Topological constraints in the reconnection of vortex braids

We study the relaxation of a topologically nontrivial vortex braid with zero net helicity in a barotropic fluid. The aim is to investigate the extent to which the topology of the vorticity field—characterized by braided vorticity field lines—determines the dynamics, particularly the asymptotic behavior under vortex reconnection in evolution at high Reynolds numbers (25 000). Analogous to the evolution of braided magnetic fields in plasma, we find that the relaxation of our vortex braid leads to a simplification of the topology into large-scale regions of opposite swirl, consistent with an inverse cascade of the helicity. The change of topology is facilitated by a cascade of vortex reconnection events. During this process, the existence of regions of positive and negative kinetic helicities imposes a lower bound for the kinetic energy. For the enstrophy, we derive analytically a lower bound given by the presence of unsigned kinetic helicity, which we confirm in our numerical experiments

Minimum quadratic helicity states

Building on previous results on the quadratic helicity in magnetohydrodynamics (MHD) we investigate particular minimum helicity states. Those are eigenfunctions of the curl operator and are shown to constitute solutions of the quasi-stationary incompressible ideal MHD equations. We then show that these states have indeed minimum quadratic helicity.Comment: 13 pages, 2 figure

Is there a left-handed magnetic field in the solar neighborhood?:Exploring helical magnetic fields in the interstellar medium through dust polarization power spectra

The full-sky Planck polarization data at 850um revealed unexpected properties of the E and B mode power spectra of dust emission in the interstellar medium (ISM). The positive cross-correlation between the total dust intensity, T, with the B modes has raised new questions about the physical mechanisms that affect dust polarization, such as the Galactic magnetic-field structure. This is key both to better understanding ISM dynamics and to accurately describing Galactic foregrounds to the polarization of the Cosmic Microwave Background (CMB). In this theoretical paper we investigate the possibility that the observed cross-correlations in the dust polarization power spectra, and specifically between T and B, can be related to a parity-odd quantity in the ISM such as the magnetic helicity. We produce synthetic dust polarization data, derived from 3D analytical toy models of density structures and helical magnetic fields, to compare with the E and B modes of observations. Focusing on the observed T-B correlation, we propose a new line of interpretation of the Planck observations based on a large-scale helical component of the Galactic magnetic field in the solar neighborhood. Our analysis shows that: I) the sign of magnetic helicity does not affect E and B modes for isotropic magnetic-field configurations; II) helical magnetic fields threading interstellar filaments cannot reproduce the Planck results; III) a weak helical left-handed magnetic field structure in the solar neighborhood may explain the T-B correlation seen in the Planck data. This work suggests a new perspective for the interpretation of the dust polarization power spectra, which strongly supports the imprint of a large-scale structure of the Galactic magnetic field in the solar neighborhood.Comment: Accepted by Astronomy & Astrophysics on November 24, 201

Quantifying the tangling of trajectories using the topological entropy

We present a simple method to efficiently compute a lower limit of the topological entropy and its spatial distribution for two-dimensional mappings. These mappings could represent either two-dimensional time-periodic fluid flows or three-dimensional magnetic fields, which are periodic in one direction. This method is based on measuring the length of a material line in the flow. Depending on the nature of the flow, the fluid can be mixed very efficiently which causes the line to stretch. Here we study a method that adaptively increases the resolution at locations along the line where folds lead to high curvature. This reduces the computational cost greatly which allows us to study unprecedented parameter regimes. We demonstrate how this efficient implementation allows the computation of the variation of the finite-time topological entropy in the mapping. This measure quantifies spatial variations of the braiding efficiency, important in many practical applications.Comment: 11 pages, 9 figure

Braided magnetic fields:equilibria, relaxation and heating

We examine the dynamics of magnetic flux tubes containing non-trivial field line braiding (or linkage), using mathematical and computational modelling, in the context of testable predictions for the laboratory and their significance for solar coronal heating. We investigate the existence of braided force-free equilibria, and demonstrate that for a field anchored at perfectly-conducting plates, these equilibria exist and contain current sheets whose thickness scales inversely with the braid complexity - as measured for example by the topological entropy. By contrast, for a periodic domain braided exact equilibria typically do not exist, while approximate equilibria contain thin current sheets. In the presence of resistivity, reconnection is triggered at the current sheets and a turbulent relaxation ensues. We finish by discussing the properties of the turbulent relaxation and the existence of constraints that may mean that the final state is not the linear force-free field predicted by Taylor's hypothesis.Comment: To appear in Plasma Physics and Controlled Fusio

