Water Quality, nutrients and the European Union’s Water Framework Directive in a lowland agricultural region: Suffolk, south-east England.

The water quality of 13 rivers in the lowland, agricultural county of Suffolk is investigated using routine monitoring data for the period 1981 to 2006 collected by the Environment Agency of England and Wales (EA), and its predecessors, with particular emphasis on phosphorus (as total reactive phosphorus, TRP) and total (dissolved and particulate) oxidised nitrogen (TOxN – predominantly nitrate NO3). Major ion and flow data are used to outline fundamental hydrochemical characteristics related to the groundwater provenance of base-flow waters. Relative load contributions from point and diffuse sources are approximated using Load Apportionment Modelling for both TRP and TOxN where concurrent flow and concentration data are available. Analyses indicate a mixture of point and diffuse sources of TRP, with the former being dominant during low flow periods, while for TOxN diffuse sources dominate. Out of 59 sites considered, 53 (90%) were found to have annual average TRP concentrations greater than 0.05 mg P l-1, and 36 (61%) had average concentrations over 0.120 mg P l-1, the upper thresholds for ‘High’ and ‘Good’ ecological status, respectively. Correspondingly, for TOxN, most of the rivers are already within 70% of the 11.3 mg N l-1 threshold, with two rivers (Wang and Ore) being consistently greater than this. It is suggested that the major challenge is to characterise and control point-source TRP inputs which, being predominant during the late spring and summer low-flow period, coincide with the peak of primary biological production, thus presenting the major challenge to achieving ‘good’ ecological status under the Water Framework Directive. Results show that considerable effort is still required to ensure appropriate management and develop tools for decision-support

Corrfunc: Blazing fast correlation functions with AVX512F SIMD Intrinsics

Correlation functions are widely used in extra-galactic astrophysics to extract insights into how galaxies occupy dark matter halos and in cosmology to place stringent constraints on cosmological parameters. A correlation function fundamentally requires computing pair-wise separations between two sets of points and then computing a histogram of the separations. Corrfunc is an existing open-source, high-performance software package for efficiently computing a multitude of correlation functions. In this paper, we will discuss the SIMD AVX512F kernels within Corrfunc, capable of processing 16 floats or 8 doubles at a time. The latest manually implemented Corrfunc AVX512F kernels show a speedup of up to $\sim 4\times$ relative to compiler-generated code for double-precision calculations. The AVX512F kernels show $\sim 1.6\times$ speedup relative to the AVX kernels and compare favorably to a theoretical maximum of $2\times$. In addition, by pruning pairs with too large of a minimum possible separation, we achieve a $\sim 5-10\%$ speedup across all the SIMD kernels. Such speedups highlight the importance of programming explicitly with SIMD vector intrinsics for complex calculations that can not be efficiently vectorized by compilers. Corrfunc is publicly available at https://github.com/manodeep/Corrfunc/.Comment: Paper II for the Corrfunc software package, paper I is on arXiv here: arXiv:1911.03545. Appeared in the refereed proceedings for the "Second Workshop on Software Challenges to Exascale Computing

A Direct Elliptic Solver Based on Hierarchically Low-rank Schur Complements

A parallel fast direct solver for rank-compressible block tridiagonal linear systems is presented. Algorithmic synergies between Cyclic Reduction and Hierarchical matrix arithmetic operations result in a solver with $O(N \log^2 N)$ arithmetic complexity and $O(N \log N)$ memory footprint. We provide a baseline for performance and applicability by comparing with well known implementations of the $\mathcal{H}$-LU factorization and algebraic multigrid with a parallel implementation that leverages the concurrency features of the method. Numerical experiments reveal that this method is comparable with other fast direct solvers based on Hierarchical Matrices such as $\mathcal{H}$-LU and that it can tackle problems where algebraic multigrid fails to converge

ECOSMOG: An Efficient Code for Simulating Modified Gravity

We introduce a new code, ECOSMOG, to run N-body simulations for a wide class of modified gravity and dynamical dark energy theories. These theories generally have one or more new dynamical degrees of freedom, the dynamics of which are governed by their (usually rather nonlinear) equations of motion. Solving these non-linear equations has been a great challenge in cosmology. Our code is based on the RAMSES code, which solves the Poisson equation on adaptively refined meshes to gain high resolutions in the high-density regions. We have added a solver for the extra degree(s) of freedom and performed numerous tests for the f(R) gravity model as an example to show its reliability. We find that much higher efficiency could be achieved compared with other existing mesh/grid-based codes thanks to two new features of the present code: (1) the efficient parallelisation and (2) the usage of the multigrid relaxation to solve the extra equation(s) on both the regular domain grid and refinements, giving much faster convergence even under much more stringent convergence criteria. This code is designed for performing high-accuracy, high-resolution and large-volume cosmological simulations for modified gravity and general dark energy theories, which can be utilised to test gravity and the dark energy hypothesis using the upcoming and future deep and high-resolution galaxy surveys.Comment: 17 pages, 12 figures, 1 tabl

