Modelling the Fisher hypothesis: World wide evidence

In this paper we follow an empirical approach to examine the implications of the Fisher hypothesis, namely cointegration linking interest rates and inflation, and stationarity of the real interest rate implying in turn homogeneity of the potential equilibrium relation. The considered sample is an unbalanced panel and comprises monthly time series data from more than 100 economies covering at most a period of about 45 years. In total more than 31000 observations enter our empirical analysis. From cross sectional error correction and dynamic OLS regressions we find that the presumed dynamic relation is hardly homogeneous over the cross section. Therefore, building on cross sectional parameter homogeneity nonstationary panel data models are provided merely as a complement to cross section specific analyses. Apart from standard between regressions we exploit the cross section dimension to infer on parameter homogeneity over particular economic states. For this purpose we rely on semiparametric implementations of so-called functional coefficient models. The latter are suitable to relate key model parameters on economic states, as e.g. periods of higher vs. lower inflation or inflation risk. From the latter approach we find that time or state invariance of key model parameters is not supported empirically. Moreover the evidence in favor of cointegration is weak over periods of high inflation. The Fisher coefficient turns out to be remarkably stable and is, over most considered states, significantly less than unity. --Fisher hypothesis,Panel cointegration analysis,Functional coefficient models

A divergence-cleaning scheme for cosmological SPMHD simulations

In magnetohydrodynamics (MHD), the magnetic field is evolved by the induction equation and coupled to the gas dynamics by the Lorentz force. We perform numerical smoothed particle magnetohydrodynamics (Spmhd) simulations and study the influence of a numerical magnetic divergence. For instabilities arising from divergence B related errors, we find the hyperbolic/parabolic cleaning scheme suggested by Dedner et al. 2002 to give good results and prevent numerical artifacts from growing. Additionally, we demonstrate that certain current Spmhd implementations of magnetic field regularizations give rise to unphysical instabilities in long-time simulations. We also find this effect when employing Euler potentials (divergenceless by definition), which are not able to follow the winding-up process of magnetic field lines properly. Furthermore, we present cosmological simulations of galaxy cluster formation at extremely high resolution including the evolution of magnetic fields. We show synthetic Faraday rotation maps and derive structure functions to compare them with observations. Comparing all the simulations with and without divergence cleaning, we are able to confirm the results of previous simulations performed with the standard implementation of MHD in Spmhd at normal resolution. However, at extremely high resolution, a cleaning scheme is needed to prevent the growth of numerical errors at small scales.Comment: 15 pages, 19 figures, submitted to MNRA

Smoothed Particle Hydrodynamics in cosmology: a comparative study of implementations

We analyse the performance of twelve different implementations of Smoothed Particle Hydrodynamics (SPH) using seven tests designed to isolate key hydrodynamic elements of cosmological simulations which are known to cause the SPH algorithm problems. In order, we consider a shock tube, spherical adiabatic collapse, cooling flow model, drag, a cosmological simulation, rotating cloud-collapse and disc stability. In the implementations special attention is given to the way in which force symmetry is enforced in the equations of motion. We study in detail how the hydrodynamics are affected by different implementations of the artificial viscosity including those with a shear-correction modification. We present an improved first-order smoothing-length update algorithm that is designed to remove instabilities that are present in the Hernquist and Katz (1989) algorithm. For all tests we find that the artificial viscosity is the most important factor distinguishing the results from the various implementations. The second most important factor is the way force symmetry is achieved in the equation of motion. Most results favour a kernel symmetrization approach. The exact method by which SPH pressure forces are included has comparatively little effect on the results. Combining the equation of motion presented in Thomas and Couchman (1992) with a modification of the Monaghan and Gingold (1983) artificial viscosity leads to an SPH scheme that is both fast and reliable.Comment: 30 pages, 26 figures and 9 tables included. Submitted to MNRAS. Postscript version available at ftp://phobos.astro.uwo.ca/pub/etittley/papers/sphtest.ps.g

Wilson and Domainwall Kernels on Oakforest-PACS

We report the performance of Wilson and Domainwall Kernels on a new Intel Xeon Phi Knights Landing based machine named Oakforest-PACS, which is co-hosted by University of Tokyo and Tsukuba University and is currently fastest in Japan. This machine uses Intel Omni-Path for the internode network. We compare performance with several types of implementation including that makes use of the Grid library. The code is incorporated with the code set Bridge++.Comment: 8 pages, 9 figures, Proceedings for the 35th International Symposium on Lattice Field Theory (Lattice 2017

Hydrodynamic simulations with the Godunov SPH

We present results based on an implementation of the Godunov Smoothed Particle Hydrodynamics (GSPH), originally developed by Inutsuka (2002), in the GADGET-3 hydrodynamic code. We first review the derivation of the GSPH discretization of the equations of moment and energy conservation, starting from the convolution of these equations with the interpolating kernel. The two most important aspects of the numerical implementation of these equations are (a) the appearance of fluid velocity and pressure obtained from the solution of the Riemann problem between each pair of particles, and (b the absence of an artificial viscosity term. We carry out three different controlled hydrodynamical three-dimensional tests, namely the Sod shock tube, the development of Kelvin-Helmholtz instabilities in a shear flow test, and the "blob" test describing the evolution of a cold cloud moving against a hot wind. The results of our tests confirm and extend in a number of aspects those recently obtained by Cha (2010): (i) GSPH provides a much improved description of contact discontinuities, with respect to SPH, thus avoiding the appearance of spurious pressure forces; (ii) GSPH is able to follow the development of gas-dynamical instabilities, such as the Kevin--Helmholtz and the Rayleigh-Taylor ones; (iii) as a result, GSPH describes the development of curl structures in the shear-flow test and the dissolution of the cold cloud in the "blob" test. We also discuss in detail the effect on the performances of GSPH of changing different aspects of its implementation. The results of our tests demonstrate that GSPH is in fact a highly promising hydrodynamic scheme, also to be coupled to an N-body solver, for astrophysical and cosmological applications. [abridged]Comment: 19 pages, 13 figures, MNRAS accepted, high resolution version can be obtained at http://adlibitum.oats.inaf.it/borgani/html/papers/gsph_hydrosim.pd