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

Steady shear flow thermodynamics based on a canonical distribution approach

A non-equilibrium steady state thermodynamics to describe shear flows is developed using a canonical distribution approach. We construct a canonical distribution for shear flow based on the energy in the moving frame using the Lagrangian formalism of the classical mechanics. From this distribution we derive the Evans-Hanley shear flow thermodynamics, which is characterized by the first law of thermodynamics $dE = T dS - Q d\gamma$ relating infinitesimal changes in energy $E$, entropy $S$ and shear rate $\gamma$ with kinetic temperature $T$. Our central result is that the coefficient $Q$ is given by Helfand's moment for viscosity. This approach leads to thermodynamic stability conditions for shear flow, one of which is equivalent to the positivity of the correlation function of $Q$. We emphasize the role of the external work required to sustain the steady shear flow in this approach, and show theoretically that the ensemble average of its power $\dot{W}$ must be non-negative. A non-equilibrium entropy, increasing in time, is introduced, so that the amount of heat based on this entropy is equal to the average of $\dot{W}$. Numerical results from non-equilibrium molecular dynamics simulation of two-dimensional many-particle systems with soft-core interactions are presented which support our interpretation.Comment: 23 pages, 7 figure

Light scattering spectra of supercooled molecular liquids

The light scattering spectra of molecular liquids are derived within a generalized hydrodynamics. The wave vector and scattering angle dependences are given in the most general case and the change of the spectral features from liquid to solidlike is discussed without phenomenological model assumptions for (general) dielectric systems without long-ranged order. Exact microscopic expressions are derived for the frequency-dependent transport kernels, generalized thermodynamic derivatives and the background spectra.Comment: 12 page

Nonequilibrium Molecular Dynamics Simulation of Interacting Many Electrons Scattered by Lattice Vibrations

We propose a new model suitable for a nonequilibrium molecular dynamics (MD) simulation of electrical conductors. The model consists of classical electrons and atoms. The atoms compose a lattice vibration system. The electrons are scattered by electron-electron and electron-atom interactions. Since the scattering cross section is physically more important than the functional form of a scattering potential, we propose to devise the electron-atom interaction potential in such a way that its scattering cross section agrees with that of quantum-mechanical one. To demonstrate advantages of the proposed model, we perform a nonequilibrium MD simulation assuming a doped semiconductor at room or higher temperature. In the linear response regime, we confirm Ohm's law, the dispersion relations and the fluctuation-dissipation relation. Furthermore, we obtain reasonable dependence of the electrical conductivity on temperature, despite the fact that our model is a classical model.Comment: 21 pages, 11 figure

Viscoélasticité et diffusion dépolarisée de la lumière dans les liquides

Les spectres de diffusion dépolarisée de la lumière dans les liquides sont liés aux propriétés viscoélastiques du milieu, qui reflètent à leur tour l'ordre local. Leur interprétation demande une théorie généralisant l'hydrodynamique. Dans cet article sont passées en revue les différentes théories permettant cette généralisation, qu'elles utilisent le formalisme de Zwanzig-Mori ou la thermodynamique hors d'équilibre. Une place à part est faite à celle développée par l'auteur qui apparaît comme la plus générale. La comparaison avec les résultats expérimentaux confirme la nécessité d'une théorie aussi complexe

Hydrodynamics of a normal fluid up to high frequencies and small wavelengths

We obtain equations of evolution for a dense fluid taking into account the orientational degrees of freedom of the molecules and the local order. We introduce two tensors. The first characterizes the local order of the center of gravity of the molecules, the second the orientational local order. Coupling these tensors with the usual stress tensor, we obtain new hydrodynamic equations. These equations show that the transverse waves are propagating for the wave number k between two values.Nous obtenons des équations d'évolution pour un liquide dense en tenant compte des degrés de liberté rotationnels des molécules et de l'ordre local. Deux tenseurs sont introduits, le premier caractérise l'ordre local des centres de gravité des molécules, le deuxième l'ordre local orientationnel. En couplant ces tenseurs avec le tenseur de contrainte usuel, nous obtenons de nouvelles équations hydrodynamiques. Ces équations montrent que les ondes transverses se propagent pour le nombre d'onde k compris entre deux valeurs

A new analysis of sound propagation near the critical point of xenon

We give a new analysis of experimental data showing that the frequency dependence observed in the absorption and dispersion of sound near the critical point of xenon is not only due, as believed up to now, to the entropy mode coupling but is also due to the density inhomogeneities. The local order theory which takes into account these inhomogeneities gives an accurate description of the data for T - Tc ≥ 1 °C. We find for the bulk viscosity a divergence law of the form (T - Tc) -1.92, in very good agreement with Kawasaki's prediction.Nous donnons une nouvelle analyse des données expérimentales montrant que la dépendance en fréquence observée dans l'absorption et la dispersion du son près du point critique du xénon, n'est pas seulement due, comme on le croyait jusqu'à présent, aux modes couplés d'entropie, mais est due également aux inhomogénéïtés de densité. La théorie de l'ordre local qui rend compte de ces inhomogénéités donne une description correcte des données pour T - Tc ≥ 1 °C. Nous trouvons, pour la viscosité de volume une loi de divergence en (T - T c)-1,92 en très bon accord avec les prédictions de Kawasaki

Local order theory of liquids : multipolar expansion

Using a multipolar expansion of the internal energy density we show that two vectors and three second rank tensors are necessary to characterize the local order in a liquid. A simple interpretation of the physical meaning of the three tensors is presented. We give the equations of evolution of the latter variables and we show how they are connected to the usual hydrodynamic variables.Nous montrons, utilisant un développement multipolaire de la densité d'énergie interne, qu'on a besoin de deux vecteurs et de trois tenseurs du deuxième ordre pour caractériser l'ordre local dans un liquide. Une interprétation simple de la signification physique de ces trois tenseurs est proposée. Nous donnons les équations d'évolution de ces dernières variables et nous montrons leurs relations avec les variables hydrodynamiques habituelles