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11.040000 0.0 Td (the ) Tj 16.440000 0.0 Td (event. ) Tj 31.200000 0.0 Td (Chap- ) Tj ET BT 1.000000 0 0 1 46.800000 387.480000 Tm 3 Tr 0 0 0 rg /F0 10.320000 Tf 0.000000 0.0 Td (man ) Tj 21.840000 0.0 Td (et ) Tj 11.040000 0.0 Td (al. ) Tj 15.000000 0.0 Td ([1999] ) Tj 27.360000 0.0 Td (focused ) Tj 35.400000 0.0 Td (on ) Tj 13.560000 0.0 Td (the ) Tj 16.200000 0.0 Td (statistics ) Tj 41.280000 0.0 Td (of ) Tj 10.680000 0.0 Td (large ) Tj 24.360000 0.0 Td (\(5000 ) Tj ET BT 1.000000 0 0 1 45.840000 376.680000 Tm 3 Tr 0 0 0 rg /F0 10.320000 Tf 0.000000 0.0 Td (cell\) ) Tj 21.120000 0.0 Td (systems. ) Tj 41.160000 0.0 Td (Their ) Tj 26.880000 0.0 Td (results ) Tj 31.440000 0.0 Td (showed ) Tj 34.200000 0.0 Td (that ) Tj 20.760000 0.0 Td (for ) Tj 14.760000 0.0 Td (slow ) Tj 21.240000 0.0 Td (fueling ) Tj ET BT 1.000000 0 0 1 45.960000 366.240000 Tm 3 Tr 0 0 0 rg /F0 10.680000 Tf 0.000000 0.0 Td (rate ) Tj 20.280000 0.0 Td (\(g ) Tj 11.520000 0.0 Td (<< ) Tj 13.080000 0.0 Td (\(z*\)\), ) Tj 26.400000 0.0 Td (the ) Tj 16.320000 0.0 Td (normalized ) Tj 50.640000 0.0 Td (probability ) Tj 50.280000 0.0 Td (Pro\(AXE\) ) Tj 39.000000 0.0 Td (ex- ) Tj ET BT 1.000000 0 0 1 46.080000 353.280000 Tm 3 Tr 0 0 0 rg /F0 12.720000 Tf 0.000000 0.0 Td (hibits ) Tj 28.560000 0.0 Td (two ) Tj 19.800000 0.0 Td (distinct ) Tj 36.960000 0.0 Td (regimes' ) Tj 42.000000 0.0 Td (PB ) Tj 17.040000 0.0 Td (cr ) Tj 12.360000 0.0 Td (\(AXE\) ) Tj 23.880000 0.0 Td (-\370'65 ) Tj 24.600000 0.0 Td (at ) Tj 12.480000 0.0 Td (small ) Tj ET BT 1.000000 0 0 1 57.120000 317.640000 Tm 3 Tr 0 0 0 rg /F0 7.800000 Tf 0.000000 0.0 Td (10 ) Tj 7.440000 0.0 Td (\370 ) Tj ET BT 1.000000 0 0 1 56.880000 277.320000 Tm 3 Tr 0 0 0 rg /F0 7.920000 Tf 0.000000 0.0 Td (10-' ) Tj ET BT 1.000000 0 0 1 47.400000 237.240000 Tm 3 Tr 0 0 0 rg /F0 7.920000 Tf 9.120000 0.0 Td (10-2 ) Tj ET BT 1.000000 0 0 1 56.520000 193.680000 Tm 3 Tr 0 0 0 rg /F0 8.040000 Tf 0.000000 0.0 Td (10 ) Tj 7.440000 0.0 Td (-3 ) Tj ET BT 1.000000 0 0 1 55.800000 147.240000 Tm 3 Tr 0 0 0 rg /F0 13.560000 Tf 0.000000 0.0 Td (10-'\17710 ) Tj 19.920000 0.0 Td (o ) Tj ET BT 1.000000 0 0 1 125.160000 147.120000 Tm 3 Tr 0 0 0 rg /F0 8.520000 Tf 0.000000 0.0 