Bipartite partial duals and circuits in medial graphs

It is well known that a plane graph is Eulerian if and only if its geometric dual is bipartite. We extend this result to partial duals of plane graphs. We then characterize all bipartite partial duals of a plane graph in terms of oriented circuits in its medial graph.Comment: v2: minor changes. To appear in Combinatoric

Large Scale Structures a Gradient Lines: the case of the Trkal Flow

A specific asymptotic expansion at large Reynolds numbers (R)for the long wavelength perturbation of a non stationary anisotropic helical solution of the force less Navier-Stokes equations (Trkal solutions) is effectively constructed of the Beltrami type terms through multi scaling analysis. The asymptotic procedure is proved to be valid for one specific value of the scaling parameter,namely for the square root of the Reynolds number (R).As a result large scale structures arise as gradient lines of the energy determined by the initial conditions for two anisotropic Beltrami flows of the same helicity.The same intitial conditions determine the boundaries of the vortex-velocity tubes, containing both streamlines and vortex linesComment: 27 pages, 2 figure

Turbulent Contributions to Ohm's Law in Axisymmetric Magnetized Plasmas

The effect of magnetic turbulence in shaping the current density in axisymmetric magnetized plasma is analyzed using a turbulent extension of Ohm's law derived from the self-consistent action-angle transport theory. Besides the well-known hyper-resistive (helicity-conserving) contribution, the generalized Ohm's law contains an anomalous resistivity term, and a turbulent bootstrap-like term proportional to the current density derivative. The numerical solution of the equation for equilibrium and turbulence profiles characteristic of conventional and advanced scenarios shows that, trough "turbulent bootstrap" effect and anomalous resistivity turbulence can generate power and parallel current which are a sizable portion (about 20-25%) of the corresponding effects associated with the neoclassical bootstrap effect. The degree of alignment of the turbulence peak and the pressure gradient plays an important role in defining the steady-state regime. In fully bootstrapped tokamak, the hyper-resistivity is essential in overcoming the intrinsic limitation of the hollow current profile.Comment: 19 pages, 6 figures, journal pape

Helicity cascades in rotating turbulence

The effect of helicity (velocity-vorticity correlations) is studied in direct numerical simulations of rotating turbulence down to Rossby numbers of 0.02. The results suggest that the presence of net helicity plays an important role in the dynamics of the flow. In particular, at small Rossby number, the energy cascades to large scales, as expected, but helicity then can dominate the cascade to small scales. A phenomenological interpretation in terms of a direct cascade of helicity slowed down by wave-eddy interactions leads to the prediction of new inertial indices for the small-scale energy and helicity spectra.Comment: 7 pages, 8 figure

Analytical theory of forced rotating sheared turbulence: The perpendicular case

Rotation and shear flows are ubiquitous features of many astrophysical and geophysical bodies. To understand their origin and effect on turbulent transport in these systems, we consider a forced turbulence and investigate the combined effect of rotation and shear flow on the turbulence properties. Specifically, we study how rotation and flow shear influence the generation of shear flow (e.g., the direction of energy cascade), turbulence level, transport of particles and momentum, and the anisotropy in these quantities. In all the cases considered, turbulence amplitude is always quenched due to strong shear (ξ=νky2/A⪡1, where A is the shearing rate, ν is the molecular viscosity, and ky is a characteristic wave number of small-scale turbulence), with stronger reduction in the direction of the shear than those in the perpendicular directions. Specifically, in the large rotation limit (Ω⪢A), they scale as A−1 and A−1|ln ξ|, respectively, while in the weak rotation limit (Ω⪡A), they scale as A−1 and A−2/3, respectively. Thus, flow shear always leads to weak turbulence with an effectively stronger turbulence in the plane perpendicular to shear than in the shear direction, regardless of rotation rate. The anisotropy in turbulence amplitude is, however, weaker by a factor of ξ1/3|ln ξ| (∝A−1/3|ln ξ|) in the rapid rotation limit (Ω⪢A) than that in the weak rotation limit (Ω⪡A) since rotation favors almost-isotropic turbulence. Compared to turbulence amplitude, particle transport is found to crucially depend on whether rotation is stronger or weaker than flow shear. When rotation is stronger than flow shear (Ω⪢A), the transport is inhibited by inertial waves, being quenched inversely proportional to the rotation rate (i.e., ∝Ω−1) while in the opposite case, it is reduced by shearing as A−1. Furthermore, the anisotropy is found to be very weak in the strong rotation limit (by a factor of 2) while significant in the strong shear limit. The turbulent viscosity is found to be negative with inverse cascade of energy as long as rotation is sufficiently strong compared to flow shear (Ω⪢A) while positive in the opposite limit of weak rotation (Ω⪡A). Even if the eddy viscosity is negative for strong rotation (Ω⪢A), flow shear, which transfers energy to small scales, has an interesting effect by slowing down the rate of inverse cascade with the value of negative eddy viscosity decreasing as |νT|∝A−2 for strong shear. Furthermore, the interaction between the shear and the rotation is shown to give rise to a nondiffusive flux of angular momentum (Λ effect), even in the absence of external sources of anisotropy. This effect provides a mechanism for the existence of shearing structures in astrophysical and geophysical systems

