arXiv subjects

Lei Ni

Publications and source records attributed to Lei Ni.

At least 73 records · Page 4Linked to original sources

arXiv2013

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, $η\sim T^{-3/2}$, 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.

astro-ph.SR↗

arXiv2013

Effects of the non-uniform initial environment and the guide field on the plasmoid instability

Effects of non-uniform initial mass density and temperature on the plasmoid instability are studied via 2.5-dimensional resistive magnetohydrodynamic(MHD) simulations. Our results indicate that the development of the plasmoid instability is apparently prevented when the initial plasma density at the center of the current sheet is higher than that in the upstream region. As a result, the higher the plasma density at the center and the lower the plasma $β$ in the upstream region, the higher the critical Lundquist number needed for triggering secondary instabilities. When $β=0.2$, the critical Lundquist number is higher than $10^4$. For the same Lundquist number, the magnetic reconnection rate is lower for the lower plasma $β$ case. Oppositely, when the initial mass density is uniform and the Lundquist number is low, the magnetic reconnection rate turns out to be higher for the lower plasma $β$ case. For the high Lundquist number case ($>10^4$) with uniform initial mass density, the magnetic reconnection is not affected by the initial plasma $β$ and the temperature distribution. Our results indicate that the guide field has a limited impact on the plasmoid instability in resistive MHD.

physics.space-ph↗

arXiv2013

Entropy and a convergence theorem for Gauss curvature flow in high dimension

In this paper we prove uniform regularity estimates for the normalized Gauss curvature flow in higher dimensions. The convergence of solutions in $C^\infty$-topology to a smooth strictly convex soliton as $t$ approaches to infinity is obtained as a consequence of these estimates together with an earlier result of Andrews. The estimates are established via the study of a new entropy functional for the flow.

math.DG↗

arXiv2013

The plasmoid instability during asymmetric inflow magnetic reconnection

Theoretical studies of the plasmoid instability generally assume that the reconnecting magnetic fields are symmetric. We relax this assumption by performing two-dimensional resistive magnetohydrodynamic simulations of the plasmoid instability during asymmetric inflow magnetic reconnection. Magnetic asymmetry modifies the onset, scaling, and dynamics of this instability. Magnetic islands develop preferentially into the weak magnetic field upstream region. Outflow jets from individual X-points impact plasmoids obliquely rather than directly as in the symmetric case. Consequently, deposition of momentum by the outflow jets into the plasmoids is less efficient, the plasmoids develop net vorticity, and shear flow slows down secondary merging between islands. Secondary merging events have asymmetry along both the inflow and outflow directions. Downstream plasma is more turbulent in cases with magnetic asymmetry because islands are able to roll around each other after exiting the current sheet. As in the symmetric case, plasmoid formation facilitates faster reconnection for at least small and moderate magnetic asymmetries. However, when the upstream magnetic field strengths differ by a factor of four, the reconnection rate plateaus at a lower value than expected from scaling the symmetric results. We perform a parameter study to investigate the onset of the plasmoid instability as a function of magnetic asymmetry and domain size. There exist domain sizes for which symmetric simulations are stable but asymmetric simulations are unstable, suggesting that moderate magnetic asymmetry is somewhat destabilizing. We discuss the implications for plasmoid and flux rope formation in solar eruptions, laboratory reconnection experiments, and space plasmas. The differences between symmetric and asymmetric simulations provide some hints regarding the nature of the three-dimensional plasmoid instability.

physics.plasm-ph↗

arXiv2012

Poincaré-Lelong equation via the Hodge Laplace heat equation

In this paper, we develop a method of solving the Poincaré-Lelong equation, mainly via the study of the large time asymptotics of a global solution to the Hodge-Laplace heat equation on $(1, 1)$-forms. The method is effective in proving an optimal result when $M$ has nonnegative bisectional curvature. It also provides an alternate proof of a recent gap theorem of the first author.

math.DG↗

arXiv2011

Eigenvalue comparison on Bakry-Emery manifolds

We prove a comparison theorem on the first Neumann eigenvalue on Bakry-Emery manifolds. Examples are constructed to illustrate the sharpness of the result. A linear explicit lower bound is also proved. We also discuss the asymptotic sharpness of such a result.

math.AP↗

arXiv2011

Estimates on the modulus of expansion for vector fields solving nonlinear equations

By adapting methods of \cite{AC} we prove a sharp estimate on the expansion modulus of the gradient of the log of the parabolic kernel to the Schördinger operator with convex potential, which improves an earlier work of Brascamp-Lieb. We also include alternate proofs to the improved log-concavity estimate, and to the fundamental gap theorem of Andrews-Clutterbuck via the elliptic maximum principle. Some applications of the estimates are also obtained, including a sharp lower bound on the first eigenvalue.

math.DG↗

arXiv2011

An optimal gap theorem

By solving the Cauchy problem for the Hodge-Laplace heat equation for $d$-closed, positive $(1, 1)$-forms, we prove an optimal gap theorem for Kähler manifolds with nonnegative bisectional curvature which asserts that the manifold is flat if the average of the scalar curvature over balls of radius $r$ centered at any fixed point $o$ is a function of $o(r^{-2})$. Furthermore via a relative monotonicity estimate we obtain a stronger statement, namely a `positive mass' type result, asserting that if $(M, g)$ is not flat, then $\liminf_{r\to \infty} \frac{r^2}{V_o(r)}\int_{B_o(r)}\mathcal{S}(y)\, dμ(y)>0$ for any $o\in M$.