Td (10 ) Tj 7.680000 0.0 Td (\177 ) Tj 51.960000 0.0 Td (10 ) Tj 7.200000 0.0 Td (2 ) Tj 49.920000 0.0 Td (10 ) Tj 7.440000 0.0 Td (3 ) Tj ET BT 1.000000 0 0 1 167.280000 138.600000 Tm 3 Tr 0 0 0 rg /F0 5.280000 Tf 0.000000 0.0 Td (L ) Tj ET BT 1.000000 0 0 1 46.080000 121.680000 Tm 3 Tr 0 0 0 rg /F0 9.840000 Tf 0.000000 0.0 Td (Figure ) Tj 38.280000 0.0 Td (1. ) Tj 16.800000 0.0 Td (The ) Tj 22.200000 0.0 Td (probability ) Tj 52.920000 0.0 Td (distribution ) Tj 55.560000 0.0 Td (of ) Tj 12.960000 0.0 Td (avalanche ) Tj ET BT 1.000000 0 0 1 45.960000 110.880000 Tm 3 Tr 0 0 0 rg /F0 9.840000 Tf 0.000000 0.0 Td (lengths ) Tj 35.400000 0.0 Td (for ) Tj 16.200000 0.0 Td (four ) Tj 21.960000 0.0 Td (runs, ) Tj 26.160000 0.0 Td (corresponding ) Tj 65.520000 0.0 Td (to ) Tj 12.960000 0.0 Td (top-hat ) Tj 36.360000 0.0 Td (distri- ) Tj ET BT 1.000000 0 0 1 45.960000 98.880000 Tm 3 Tr 0 0 0 rg /F0 11.640000 Tf 0.000000 0.0 Td (butions ) Tj 36.120000 0.0 Td (P\(zj\) ) Tj 28.800000 0.0 Td (with ) Tj 23.160000 0.0 Td (mean ) Tj 27.000000 0.0 Td (value ) Tj 26.760000 0.0 Td (i ) Tj 7.920000 0.0 Td (and ) Tj 19.560000 0.0 Td (different ) Tj 39.720000 0.0 Td (widths. ) Tj ET BT 1.000000 0 0 1 45.960000 87.480000 Tm 3 Tr 0 0 0 rg /F0 10.320000 Tf 0.000000 0.0 Td (Marked ) Tj 37.440000 0.0 Td (with ) Tj 23.520000 0.0 Td (symbols ) Tj 39.360000 0.0 Td (are ) Tj 17.520000 0.0 Td (cases ) Tj 26.160000 0.0 Td (with ) Tj 23.640000 0.0 Td (widths ) Tj 33.000000 0.0 Td (0.01 ) Tj 22.320000 0.0 Td (\([2\), ) Tj ET BT 1.000000 0 0 1 45.960000 77.400000 Tm 3 Tr 0 0 0 rg /F0 10.440000 Tf 0.000000 0.0 Td (0.1 ) Tj 16.920000 0.0 Td (\(,\) ) Tj 16.080000 0.0 Td (and ) Tj 20.280000 0.0 Td (1 ) Tj 8.640000 0.0 Td (\(o\), ) Tj 18.960000 0.0 Td (and ) Tj 19.800000 0.0 Td (marked ) Tj 36.120000 0.0 Td (with ) Tj 23.160000 0.0 Td (bars ) Tj 21.840000 0.0 Td (is ) Tj 10.440000 0.0 Td (the ) Tj 17.520000 0.0 Td (analyt- ) Tj ET BT 1.000000 0 0 1 45.720000 67.080000 Tm 3 Tr 0 0 0 rg /F0 9.600000 Tf 0.000000 0.0 Td (ically ) Tj 27.720000 0.0 Td (soluble ) Tj 34.560000 0.0 Td (case ) Tj 22.800000 0.0 Td (where ) Tj 30.240000 0.0 Td (the ) Tj 18.600000 0.0 Td (critical ) Tj 34.440000 0.0 Td (gradient ) Tj 40.440000 0.0 Td (takes ) Tj 27.120000 0.0 Td (a ) Tj ET