55,445 research outputs found
On the significance of polarization charge and isomagnetic surface in the interaction between conducting fluid and magnetic field
From the frozen-in field lines concept, a highly conducting fluid can move
freely along, but not traverse to, magnetic field lines. We discuss this topic
and find that in the study of the frozen-in field lines concept, the effects of
inductive and capacitive reactance have been omitted. When admitted, the
relationships among the motional electromotive field, the induced electric
field, the eddy electric current, and the magnetic field becomes clearer and
the frozen-in field line concept can be reconsidered. We emphasize the
importance of isomagnetic surfaces and polarization charges, and show
analytically that whether a conducting fluid can freely traverse magnetic field
lines or not depends solely on the magnetic gradient in the direction of fluid
motion. If a fluid does not change its density distribution and shape (can be
regarded as a quasi-rigid body), and as long as it is moving along an
isomagnetic surface, it can freely traverse magnetic field lines without any
magnetic resistance no matter how strong the magnetic field is. When our
analysis is applied, the origin of the magnetic field of sunspots can be
interpreted easily. In addition, we also present experimental results to
support our analysis.Comment: 12 pages, 12 figures, 4 table
On the weighted forward reduced Entropy of Ricci flow
In this paper, we first introduce the weighted forward reduced volume of
Ricci flow. The weighted forward reduced volume, which related to expanders of
Ricci flow, is well-defined on noncompact manifolds and monotone non-increasing
under Ricci flow. Moreover, we show that, just the same as the Perelman's
reduced volume, the weighted reduced volume entropy has the value
if and only if the Ricci flow is the trivial flow on
flat Euclidean space.Comment: 10 page
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