Impact of Temperature-dependent resistivity and thermal conduction on plasmoid Instabilities in current sheets in the solar corona

In this paper we investigate, by means of two-dimensional magnetohydrodynamic simulations, the impact of temperature-dependent resistivity and thermal conduction on the development of plasmoid instabilities in reconnecting current sheets in the solar corona. We find that the plasma temperature in the current sheet region increases with time and it becomes greater than that in the inflow region. As secondary magnetic islands appear, the highest temperature is not always found at the reconnection $X$-points, but also inside the secondary islands. One of the effects of anisotropic thermal conduction is to decrease the temperature of the reconnecting $X-$points and transfer the heat into the $O-$points, the plasmoids, where it gets trapped. In the cases with temperature-dependent magnetic diffusivity, $eta sim T^{-3/2}$, the decrease in plasma temperature at the $X-$points leads to: (i) increase in the magnetic diffusivity until the characteristic time for magnetic diffusion becomes comparable to that of thermal conduction; (ii) increase in the reconnection rate; and, (iii) more efficient conversion of magnetic energy into thermal energy and kinetic energy of bulk motions. These results provide further explanation of the rapid release of magnetic energy into heat and kinetic energy seen during flares and coronal mass ejections. In this work, we demonstrate that the consideration of anisotropic thermal conduction and Spitzer-type, temperature-dependent magnetic diffusivity, as in the real solar corona, are crucially important for explaining the occurrence of fast reconnection during solar eruptions.

Sharp logarithmic Sobolev inequalities on gradient solitons and applications

We show that gradient shrinking, expanding or steady Ricci solitons have potentials leading to suitable reference probability measures on the manifold. For shrinking solitons, as well as expanding soltions with nonnegative Ricci curvature, these reference measures satisfy sharp logarithmic Sobolev inequalities with lower bounds characterized by the geometry of the manifold. The geometric invariant appearing in the sharp lower bound is shown to be nonnegative. We also characterize the expanders when such invariant is zero. In the proof various useful volume growth estimates are also established for gradient shrinking and expanding solitons. In particular, we prove that the {it asymptotic volume ratio} of any gradient shrinking soliton with nonnegative Ricci curvature must be zero.

An Adaptive Checkpointing Scheme for Peer-to-Peer Based Volunteer Computing Work Flows

Volunteer Computing, sometimes called Public Resource Computing, is an emerging computational model that is very suitable for work-pooled parallel processing. As more complex grid applications make use of work flows in their design and deployment it is reasonable to consider the impact of work flow deployment over a Volunteer Computing infrastructure. In this case, the inter work flow I/O can lead to a significant increase in I/O demands at the work pool server. A possible solution is the use of a Peer-to- Peer based parallel computing architecture to off-load this I/O demand to the workers; where the workers can fulfill some aspects of work flow coordination and I/O checking, etc. However, achieving robustness in such a large scale system is a challenging hurdle towards the decentralized execution of work flows and general parallel processes. To increase robustness, we propose and show the merits of using an adaptive checkpoint scheme that efficiently checkpoints the status of the parallel processes according to the estimation of relevant network and peer parameters. Our scheme uses statistical data observed during runtime to dynamically make checkpoint decisions in a completely de- centralized manner. The results of simulation show support for our proposed approach in terms of reduced required runtime.

On 4-dimensional gradient shrinking solitons

In this paper we classify the four dimensional gradient shrinking solitons under certain curvature conditions satisfied by all solitons arising from finite time singularities of Ricci flow on compact four manifolds with positive isotropic curvature. As a corollary we generalize a result of Perelman on three dimensional gradient shrinking solitons to dimension four.

On a classification of the gradient shrinking solitons

The main purpose of this article is to provide an alternate proof to a result of Perelman on gradient shrinking solitons. In dimension three we also generalize the result by removing the $kappa$-non-collapsing assumption. In high dimension this new method allows us to prove a classification result on gradient shrinking solitons with vanishing Weyl curvature tensor, which includes the rotationally symmetric ones.