phenomena such as tropical Atlantic interannual to decadal variability and climate change; multidecadal variability and its links to the meridional overturning circulation; air-sea fluxes of CO2 and their implications for the fate of anthropogenic CO2; the Amazon River plume and its interactions with biogeochemistry, vertical mixing, and hurricanes; the highly productive eastern boundary and equatorial upwelling systems; and oceanic oxygen minimum zones, their impacts on biogeochemical cycles and marine ecosystems, and their feedbacks to climate. Past success of the tropical Atlantic observing system is the result of an international commitment to sustained observations and scientific cooperation, a willingness to evolve with changing research and monitoring needs, and a desire to share data openly with the scientific community and operational centers. The observing system must continue to evolve in order to meet an expanding set of research priorities and operational challenges. This paper discusses the tropical Atlantic observing system, including emerging scientific questions that demand sustained ocean observations, the potential for further integration of the observing system, and the requirements for sustaining and enhancing the tropical Atlantic observing system