Scale Dependence of Halo Bispectrum from Non-Gaussian Initial Conditions in Cosmological N-body Simulations

We study the halo bispectrum from non-Gaussian initial conditions. Based on a set of large $N$-body simulations starting from initial density fields with local type non-Gaussianity, we find that the halo bispectrum exhibits a strong dependence on the shape and scale of Fourier space triangles near squeezed configurations at large scales. The amplitude of the halo bispectrum roughly scales as $f_nl^2$. The resultant scaling on the triangular shape is consistent with that predicted by Jeong & Komatsu based on perturbation theory. We systematically investigate this dependence with varying redshifts and halo mass thresholds. It is shown that the $f_nl$ dependence of the halo bispectrum is stronger for more massive haloes at higher redshifts. This feature can be a useful discriminator of inflation scenarios in future deep and wide galaxy redshift surveys.Comment: 27 pages, 10 figures; revised argument in section 6, added appendix C, JCAP accepted versio

Algorithm for numerical integration of the rigid-body equations of motion

A new algorithm for numerical integration of the rigid-body equations of motion is proposed. The algorithm uses the leapfrog scheme and the quantities involved are angular velocities and orientational variables which can be expressed in terms of either principal axes or quaternions. Due to specific features of the algorithm, orthonormality and unit norms of the orientational variables are integrals of motion, despite an approximate character of the produced trajectories. It is shown that the method presented appears to be the most efficient among all known algorithms of such a kind.Comment: 4 pages, 1 figur

Crystallization of a classical two-dimensional electron system: Positional and orientational orders

Crystallization of a classical two-dimensional one-component plasma (electrons interacting with the Coulomb repulsion in a uniform neutralizing positive background) is investigated with a molecular dynamics simulation. The positional and the orientational correlation functions are calculated for the first time. We have found an indication that the solid phase has a quasi-long-range (power-law) positional order along with a long-range orientational order. This indicates that, although the long-range Coulomb interaction is outside the scope of Mermin's theorem, the absence of ordinary crystalline order at finite temperatures applies to the electron system as well. The `hexatic' phase, which is predicted between the liquid and the solid phases by the Kosterlitz-Thouless-Halperin-Nelson-Young theory, is also discussed.Comment: 3 pages, 4 figures; Corrected typos; Double columne

Fourier Acceleration of Langevin Molecular Dynamics

Fourier acceleration has been successfully applied to the simulation of lattice field theories for more than a decade. In this paper, we extend the method to the dynamics of discrete particles moving in continuum. Although our method is based on a mapping of the particles' dynamics to a regular grid so that discrete Fourier transforms may be taken, it should be emphasized that the introduction of the grid is a purely algorithmic device and that no smoothing, coarse-graining or mean-field approximations are made. The method thus can be applied to the equations of motion of molecular dynamics (MD), or its Langevin or Brownian variants. For example, in Langevin MD simulations our acceleration technique permits a straightforward spectral decomposition of forces so that the long-wavelength modes are integrated with a longer time step, thereby reducing the time required to reach equilibrium or to decorrelate the system in equilibrium. Speedup factors of up to 30 are observed relative to pure (unaccelerated) Langevin MD. As with acceleration of critical lattice models, even further gains relative to the unaccelerated method are expected for larger systems. Preliminary results for Fourier-accelerated molecular dynamics are presented in order to illustrate the basic concepts. Possible extensions of the method and further lines of research are discussed.Comment: 11 pages, two illustrations included using graphic

Assessing Contention Effects on MPI_Alltoall Communications

12 pagesInternational audienceOne of the most important collective communication patterns used in scientific applications is the complete exchange, also called All-to-All. Although efficient algorithms have been studied for specific networks, general solutions like those available in well-known MPI distributions (e.g. the MPI_Alltoall operation) are strongly influenced by the congestion of network resources. In this paper we present an integrated approach to model the performance of the All-to-All collective operation, which consists in identifying a contention signature that characterizes a given network environment, using it to augment a contention-free communication model. This approach, assessed by experimental results, allows an accurate prediction of the performance of the All-to-All operation over different network architectures with a small overhead