Topological constraints on magnetic field relaxation

Magnetic field relaxation is determined by both the field's geometry and its topology. For relaxation processes, however, it turns out that its topology is a much more stringent constraint. As quantifier for the topology we use magnetic helicity and test whether it is a stronger condition than the linking of field lines. Further, we search for evidence of other topological invariants, which give rise to further restrictions in the field's relaxation. We find that magnetic helicity is the sole determinant in most cases. Nevertheless, we see evidence for restrictions not captured through magnetic helicity.Comment: 5 pages, 5 figures, proceedings of IAU Symp. 294, Solar and Astrophysical Dynamos and Magnetic Activit

Baseline Determination at Government Discretion: Multi-Project Baselines for the First Track of Joint Implementation?

The "first track" of Joint Implementation under the Kyoto Protocol gives host and investor countries total freedom in choosing a baseline for a project reducing or sequestering greenhouse gases. This is due to the fact that an overly generous granting of emission credits leads to a corresponding reduction of the host country's emission budget. Standardised, multi-project baselines can reduce transaction costs, especially in relatively homogeneous sectors such as electricity production or landfill methane collection. Host countries need capacity to calculate such baselines which currently does not exist. "Boundary organisations" can bridge the gap between technical analysis and strategic considerations. Interviews with government officials and other stakeholders in East European EU accession countries lead us to the conclusion that countries have not yet realised the chances and pitfalls of baseline definition under the first track, especially as they assume that the EU will define the "acquis communautaire" as the baseline. However, this would make international emissions trading more attractive than JI.Joint Implementation, baselines, institutions, host countries, Environmental Economics and Policy, Q25, O13,

Magnetic helicity fluxes and their effect on stellar dynamos

Magnetic helicity fluxes in turbulently driven alpha^2 dynamos are studied to demonstrate their ability to alleviate catastrophic quenching. A one-dimensional mean-field formalism is used to achieve magnetic Reynolds numbers of the order of 10^5. We study both diffusive magnetic helicity fluxes through the mid-plane as well as those resulting from the recently proposed alternate dynamic quenching formalism. By adding shear we make a parameter scan for the critical values of the shear and forcing parameters for which dynamo action occurs. For this $\alpha\Omega$ dynamo we find that the preferred mode is antisymmetric about the mid-plane. This is also verified in 3-D direct numerical simulations.Comment: 5 pages, 6 figures, proceedings of IAU Symp. 286, Comparative Magnetic Minima: characterizing quiet times in the Sun and star

A Navier Stokes Phase Field Crystal Model for Colloidal Suspensions

We develop a fully continuous model for colloidal suspensions with hydrodynamic interactions. The Navier Stokes Phase Field Crystal (NS-PFC) model combines ideas of dynamic density functional theory with particulate flow approaches and is derived in detail and related to other dynamic density functional theory approaches with hydrodynamic interactions. The derived system is numerically solved using adaptive finite elements and used to analyse colloidal crystallization in flowing environments demonstrating a strong coupling in both directions between the crystal shape and the flow field. We further validate the model against other computational approaches for particulate flow systems for various colloidal sedimentation problems

Magnetic field decay of three interlocked flux rings with zero linking number

The resistive decay of chains of three interlocked magnetic flux rings is considered. Depending on the relative orientation of the magnetic field in the three rings, the late-time decay can be either fast or slow. Thus, the qualitative degree of tangledness is less important than the actual value of the linking number or, equivalently, the net magnetic helicity. Our results do not suggest that invariants of higher order than that of the magnetic helicity need to be considered to characterize the decay of the field.Comment: 7 pages, 10 figure

Influence of Magnetic Helicity in MHD

Observations have shown that the Sun's magnetic field has helical structures. The helicity content in magnetic field configurations is a crucial constraint on the dynamical evolution of the system. Since helicity is connected with the number of links we investigate configurations with interlocked magnetic flux rings and one with unlinked rings. It turns out that it is not the linking of the tubes which affects the magnetic field decay, but the content of magnetic helicity.Comment: 2 pages, 3 figures, proceedings of IAU Symp. 271, Astrophysical Dynamics: from Stars to Galaxies, ed. N. Brummell and A.S. Brun, CU

