PyFR: An Open Source Framework for Solving Advection-Diffusion Type Problems on Streaming Architectures using the Flux Reconstruction Approach

High-order numerical methods for unstructured grids combine the superior accuracy of high-order spectral or finite difference methods with the geometric flexibility of low-order finite volume or finite element schemes. The Flux Reconstruction (FR) approach unifies various high-order schemes for unstructured grids within a single framework. Additionally, the FR approach exhibits a significant degree of element locality, and is thus able to run efficiently on modern streaming architectures, such as Graphical Processing Units (GPUs). The aforementioned properties of FR mean it offers a promising route to performing affordable, and hence industrially relevant, scale-resolving simulations of hitherto intractable unsteady flows within the vicinity of real-world engineering geometries. In this paper we present PyFR, an open-source Python based framework for solving advection-diffusion type problems on streaming architectures using the FR approach. The framework is designed to solve a range of governing systems on mixed unstructured grids containing various element types. It is also designed to target a range of hardware platforms via use of an in-built domain specific language based on the Mako templating engine. The current release of PyFR is able to solve the compressible Euler and Navier-Stokes equations on grids of quadrilateral and triangular elements in two dimensions, and hexahedral elements in three dimensions, targeting clusters of CPUs, and NVIDIA GPUs. Results are presented for various benchmark flow problems, single-node performance is discussed, and scalability of the code is demonstrated on up to 104 NVIDIA M2090 GPUs. The software is freely available under a 3-Clause New Style BSD license (see www.pyfr.org)

Multi-switching combination synchronization of chaotic systems

A novel synchronization scheme is proposed for a class of chaotic systems, extending the concept of multi-switching synchronization to combination synchronization such that the state variables of two or more driving systems synchronize with different state variables of the response system, simultaneously. The new scheme, multi-switching combination synchronization (MSCS), represents a significant extension of earlier multi-switching schemes in which two chaotic systems, in a driver-response configuration, are multi-switched to synchronize up to a scaling factor. In MSCS, the chaotic driving systems multi-switch a response chaotic system in combination synchronization. For certain choices of the scaling factors, MSCS reduces to multi-switching synchronization, implying that the latter is a special case of MSCS. A theoretical approach to control design, based on backstepping, is presented and validated using numerical simulations

Optical interferometer in space

The present design concepts for a Laser Gravitational Wave Observatory in Space are described. Laser heterodyne distance measurements are made between test masses located in three spacecraft separated by roughly 10(exp 6) km. The major technology issues are: the reduction of spurious acceleration noise for the test masses to below 2 x 10(exp -15) cm/sq sec/Hz(0.5) from 10(exp -5) to 10(exp -3) Hz; and the measurement of changes in the difference of the antenna arm lengths to 5 x 10(exp -11) cm/Hz(0.5) from 10(exp -3) to 1 Hz with high reliability. The science objectives are: to measure discrete sinusoidal gravitational wave signals from individual sources with periods of 1 second to 1 day; to measure the stochastic background due to unresolved binaries; and to search for gravitational wave pulses with periods longer than 1 sec from possible exotic sources such as gravitational collapse of very massive objects

Hfq binding changes the structure of Escherichia coli small noncoding RNAs OxyS and RprA, which are involved in the riboregulation of rpoS

OxyS and RprA are two small noncoding RNAs (sRNAs) that modulate the expression of rpoS, encoding an alternative sigma factor that activates transcription of multiple Escherichia coli stress-response genes. While RprA activates rpoS for translation, OxyS down-regulates the transcript. Crucially, the RNA binding protein Hfq is required for both sRNAs to function, although the specific role played by Hfq remains unclear. We have investigated RprA and OxyS interactions with Hfq using biochemical and biophysical approaches. In particular, we have obtained the molecular envelopes of the Hfq–sRNA complexes using small-angle scattering methods, which reveal key molecular details. These data indicate that Hfq does not substantially change shape upon complex formation, whereas the sRNAs do. We link the impact of Hfq binding, and the sRNA structural changes induced, to transcript stability with respect to RNase E degradation. In light of these findings, we discuss the role of Hfq in the opposing regulatory functions played by RprA and OxyS in rpoS regulation

