Reconnection of Magnetic Lines in An Ideal Fluid
Reconnection of Magnetic Lines in An Ideal Fluid
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In our eReader you can find the full English version of the book. Read Reconnection of Magnetic Lines in An Ideal Fluid Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Reconnection of Magnetic Lines in An Ideal Fluid
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This seems to ■21- contradict the second corner solution above with 9^ > 0^^^ (S has the same sign as A). There is no strict contradiction since the standard elliptic existence theorem referred to does not apply to an unbounded sector. To consider just the relation of the sign of ^ to the sign of A, we employ the Green's function of the sector (always negative), ij^ = A I g|4'|'^ dx dy This implies that the sign of ^ is opposite to that of A except that a simple estimate shows that the integral... ceases to converge for r -*■ °° when > 9 ; thus there is no ^ o vac contradiction in the unbounded sector.
We see that the large angle solution, > Q^^^, / is not valid for the neighborhood of a corner inside an island (cf. Fig. 1). However, there is no reason to discard it in a nonsimple region (e. G. Outside the figure-eight in Fig. 1). The reader can verify that the sign of \p can change in an annulus .
A similar argument gives a somewhat different conclusion for bounded current, say Aijj = 1 .
What to read after Reconnection of Magnetic Lines in An Ideal Fluid?
You can find similar books in the "Read Also" column, or choose other free books by Harold Grad to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
This seems to ■21- contradict the second corner solution above with 9^ > 0^^^ (S has the same sign as A). There is no strict contradiction since the standard elliptic existence theorem referred to does not apply to an unbounded sector. To consider just the relation of the sign of ^ to the sign of A, we employ the Green's function of the sector (always negative), ij^ = A I g|4'|'^ dx dy This implies that the sign of ^ is opposite to that of A except that a simple estimate shows that the integral... ceases to converge for r -*■ °° when > 9 ; thus there is no ^ o vac contradiction in the unbounded sector.
We see that the large angle solution, > Q^^^, / is not valid for the neighborhood of a corner inside an island (cf. Fig. 1). However, there is no reason to discard it in a nonsimple region (e. G. Outside the figure-eight in Fig. 1). The reader can verify that the sign of \p can change in an annulus .
A similar argument gives a somewhat different conclusion for bounded current, say Aijj = 1 .
What to read after Reconnection of Magnetic Lines in An Ideal Fluid?
You can find similar books in the "Read Also" column, or choose other free books by Harold Grad to read onlineMoreLess
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