Decay of helical and non-helical magnetic knots

We present calculations of the relaxation of magnetic field structures that have the shape of particular knots and links. A set of helical magnetic flux configurations is considered, which we call $n$-foil knots of which the trefoil knot is the most primitive member. We also consider two nonhelical knots; namely, the Borromean rings as well as a single interlocked flux rope that also serves as the logo of the Inter-University Centre for Astronomy and Astrophysics in Pune, India. The field decay characteristics of both configurations is investigated and compared with previous calculations of helical and nonhelical triple-ring configurations. Unlike earlier nonhelical configurations, the present ones cannot trivially be reduced via flux annihilation to a single ring. For the $n$-foil knots the decay is described by power laws that range form $t^{-2/3}$ to $t^{-1/3}$, which can be as slow as the $t^{-1/3}$ behavior for helical triple-ring structures that were seen in earlier work. The two nonhelical configurations decay like $t^{-1}$, which is somewhat slower than the previously obtained $t^{-3/2}$ behavior in the decay of interlocked rings with zero magnetic helicity. We attribute the difference to the creation of local structures that contain magnetic helicity which inhibits the field decay due to the existence of a lower bound imposed by the realizability condition. We show that net magnetic helicity can be produced resistively as a result of a slight imbalance between mutually canceling helical pieces as they are being driven apart. We speculate that higher order topological invariants beyond magnetic helicity may also be responsible for slowing down the decay of the two more complicated nonhelical structures mentioned above.Comment: 11 pages, 27 figures, submitted to Phys. Rev.

Magnetic helicity transport in the advective gauge family

Magnetic helicity fluxes are investigated in a family of gauges in which the contribution from ideal magnetohydrodynamics takes the form of a purely advective flux. Numerical simulations of magnetohydrodynamic turbulence in this advective gauge family exhibit instabilities triggered by the build-up of unphysical irrotational contributions to the magnetic vector potential. As a remedy, the vector potential is evolved in a numerically well behaved gauge, from which the advective vector potential is obtained by a gauge transformation. In the kinematic regime, the magnetic helicity density evolves similarly to a passive scalar when resistivity is small and turbulent mixing is mild, i.e. when the fluid Reynolds number is not too large. In the dynamical regime, resistive contributions to the magnetic helicity flux in the advective gauge are found to be significant owing to the development of small length scales in the irrotational part of the magnetic vector potential.Comment: 11 pages, 10 figures, submitted to Physics of Plasma

Speeding up Polyhedral Analysis by Identifying Common Constraints

AbstractSets of linear inequalities are an expressive reasoning tool for approximating the reachable states of a program. However, the most precise way to join two states is to calculate the convex hull of the two polyhedra that are represented by the inequality sets, an operation that is exponential in the dimension of the polyhedra. We investigate how similarities in the two input polyhedra can be exploited to improve the performance of this costly operation. In particular, we discuss how common equalities and certain inequalities can be omitted from the calculation without affecting the result. We expose a maximum of common equalities and inequalities by converting the polyhedra into a normal form and give experimental evidence of the merit of our method

Cooling in the shade of warped transition disks

The mass of the gaseous reservoir in young circumstellar disks is a crucial initial condition for the formation of planetary systems, but estimates vary by orders of magnitude. In some disks with resolvable cavities, sharp inner disk warps cast two-sided shadows on the outer rings; can the cooling of the gas as it crosses the shadows bring constraints on its mass? The finite cooling timescale should result in dust temperature decrements shifted ahead of the optical/IR shadows in the direction of rotation. However, some systems show temperature drops, while others do not. The depth of the drops and the amplitude of the shift depend on the outer disk surface density Sigma through the extent of cooling during the shadow crossing time, and also on the efficiency of radiative diffusion. These phenomena may bear observational counterparts, which we describe with a simple one-dimensional model. An application to the HD142527 disk suggests an asymmetry in its shadows, and predicts a >~10deg shift for a massive gaseous disk, with peak Sigma > 8.3 g/cm2. Another application to the DoAr44 disk limits the peak surface density to Sigma < 13g/cm2Comment: accepted to MNRAS Letter