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(E. Altshuler, T.H. Johansen, Y. Paltiel, 1: , S. Field, J. Witt, F. Nori, X. Ling, " Superconducting Vortex Avalanches", Phys. Rev. Lett. 74, 1206{1209, ( 1995). . , , . .

P. Jin, O. Ramos, K.E. Bassler, G. Reiter, E. Zeldov, C.W. Chu, \ Vortex avalanches with robust statistics observed in superconducting niobium", Phys. Rev. B 70, 140505 ( 2004)). , , .

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Rev. Lett., 64, 1613{1616 (1990)). -, , , . , , , .

(K.E. Bassler, M. Paczuski, \ Simple Model of Superconducting Vortex Avalanches", Phys. Rev.

Lett., 81, 3761{3764 (1998) K.E. Bassler, M. Paczuski, E. Altshuler, \ Simple model for plastic dynamics of a disordered ux-line lattice", Phys. Rev. B. 64, 224517 ( 2001)). , , , , . , .

, , : , (J.R. Clem, \ Granular and Superconducting Glass properties of the high-temperature superconductors", Physica C 153{155, 50{55 (1988)) { , . , , (S.L. Ginzburg, V.P. Khavronin, G.Yu. Logvinova, I.D. Lusyanin et al., \ Low- eld electrodynamics of high-Tc superconductors { theory and experiment", Physica C 174, 109{116 (1991)). (D.-X. Chen, J.J. Moreno, A. Hernando, \ Evolution from the vortex state to the critical state in a square-columnar Josephson-junction array", Phys. Rev. B 53, 6579{6584 (1996) A. Manjhofer, linebreake T. Wolf, W. Dieterich, \ Irreversible magnetization e ect in a network of resistively shunted tunnel junctions", Phys. Rev. B 44, 9634{9638 (1991)) , ( ).

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(G.A. Held, D.H. Solina, D.T. Keane, W.G. Hang, P.M. Horn, G. Grinstein, \ Experimental study of critical-mass uctuations in an evolving sandpile" Phys. Rev. Lett., 65, 1120{1123 (1990)). . . .

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2.1 - 'i, , Hext. @'i V sin 'i + @t = [Ji'i+1 ; ( Ji + Ji;1 )'i + Ji;1 'i;1 ] i =1 N @'V sin '1 + =[J1'2 ; J1'1 ] ; 2 hext @t @'N V sin 'N + =[;JN;1 'N + JN;1'N;1] +2 hext @t 16 al jc 8 al L L V = = a 2 a L Ji = hext = Hext (1) bi jc | , | L , | , a | , | .

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0,1,b a (W) (W) 0,0,(u/0) 0,20 (u/0) 0,0,0,0,0,0,0,0 0,0 50 100 150 200 250 300 332,48 32,50 32,52 32,u/0,W u/0,W 1110-1 c d 10-10-10-10-10- (W) 1x10- (W) 1x10-1x10-(u/0) (u/0) 1x10-10-10-1 10 11 u/0,W u/0,W1 3: , (u= ) (W) : a) Ji 1, b) Ji 1 1.01, c) Ji 1 1.2, = ;1:62, d) Ji 1 1.4, = ;1:2. [10]. . , .

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, , \ " , , , , . , , , (C.M. Aegerter, M.S. Welling, R.J. Wijngaarden, \ Self-organized croticality in Bean State in YBa2Cu3O7;x thin lms", Europhys. Lett. 65 753{7(2004)). , , , , . , , . ( 5).

4.1 - 'ij, #ij , Hext. d ij V sin + = sij( 'ij + ; 'i+1j ; ) ij ij+1 ij dt ; sij;1 ('ij;1 + ; 'i+1j;1 ; ) ij ij; 5: ( x y) . . , | , . [12].

d'ij V sin 'ij + = si;1j ( 'i;1j + ; 'ij ; ) i;1j+1 i;1j dt ; sij('ij + ; 'i+1j ; ) ij+1 ij 8 a2l 4 a2l V = jc = asij = a2 = hSiji : (2) Sij :

d iV sin + = si1 ('i1 + ; 'i+11 ; ) ; 2 hext i1 i2 idt d'1j V sin '1j + =2 hext ; s1j ('1j + ; '2j ; ) (3) 1j+1 1j dt hext = Hexta2=. .

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hn = hextn ; hextn;1 : (4) , ( 7).

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[1] S.L. Ginzburg, M.A. Pustovoit, N.E. Savitskaya, \ Interavalanche correlations in self-organized critical state of multijunction SQUID", Phys. Rev. E 57 (1998) 1319{1326.

[2] .. , .. , \ ", (1998) 688{694.

[3] .. and .. , \ ", 69 (1999) 119.

[4] .., .., " ", , 117 (2000) 227{241.

[5] .. , .. , \ ", 73 (2001) 163{166.

[6] .. , .. , , \ 1=f- ", 73 (2001) 243{247.

[7] S.L. Ginzburg and N.E. Savitskaya, \ Granular Superconductors and Sandpile Model with Intrinsic Spatial Randomness", Phys.

Rev. E 66 (2002) 026128.

[8] S.L. Ginzburg and N.E. Savitskaya \ Self-organization ofthe critical state in the physical systems described b y di erential equations", Acta Physica Slovaca, 52 (6) (2002) 597.

[9] S.L. Ginzburg and N.E. Savitskaya, \ Self-organized criticality in granular superconductors", LXXVII \Slow relaxation and nonequilibrium dynamics in condensed matter", Les Houches, France, 2002. Springer, 706{ 718 (2003).

[10] S.L. Ginzburg and N.E. Savitskaya, \ Self-organization of the critical state in granular superconductors", Jornal of Low Temperature Physics 130, No. 3/4 ( 2003) 333.

[11] S.L. Ginzburg, A.V. Nakin, N.E. Savitskaya, \ The magnetic ux dynamics in the critical state of one-dimensional discrete superconductor", Physica C 436/1 (2006) 17.

[12] .. , .. , .. , \ ", 130 (2006) 862{872.

[13] .., .., " ", - (2007) 156 .

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