A Kolmogorov-Like Exact Relation for Compressible Polytropic Turbulence

Compressible hydrodynamic turbulence is studied under the assumption of a polytropic closure. Following Kolmogorov, we derive an exact relation for some two-point correlation functions in the asymptotic limit of a high Reynolds number

The density structure and star formation rate of non-isothermal polytropic turbulence

The interstellar medium of galaxies is governed by supersonic turbulence, which likely controls the star formation rate (SFR) and the initial mass function (IMF). Interstellar turbulence is non-universal, with a wide range of Mach numbers, magnetic fields strengths, and driving mechanisms. Although some of these parameters were explored, most previous works assumed that the gas is isothermal. However, we know that cold molecular clouds form out of the warm atomic medium, with the gas passing through chemical and thermodynamic phases that are not isothermal. Here we determine the role of temperature variations by modelling non-isothermal turbulence with a polytropic equation of state (EOS), where pressure and temperature are functions of gas density, P~rho^Gamma, T~rho^(Gamma-1). We use grid resolutions of 2048^3 cells and compare polytropic exponents Gamma=0.7 (soft EOS), Gamma=1 (isothermal EOS), and Gamma=5/3 (stiff EOS). We find a complex network of non-isothermal filaments with more small-scale fragmentation occurring for Gamma<1, while Gamma>1 smoothes out density contrasts. The density probability distribution function (PDF) is significantly affected by temperature variations, with a power-law tail developing at low densities for Gamma>1. In contrast, the PDF becomes closer to a lognormal distribution for Gamma<=1. We derive and test a new density variance - Mach number relation that takes Gamma into account. This new relation is relevant for theoretical models of the SFR and IMF, because it determines the dense gas mass fraction of a cloud, from which stars form. We derive the SFR as a function of Gamma and find that it decreases by a factor of ~5 from Gamma=0.7 to Gamma=5/3.Comment: 18 pages, 10 figures, MNRAS accepted, simulation movies at http://www.mso.anu.edu.au/~chfeder/pubs/polytropic/polytropic.htm

Statistics of incompressible hydrodynamic turbulence: An alternative approach

Using a recent alternative form of the Kolmogorov-Monin exact relation for fully developed hydrodynamics (HD) turbulence, the incompressible energy cascade rate is computed. Under this current theoretical framework, for three-dimensional (3D) freely decaying homogeneous turbulence, the statistical properties of the fluid velocity (u), vorticity (ω= ×u), and Lamb vector (L=ω×u) are numerically studied. For different spatial resolutions, the numerical results show that can be obtained directly as the simple products of two-point increments of u and L, without the assumption of isotropy. Finally, the results for the largest spatial resolutions show a clear agreement with the cascade rates computed from the classical four-thirds law for isotropic homogeneous HD turbulence.Fil: Andrés, Nahuel. Universidad de Buenos Aires. Facultad de Cs.exactas y Naturales. Departamento de Física. Grupo de Plasmas Astrofisicos; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Laboratoire de Physique des Plasmas; FranciaFil: Banerjee, Supratik. Indian Institute Of Technology Kanpur; Indi

Binary Task Offloading Model For Mobile Edge Computing using NDN Architecture

Driven by the advantages of Mobile Edge Computing (MEC) and Information-Centric Networking (ICN) in nextgeneration networks we propose an architecture for MEC using Named Data Networking (NDN). NDN is one of the prominent architectures of ICN having features like unique-naming, in-network caching, inherit support for multicasting, and support for mobility. Placing MEC in NDN provides the additional facilities of edge computing like pushing of resource-hungry and time-critical applications of the mobile devices to the edge-computing server. Therefore, one of the research challenges is the decision regarding the task offloading process by the end-users to the edge-computing server. We propose a mathematical model that enables the end-user to take decisions in Yes/No regarding the binary task offloading process

Scale-to-scale energy transfer rate in compressible two-fluid plasma turbulence

We derive the exact relation for the energy transfer in three-dimensional compressible two-fluid plasma turbulence. In the long-time limit, we obtain an exact law which expresses the scale-to-scale average energy flux rate in terms of two point increments of the fluid variables of each species, electric and magnetic field and current density, and puts a strong constraint on the turbulent dynamics. The incompressible single fluid and two-fluid limits and the compressible single fluid limit are recovered under appropriate assumption. In the single fluid limits, analyses are done with and without neglecting the electron mass thereby making the exact relation suitable for a broader range of application. In the compressible two-fluid regime, the total energy flux rate, unlike the single fluid case, is found to be unaltered by the presence of a background magnetic field. The exact relation provides a way to test whether a range of scales in a plasma is inertial or dissipative and is essential to understand the nonlinear nature of both space and dilute astrophysical plasmas.Fil: Banerjee, Supratik. Indian Institute of Technology Kanpur; IndiaFil: Andrés, Nahuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; Argentin