BT 1.000000 0 0 1 45.720000 56.640000 Tm 3 Tr 0 0 0 rg /F0 9.480000 Tf 0.000000 0.0 Td (single ) Tj 28.200000 0.0 Td (value. ) Tj ET BT 1.000000 0 0 1 300.000000 737.400000 Tm 3 Tr 0 0 0 rg /F0 12.240000 Tf 0.000000 0.0 Td (AXE, ) Tj 24.000000 0.0 Td (but ) Tj 19.800000 0.0 Td (proportional ) Tj 59.160000 0.0 Td (to ) Tj 14.520000 0.0 Td (\(AXE\) ) Tj 24.000000 0.0 Td (-\177 ) Tj 15.480000 0.0 Td (at ) Tj 13.440000 0.0 Td (large ) Tj 26.280000 0.0 Td (AXE, ) Tj 24.120000 0.0 Td (with ) Tj ET BT 1.000000 0 0 1 299.880000 728.880000 Tm 3 Tr 0 0 0 rg /F0 8.040000 Tf 0.000000 0.0 Td (transition ) Tj 45.960000 0.0 Td (at ) Tj 12.480000 0.0 Td (avalanches ) Tj 49.560000 0.0 Td (of ) Tj 11.880000 0.0 Td (size ) Tj 19.800000 0.0 Td (L ) Tj 9.960000 0.0 Td (\177 ) Tj 11.160000 0.0 Td (64 ) Tj 13.440000 0.0 Td (cells. ) Tj 26.760000 0.0 Td (Both ) Tj 25.440000 0.0 Td (the ) Tj ET BT 1.000000 0 0 1 299.880000 716.280000 Tm 3 Tr 0 0 0 rg /F0 10.080000 Tf 0.000000 0.0 Td (power ) Tj 29.280000 0.0 Td (law ) Tj 18.480000 0.0 Td (indices ) Tj 33.240000 0.0 Td (and ) Tj 19.800000 0.0 Td (the ) Tj 17.640000 0.0 Td (location ) Tj 38.280000 0.0 Td (of ) Tj 11.760000 0.0 Td (the ) Tj 17.640000 0.0 Td (transition ) Tj 45.840000 0.0 Td (in ) Tj ET BT 1.000000 0 0 1 300.000000 705.240000 Tm 3 Tr 0 0 0 rg /F0 10.560000 Tf 0.000000 0.0 Td (Pz\(AXE\) ) Tj 40.440000 0.0 Td (were ) Tj 23.160000 0.0 Td (shown ) Tj 30.960000 0.0 Td (to ) Tj 12.360000 0.0 Td (be ) Tj 13.920000 0.0 Td (robust ) Tj 31.800000 0.0 Td (against ) Tj 34.440000 0.0 Td (the ) Tj 17.640000 0.0 Td (parame- ) Tj ET BT 1.000000 0 0 1 299.880000 693.720000 Tm 3 Tr 0 0 0 rg /F0 11.760000 Tf 0.000000 0.0 Td (ter ) Tj 15.480000 0.0 Td (values ) Tj 29.400000 0.0 Td (of ) Tj 11.760000 0.0 Td (the ) Tj 17.160000 0.0 Td (top-hat ) Tj 35.880000 0.0 Td (distribution ) Tj 54.720000 0.0 Td (P\(z\177\). ) Tj 32.520000 0.0 Td (Of ) Tj 14.160000 0.0 Td (impor- ) Tj ET BT 1.000000 0 0 1 300.000000 683.400000 Tm 3 Tr 0 0 0 rg /F0 9.840000 Tf 0.000000 0.0 Td (tance ) Tj 26.040000 0.0 Td (to ) Tj 11.520000 0.0 Td (magnetospheric ) Tj 71.040000 0.0 Td (dynamics, ) Tj 46.800000 0.0 Td (the ) Tj 16.680000 0.0 Td (system ) Tj 32.640000 0.0 Td (was ) Tj 18.960000 0.0 Td (also ) Tj ET BT 1.000000 0 0 1 