SpECTRE: A Task-based Discontinuous Galerkin Code for Relativistic Astrophysics

We introduce a new relativistic astrophysics code, SpECTRE, that combines a discontinuous Galerkin method with a task-based parallelism model. SpECTRE's goal is to achieve more accurate solutions for challenging relativistic astrophysics problems such as core-collapse supernovae and binary neutron star mergers. The robustness of the discontinuous Galerkin method allows for the use of high-resolution shock capturing methods in regions where (relativistic) shocks are found, while exploiting high-order accuracy in smooth regions. A task-based parallelism model allows efficient use of the largest supercomputers for problems with a heterogeneous workload over disparate spatial and temporal scales. We argue that the locality and algorithmic structure of discontinuous Galerkin methods will exhibit good scalability within a task-based parallelism framework. We demonstrate the code on a wide variety of challenging benchmark problems in (non)-relativistic (magneto)-hydrodynamics. We demonstrate the code's scalability including its strong scaling on the NCSA Blue Waters supercomputer up to the machine's full capacity of 22,380 nodes using 671,400 threads.Comment: 41 pages, 13 figures, and 7 tables. Ancillary data contains simulation input file

Magneto-optical Kerr Effect Studies of Square Artificial Spin Ice

We report a magneto-optical Kerr effect study of the collective magnetic response of artificial square spin ice, a lithographically-defined array of single-domain ferromagnetic islands. We find that the anisotropic inter-island interactions lead to a non-monotonic angular dependence of the array coercive field. Comparisons with micromagnetic simulations indicate that the two perpendicular sublattices exhibit distinct responses to island edge roughness, which clearly influence the magnetization reversal process. Furthermore, such comparisons demonstrate that disorder associated with roughness in the island edges plays a hitherto unrecognized but essential role in the collective behavior of these systems.Comment: Physical Review B, Rapid Communications (in press

Nonlinear growth and mathematical modelling of COVID-19 in some African countries with the Atangana-Baleanu fractional derivative

We analyse the time-series evolution of the cumulative number of confirmed cases of COVID-19, the novel coronavirus disease, for some African countries. We propose a mathematical model, incorporating non-pharmaceutical interventions to unravel the disease transmission dynamics. Analysis of the stability of the model’s steady states was carried out, and the reproduction number R0, a vital key for flattening the time-evolution of COVID-19 cases, was obtained by means of the next generation matrix technique. By dividing the time evolution of the pandemic for the cumulative number of confirmed infected cases into different regimes or intervals, hereafter referred to as phases, numerical simulations were performed to fit the proposed model to the cumulative number of confirmed infections for different phases of COVID-19 during its first wave. The estimated R0 declined from 2.452 – 9.179 during the first phase of the infection to 1.374 – 2.417 in the last phase. Using the Atangana-Baleanu fractional derivative, a fractional COVID-19 model is proposed and numerical simulations performed to establish the dependence of the disease dynamics on the order of the fractional derivatives. An elasticity and sensitivity analysis of R0 was carried out to determine the most significant parameters for combating the disease outbreak. These were found to be the effective disease transmission rate, the disease diagnosis or case detection rate, the proportion of susceptible individuals taking precautions, and the disease infection rate. Our results show that if the disease infection rate is less than 0.082/day, then R0 is always less than 1; and if at least 55.29% of the susceptible population take precautions such as regular hand washing with soap, use of sanitizers, and the wearing of face masks, then the reproduction number R0 remains below unity irrespective of the disease infection rate. Keeping R0 values below unity leads to a decrease in COVID-19 prevalence

The virulent, emerging genotype B of Deformed wing virus is closely linked to overwinter honeybee worker loss

Bees are considered to be threatened globally, with severe overwinter losses of the most important commercial pollinator, the Western honeybee, a major concern in the Northern Hemisphere. Emerging infectious diseases have risen to prominence due to their temporal correlation with colony losses. Among these is Deformed wing virus (DWV), which has been frequently linked to colony mortality. We now provide evidence of a strong statistical association between overwintering colony decline in the field and the presence of DWV genotype-B (DWV-B), a genetic variant of DWV that has recently been shown to be more virulent than the original DWV genotype-A. We link the prevalence of DWV-B directly to a quantitative measure of overwinter decline (workforce mortality) of honeybee colonies in the field. We demonstrate that increased prevalence of virus infection in individual bees is associated with higher overwinter mortality. We also observed a substantial reduction of infected colonies in the spring, suggesting that virus-infected individuals had died during the winter. Our findings demonstrate that DWV-B, plus possible A/B recombinants exhibiting DWV-B at PCR primer binding sites, may be a major cause of elevated overwinter honeybee loss. Its potential emergence in naïve populations of bees may have far-reaching ecological and economic impacts

Hyperchaos and bifurcations in a driven Van der Pol–Duffing oscillator circuit

We investigate the dynamics of a driven Van der Pol–Duffing oscillator circuit and show the existence of higher-dimensional chaotic orbits (or hyperchaos), transient chaos, strange-nonchaotic attractors, as well as quasiperiodic orbits born from Hopf bifurcating orbits. By computing all the Lyapunov exponent spectra, scanning a wide range of the driving frequency and driving amplitude parameter space, we explore in two-parameter space the regimes of different dynamical behaviours