A Fast and Accurate Universal Kepler Solver without Stumpff Series

We derive and present a fast and accurate solution of the initial value problem for Keplerian motion in universal variables that does not use the Stumpff series. We find that it performs better than methods based on the Stumpff series.Comment: 10 pages, 7 figures. Accepted by MNRAS, resubmitted because of a typo in the title, added author affiliation

Climate variability and maize yield in South Africa: Results from GME and MELE methods

"This paper investigates the impact of climate variability on maize yield in the Limpopo Basin of South Africa using the Generalized Maximum Entropy (GME) estimator and Maximum Entropy Leuven Estimator (MELE). Precipitation and temperature were used as proxies for climate variability, which were combined with traditional inputs variables (i.e., labor, fertilizer, seed, and irrigation). We found that the MELE fits the data better than the GME. In addition, increased precipitation, increased temperature, and irrigation have a positive impact on yield. Furthermore, results of the MELE show that the impact of precipitation on maize yield is stronger than that of temperature, meaning that the impact of climate variability on maize yield could be negative if the change increases temperature but reduces precipitation at the same rate and simultaneously. Moreover, the impact of irrigation on yield is positive but with a lower elasticity coefficient than that of precipitation, which supposes that irrigation may only partially mitigate the impact of reduced precipitation on yield. " from authors' abstractYield function, maize, Generalized maximum entropy, Maximum entropy Leuven estimator, Climate variability, Climate change,

Variational Integrators for the Gravitational N-Body Problem

This paper describes a fourth-order integration algorithm for the gravitational N-body problem based on discrete Lagrangian mechanics. When used with shared timesteps, the algorithm is momentum conserving and symplectic. We generalize the algorithm to handle individual time steps; this introduces fifth-order errors in angular momentum conservation and symplecticity. We show that using adaptive block power of two timesteps does not increase the error in symplecticity. In contrast to other high-order, symplectic, individual timestep, momentum-preserving algorithms, the algorithm takes only forward timesteps. We compare a code integrating an N-body system using the algorithm with a direct-summation force calculation to standard stellar cluster simulation codes. We find that our algorithm has about 1.5 orders of magnitude better symplecticity and momentum conservation errors than standard algorithms for equivalent numbers of force evaluations and equivalent energy conservation errors.Comment: 31 pages, 8 figures. v2: Revised individual-timestepping description, expanded comparison with other methods, corrected error in predictor equation. ApJ, in pres

On the Representations of a Number as the Sum of Four Fifth Powers

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135184/1/jlms0399.pd

Variational Integrators for Almost-Integrable Systems

We construct several variational integrators--integrators based on a discrete variational principle--for systems with Lagrangians of the form L = L_A + epsilon L_B, with epsilon << 1, where L_A describes an integrable system. These integrators exploit that epsilon << 1 to increase their accuracy by constructing discrete Lagrangians based on the assumption that the integrator trajectory is close to that of the integrable system. Several of the integrators we present are equivalent to well-known symplectic integrators for the equivalent perturbed Hamiltonian systems, but their construction and error analysis is significantly simpler in the variational framework. One novel method we present, involving a weighted time-averaging of the perturbing terms, removes all errors from the integration at O(epsilon). This last method is implicit, and involves evaluating a potentially expensive time-integral, but for some systems and some error tolerances it can significantly outperform traditional simulation methods.Comment: 14 pages, 4 figures. Version 2: added informative example; as accepted by Celestial Mechanics and Dynamical Astronom

Chaotic Lagrangian Trajectories around an Elliptical Vortex Patch Embedded in a Constant and Uniform Background Shear Flow

The Lagrangian flow around a Kida vortex [J. Phys. Soc. Jpn. 5 0, 3517 (1981)], an elliptical two‐dimensional vortex patch embedded in a uniform and constant background shear, is described by a nonintegrable two‐degree‐of‐freedom Hamiltonian. For small values of shear, there exist large chaotic zones surrounding the vortex, often much larger than the vortex itself and extremely close to its boundary. Motion within the vortex is integrable. Implications for two‐dimensional turbulence are discussed

A Review of Research on Cryptogams of Malawi for the Past 30 years (1987-2016): Progress, Challenges and Way Forward

Cryptogams are a unique group of plants whose ecological role in ecosystems is indisputable. Cryptogams are a key determinant of ecosystem biogeochemistry and known to support above ground biomass, control soil chemistry, provide habitats to nitrogen fixing bacteria and provide are food to other organisms. Compared with higher plants, cryptogams remain the least studied in Malawi and globally. This review aimed at assessing the scope and extent of research on Malawi‟s cryptogams, existing challenges and opportunities. A review of published literature between 1987 and 2016 was done using online search engines and library sources. This review showed that algae and bryophytes are comparatively well-studied groups represented by 70 percent (%) of all literature on cryptogams, particularly in Lake Malawi and Mulanje Mountain respectively. The ferns are the least studied, comprising just 15% of the reviewed literature. Further, no traceable study of lichens was encountered. Cryptogam research in Malawi is thus limited. This limitation could be due to lack of expertise in the field, limited laboratory infrastructure capacity and a general lack of appreciation for their importance. Considering the threat the different ecosystem in Malawi face, it is recommended that; local expertise, participation and infrastructure be improved so as to enhance cryptogam research in Malawi. Such an approach would ensure an increased local awareness of the value of cryptogams and foster informed conservation prioritization for cryptogams in Malawi. Keywords: Cryptograms, challenges, conservation, research gaps, Malaw

Chaotic Lagrangian Trajectories around an Elliptical Vortex Patch Embedded in a Constant and Uniform Background Shear Flow

The Lagrangian flow around a Kida vortex [J. Phys. Soc. Jpn. 5 0, 3517 (1981)], an elliptical two‐dimensional vortex patch embedded in a uniform and constant background shear, is described by a nonintegrable two‐degree‐of‐freedom Hamiltonian. For small values of shear, there exist large chaotic zones surrounding the vortex, often much larger than the vortex itself and extremely close to its boundary. Motion within the vortex is integrable. Implications for two‐dimensional turbulence are discussed

Effectiveness of a carbon tax to promote a climate-friendly food consumption

info:eu-repo/semantics/acceptedVersio

Pseudo-High-Order Symplectic Integrators

Symplectic N-body integrators are widely used to study problems in celestial mechanics. The most popular algorithms are of 2nd and 4th order, requiring 2 and 6 substeps per timestep, respectively. The number of substeps increases rapidly with order in timestep, rendering higher-order methods impractical. However, symplectic integrators are often applied to systems in which perturbations between bodies are a small factor of the force due to a dominant central mass. In this case, it is possible to create optimized symplectic algorithms that require fewer substeps per timestep. This is achieved by only considering error terms of order epsilon, and neglecting those of order epsilon^2, epsilon^3 etc. Here we devise symplectic algorithms with 4 and 6 substeps per step which effectively behave as 4th and 6th-order integrators when epsilon is small. These algorithms are more efficient than the usual 2nd and 4th-order methods when applied to planetary systems.Comment: 14 pages, 5 figures. Accepted for publication in the Astronomical Journa