math.DG↗

arXiv2011

Ancient solutions of Ricci flow on spheres and generalized Hopf fibrations

Ancient solutions arise in the study of Ricci flow singularities. Motivated by the work of Fateev on 3-dimensional ancient solutions we construct high dimensional ancient solutions to Ricci flow on spheres and complex projective spaces as well as the twistor spaces over a compact quaternion-Kahler manifold. Differing from Fateev's examples most of our examples are non-collapsed. The construction of this paper, different from the ad hoc anastz of Fateev, is systematic, generalizing (as well as unifying) the previous constructions of Einstein metrics by Bourguignon-Karcher, Jensen, and Ziller in the sense that the existence problem to a backward nonlinear parabolic PDE is reduced to the study of nonlinear ODE systems. The key step of solving the reduced nonlinear ODE system is to find suitable monotonic and conserved quantities under Ricci flow with symmetry. Besides supplying new possible singularity models for Ricci flow on spheres and projective spaces, our solutions are counter-examples to some folklore conjectures on ancient solutions of Ricci flow on compact manifolds. As a by-product, we infer that some nonstandard Einstein metrics on spheres and complex projective spaces are unstable fixed points of the Ricci flow.

math.DG↗

arXiv2010

Sharp differential estimates of Li-Yau-Hamilton type for positive $(p,p)$-forms on Kähler manifolds

In this paper we study the heat equation (of Hodge-Laplacian) deformation of $(p, p)$-forms on a Kähler manifold. After identifying the condition and establishing that the positivity of a $(p, p)$-form solution is preserved under such an invariant condition we prove the sharp differential Harnack (in the sense of Li-Yau-Hamilton) estimates for the positive solutions of the Hodge-Laplacian heat equation. We also prove a nonlinear version coupled with the Kähler-Ricci flow and some interpolating matrix differential Harnack type estimates for both the Kähler-Ricci flow and the Ricci flow.

math.DG↗

arXiv2009

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.

math.DG↗

arXiv2009

Manifolds with 1/4-pinched flag curvature

We say that a nonnegatively curved manifold $(M,g)$ has quarter pinched flag curvature if for any two planes which intersect in a line the ratio of their sectional curvature is bounded above by 4. We show that these manifolds have nonnegative complex sectional curvature. By combining with a theorem of Brendle and Schoen it follows that any positively curved manifold with strictly quarter pinched flag curvature must be a space form. This in turn generalizes a result of Andrews and Nguyen in dimension 4. For odd dimensional manifolds we obtain results for the case that the flag curvature is pinched with some constant below one quarter, one of which generalizes a recent work of Petersen and Tao.

math.DG↗

arXiv2008

Local Aronson-Bénilan estimates and entropy formulae for porous medium and fast diffusion equations on manifolds

In this work we derive local gradient and Laplacian estimates of the Aronson-Bénilan and Li-Yau type for positive solutions of porous medium equations posed on Riemannian manifolds with a lower Ricci curvature bound. We also prove similar results for some fast diffusion equations. Inspired by Perelman's work we discover some new entropy formulae for these equations.

math.DG↗

arXiv2007

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.

cs.DC↗

arXiv2007

Local gradient estimates of p-harmonic functions, 1/H-flow, and an entropy formula

In the first part of this paper, we prove local interior and boundary gradient estimates for p-harmonic functions on general Riemannian manifolds. With these estimates, following the strategy in recent work of R. Moser, we prove an existence theorem for weak solutions to the level set formulation of the 1/H (inverse mean curvature) flow for hypersurfaces in ambient manifolds satisfying a sharp volume growth assumption. In the second part of this paper, we consider two parabolic analogues of the p-Laplace equation and prove sharp Li-Yau type gradient estimates for positive solutions to these equations on manifolds of nonnegative Ricci curvature. For one of these equations, we also prove an entropy monotonicity formula generalizing an earlier such formula of the second author for the linear heat equation. As an application of this formula, we show that a complete Riemannian manifold with non-negative Ricci curvature and sharp L^p-logarithmic Sobolev inequality must be isometric to Euclidean space.

math.AP↗

arXiv2007

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 $κ$-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.

math.DG↗

arXiv2007

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.

math.DG↗

arXiv2007

Positive Complex Sectional Curvature, Ricci Flow and the Differential Sphere Theorem

The paper provides a different proof of the result of Brendle-Schoen on the differential sphere theorem. It is shown directly that the invariant cone of curvature operators with positive (or non-negative) complex sectional curvature is preserved by the Ricci flow. This implies, by a result of Böhm-Wilking, that the normalized Ricci flow deforms such a metric to a metric of constant positive curvature. Using earlier work of Yau and Zheng it can be shown that a metric with strictly (pointwise) 1/4-pinched sectional curvature has positive complex sectional curvature. This gives a direct proof of Brendle-Schoen's recent differential sphere theorem, bypassing any discussion of positive isotropic curvature.

math.DG↗