Initial Condition Sensitivity of Global Quantities in Magnetohydrodynamic Turbulence

In this paper we study the effect of subtle changes in initial conditions on the evolution of global quantities in two-dimensional Magnetohydrodynamic (MHD) turbulence. We find that a change in the initial phases of complex Fourier modes of the Els\"{a}sser variables, while keeping the initial values of total energy, cross helicity and Alfv\'{e}n ratio unchanged, has a significant effect on the evolution of cross helicity. On the contrary, the total energy and Alfv\'{e}n ratio are insensitive to the initial phases. Our simulations are based on direct numerical simulation using the pseudo-spectral method.Comment: 12 pages LateX, 11 ps figures. Accepted for publication by Physics of Plasma

Calculation of renormalized viscosity and resistivity in magnetohydrodynamic turbulence

A self-consistent renormalization (RG) scheme has been applied to nonhelical magnetohydrodynamic turbulence with normalized cross helicity $\sigma_c =0$ and $\sigma_c \to 1$. Kolmogorov's 5/3 powerlaw is assumed in order to compute the renormalized parameters. It has been shown that the RG fixed point is stable for $d \ge d_c \approx 2.2$. The renormalized viscosity $\nu^*$ and resistivity $\eta^*$ have been calculated, and they are found to be positive for all parameter regimes. For $\sigma_c=0$ and large Alfv\'{e}n ratio (ratio of kinetic and magnetic energies) $r_A$, $\nu^*=0.36$ and $\eta^*=0.85$. As $r_A$ is decreased, $\nu^*$ increases and $\eta^*$ decreases, untill $r_A \approx 0.25$ where both $\nu^*$ and $\eta^*$ are approximately zero. For large $d$, both $\nu^*$ and $\eta^*$ vary as $d^{-1/2}$. The renormalized parameters for the case $\sigma_c \to 1$ are also reported.Comment: 19 pages REVTEX, 3 ps files (Phys. Plasmas, v8, 3945, 2001

Grothendieck-Serre formula and bigraded Cohen-Macaulay Rees algebras

The Grothendieck-Serre formula for the difference between the Hilbert function and Hilbert polynomial of a graded algebra is generalized for bigraded standard algebras. This is used to get a similar formula for the difference between the Bhattacharya function and Bhattacharya polynomial of two m-primary ideals I and J in a local ring (A,m) in terms of local cohomology modules of Rees algebras of I and J. The cohomology of a variation of the Kirby-Mehran complex for bigraded Rees algebras is studied which is used to characterize the Cohen-Macaulay property of bigraded Rees algebra of I and J for two dimensional Cohen-Macaulay local rings.Comment: 23 page

INPOP new release: INPOP13b

Based on the use of MESSENGER radiotracking data in the construction of new Mercury ephemerides (Verma et al. 2014) a new planetary ephemerides INPOP13b was built including Mercury improvements but also improvements on the Mars orbit and on the tie of INPOP planetary ephemerides to ICRF in general.Comment: INPOP sources available http://www.imcce.fr/inpo

Novel flow apparatus for investigating shear-enhanced crystallization and structure development in semicrystalline polymers

An instrument to study the effects of shearing on the crystallization process in semicrystalline polymers is described. It can impose transient stresses similar to those encountered in polymer processing and provides in situ monitoring of microstructure development during and after cessation of flow. Box-like wall shear stress profiles (rise and fall times under 50 ms with maximum wall shear stress on the order of 0.1 MPa) can be applied for controlled durations. A unique feature of our device is that it accommodates a wide variety of real-time probes of structure such as visible and infrared polarimetry and light and x-ray scattering measurements. The design also allows us to retrieve the sample for ex situ optical and electron microscopy. Data are acquired with millisecond resolution enabling us to record the extent of shear deformation of the polymer melt during the pressure pulse. Our device works with small sample quantities (as little as 5 g; each experiment takes ~ 500 mg) as opposed to the kilogram quantities required by previous instruments capable of imposing comparable deformations. This orders-of-magnitude reduction in the sample size allows us to study model polymers and new developmental resins, both of which are typically available only in gram-scale quantities. The compact design of the shear cell makes it possible to transport it to synchrotron light sources for in situ x-ray scattering studies of the evolution of the crystalline structure. Thus, our device is a valuable new tool that can be used to evaluate the crystallization characteristics of resins with experimental compositions or molecular architectures when subjected to processing-like flow conditions. We demonstrate some of the features of this device by presenting selected results on isotactic polypropylenes