Estimating the Rate of Field Line Braiding in the Solar Corona by Photospheric Flows

In this paper, we seek to understand the timescale in which the photospheric motions on the Sun braid coronal magnetic field lines. This is a crucial ingredient for determining the viability of the braiding mechanism for explaining the high temperatures observed in the corona. We study the topological complexity induced in the coronal magnetic field, primarily using plasma motions extracted from magneto-convection simulations. This topological complexity is quantified using the field line winding, finite time topological entropy (FTTE), and passive scalar mixing. With these measures, we contrast mixing efficiencies of the magneto-convection simulation, a benchmark flow known as a "blinking vortex", and finally photospheric flows inferred from sequences of observed magnetograms using local correlation tracking. While the highly resolved magneto-convection simulations induce a strong degree of field line winding and FTTE, the values obtained from the observations from the plage region are around an order of magnitude smaller. This behavior is carried over to the FTTE. Nevertheless, the results suggest that the photospheric motions induce complex tangling of the coronal field on a timescale of hours

HCC development is associated to peripheral insulin resistance in a mouse model of NASH

NAFLD is the most common liver disease worldwide but it is the potential evolution to NASH and eventually to hepatocellular carcinoma (HCC), even in the absence of cirrhosis, that makes NAFLD of such clinical importance. Aim: we aimed to create a mouse model reproducing the pathological spectrum of NAFLD and to investigate the role of possible co-factors in promoting HCC. Methods: mice were treated with a choline-deficient L-amino-acid-defined-diet (CDAA) or its control (CSAA diet) and subjected to a low-dose i.p. injection of CCl 4 or vehicle. Insulin resistance was measured by the euglycemic-hyperinsulinemic clamp method. Steatosis, fibrosis and HCC were evaluated by histological and molecular analysis. Results: CDAA-treated mice showed peripheral insulin resistance at 1 month. At 1-3 months, extensive steatosis and fibrosis were observed in CDAA and CDAA+CCl4 groups. At 6 months, equal increase in steatosis and fibrosis was observed between the two groups, together with the appearance of tumor. At 9 months of treatment, the 100% of CDAA+ CCl4 treated mice revealed tumor versus 40% of CDAA mice. Insulin-like Growth Factor-2 (IGF-2) and Osteopontin (SPP-1) were increased in CDAA mice versus CSAA. Furthermore, Immunostaining for p-AKT, p-c-Myc and Glypican-3 revealed increased positivity in the tumors. Conclusions: the CDAA model promotes the development of HCC from NAFLD-NASH in the presence of insulin resistance but in the absence of cirrhosis. Since this condition is increasingly recognized in humans, our study provides a model that may help understanding mechanisms of carcinogenesis in NAFLD. © 2014 De Minicis et al

Ideal relaxation of the Hopf fibration

Ideal MHD relaxation is the topology-conserving reconfiguration of a magnetic field into a lower energy state where the net force is zero. This is achieved by modeling the plasma as perfectly conducting viscous fluid. It is an important tool for investigating plasma equilibria and is often used to study the magnetic configurations in fusion devices and astrophysical plasmas. We study the equilibrium reached by a localized magnetic field through the topology conserving relaxation of a magnetic field based on the Hopf fibration in which magnetic field lines are closed circles that are all linked with one another. Magnetic fields with this topology have recently been shown to occur in non-ideal numerical simulations. Our results show that any localized field can only attain equilibrium if there is a finite external pressure, and that for such a field a Taylor state is unattainable. We find an equilibrium plasma configuration that is characterized by a lowered pressure in a toroidal region, with field lines lying on surfaces of constant pressure. Therefore, the field is in a Grad-Shafranov equilibrium. Localized helical magnetic fields are found when plasma is ejected from astrophysical bodies and subsequently relaxes against the background plasma, as well as on earth in plasmoids generated by e.g.\ a Marshall gun. This work shows under which conditions an equilibrium can be reached and identifies a toroidal depression as the characteristic feature of such a configuration