Shell to shell energy transfer in MHD, Part I: steady state turbulence

We investigate the transfer of energy from large scales to small scales in fully developed forced three-dimensional MHD-turbulence by analyzing the results of direct numerical simulations in the absence of an externally imposed uniform magnetic field. Our results show that the transfer of kinetic energy from the large scales to kinetic energy at smaller scales, and the transfer of magnetic energy from the large scales to magnetic energy at smaller scales, are local, as is also found in the case of neutral fluids, and in a way that is compatible with Kolmogorov (1941) theory of turbulence. However, the transfer of energy from the velocity field to the magnetic field is a highly non-local process in Fourier space. Energy from the velocity field at large scales can be transfered directly into small scale magnetic fields without the participation of intermediate scales. Some implications of our results to MHD turbulence modeling are also discussed.Comment: Submitted to PR

Temperature perturbation model of the opto-galvanic effect in CO2-laser discharges

A detailed discharge model of the opto-galvanic effect in molecular laser gas mixtures is developed based on the temperature perturbation or discharge cooling mechanism of Smith and Brooks (1979). Excellent agreement between the model and experimental results in CO2 laser gas mixtures is obtained. The model should be applicable to other molecular systems where the OGE is being used for laser stabilisation and as a spectroscopic tool

Low magnetic Prandtl number dynamos with helical forcing

We present direct numerical simulations of dynamo action in a forced Roberts flow. The behavior of the dynamo is followed as the mechanical Reynolds number is increased, starting from the laminar case until a turbulent regime is reached. The critical magnetic Reynolds for dynamo action is found, and in the turbulent flow it is observed to be nearly independent on the magnetic Prandtl number in the range from 0.3 to 0.1. Also the dependence of this threshold with the amount of mechanical helicity in the flow is studied. For the different regimes found, the configuration of the magnetic and velocity fields in the saturated steady state are discussed.Comment: 9 pages, 14 figure

Unplugging the Universe: the neglected electromagnetic consequence of decoupling

This letter concentrates on the non-equilibrium evolution of magnetic field structures at the onset of recombination, when the charged particle current densities decay as neutrals are formed. We consider the effect that a decaying magnetic flux has on the acceleration of particles via the transient induced electric field. Since the residual charged-particle number density is small as a result of decoupling, we shall consider the magnetic and electric fields essentially to be imposed, neglecting the feedback from any minority accelerated population. We find that the electromagnetic treatment of this phase transition can produce energetic electrons scattered throughout the Universe. Such particles could have a significant effect on cosmic evolution in several ways: (i) their presence could delay the effective end of the recombination era; (ii) they could give rise to plasma concentrations that could enhance early gravitational collapse of matter by opposing cosmic expansion to a greater degree than neutral matter could; (iii) they could continue to be accelerated, and become the seed for reionisation at the later epoch $z \approx 10$.Comment: 4 pages, no figure

Primordial Magnetic Field Limits from Cosmic Microwave Background Bispectrum of Magnetic Passive Scalar Modes

Primordial magnetic fields lead to non-Gaussian signals in the cosmic microwave background (CMB) even at the lowest order, as magnetic stresses and the temperature anisotropy they induce depend quadratically on the magnetic field. In contrast, CMB non-Gaussianity due to inflationary scalar perturbations arises only as a higher order effect. Apart from a compensated scalar mode, stochastic primordial magnetic fields also produce scalar anisotropic stress that remains uncompensated till neutrino decoupling. This gives rise to an adiabatic-like scalar perturbation mode that evolves passively thereafter (called the passive mode). We compute the CMB reduced bispectrum ($b_{l_{_1}l_{_2}l_{_3}}$) induced by this passive mode, sourced via the Sachs-Wolfe effect, on large angular scales. For any configuration of bispectrum, taking a partial sum over mode-coupling terms, we find a typical value of $l_1(l_1+1)l_3(l_3+1) b_{l_{_1}l_{_2}l_{_3}} \sim 6-9 \times 10^{-16}$, for a magnetic field of $B_0 \sim 3$ nG, assuming a nearly scale-invariant magnetic spectrum . We also evaluate, in full, the bispectrum for the squeezed collinear configuration over all angular mode-coupling terms and find $l_1(l_1+1)l_3(l_3+1) b_{l_{_1}l_{_2}l_{_3}} \approx -1.4 \times 10^{-16}$. These values are more than $\sim 10^6$ times larger than the previously calculated magnetic compensated scalar mode CMB bispectrum. Observational limits on the bispectrum from WMAP7 data allow us to set upper limits of $B_0 \sim 2$ nG on the present value of the cosmic magnetic field of primordial origin. This is over 10 times more stringent than earlier limits on $B_0$ based on the compensated mode bispectrum.Comment: 9 page