299.760000 672.600000 Tm 3 Tr 0 0 0 rg /F0 10.440000 Tf 0.000000 0.0 Td (examined ) Tj 44.160000 0.0 Td (under ) Tj 27.600000 0.0 Td (fast ) Tj 18.720000 0.0 Td (fueling ) Tj 31.920000 0.0 Td (g ) Tj 8.880000 0.0 Td (> ) Tj 10.560000 0.0 Td (\(z*\) ) Tj 20.040000 0.0 Td (and ) Tj 18.480000 0.0 Td (the ) Tj 16.560000 0.0 Td (power ) Tj 28.800000 0.0 Td (law ) Tj ET BT 1.000000 0 0 1 300.000000 662.160000 Tm 3 Tr 0 0 0 rg /F0 10.200000 Tf 0.000000 0.0 Td (regime ) Tj 32.640000 0.0 Td (for ) Tj 16.440000 0.0 Td (large ) Tj 25.080000 0.0 Td (events ) Tj 31.800000 0.0 Td (was ) Tj 19.920000 0.0 Td (robust ) Tj 32.280000 0.0 Td (under ) Tj 29.040000 0.0 Td (these ) Tj 26.280000 0.0 Td (condi- ) Tj ET BT 1.000000 0 0 1 300.000000 651.360000 Tm 3 Tr 0 0 0 rg /F0 10.800000 Tf 0.000000 0.0 Td (tions ) Tj 28.320000 0.0 Td ([Chapman ) Tj 47.760000 0.0 Td (et ) Tj 11.880000 0.0 Td (al., ) Tj 17.040000 0.0 Td (1999; ) Tj 27.480000 0.0 Td (Watkins ) Tj 38.040000 0.0 Td (et ) Tj 11.640000 0.0 Td (al., ) Tj 17.040000 0.0 Td (1999]. ) Tj ET BT 1.000000 0 0 1 309.960000 641.280000 Tm 3 Tr 0 0 0 rg /F0 9.840000 Tf 0.000000 0.0 Td (In ) Tj 12.960000 0.0 Td (this ) Tj 19.920000 0.0 Td (study, ) Tj 30.480000 0.0 Td (we ) Tj 15.240000 0.0 Td (have ) Tj 23.640000 0.0 Td (obtained ) Tj 42.000000 0.0 Td (the ) Tj 17.760000 0.0 Td (statistics ) Tj 42.240000 0.0 Td (of ) Tj 12.240000 0.0 Td (the ) Tj ET BT 1.000000 0 0 1 300.240000 631.440000 Tm 3 Tr 0 0 0 rg /F0 9.360000 Tf 0.000000 0.0 Td (avalanches ) Tj 49.560000 0.0 Td (based ) Tj 28.320000 0.0 Td (on ) Tj 14.760000 0.0 Td (their ) Tj 24.240000 0.0 Td (size, ) Tj 23.160000 0.0 Td (and ) Tj 19.560000 0.0 Td (found ) Tj 28.920000 0.0 Td (the ) Tj 17.520000 0.0 Td (normal- ) Tj ET BT 1.000000 0 0 1 300.120000 619.920000 Tm 3 Tr 0 0 0 rg /F0 10.320000 Tf 0.000000 0.0 Td (ized ) Tj 21.480000 0.0 Td (probability ) Tj 52.440000 0.0 Td (P\234\(L\) ) Tj 31.320000 0.0 Td (for ) Tj 16.920000 0.0 Td (avalanches ) Tj 50.280000 0.0 Td (of ) Tj 12.480000 0.0 Td (size ) Tj 20.520000 0.0 Td (L. ) Tj 17.280000 0.0 Td (Fig- ) Tj ET BT 1.000000 0 0 1 300.240000 609.360000 Tm 3 Tr 0 0 0 rg /F0 10.560000 Tf 0.000000 0.0 Td (ure ) Tj 17.280000 0.0 Td (i ) Tj 7.080000 0.0 Td (shows ) Tj 28.800000 0.0 Td (P\234\(L\) ) Tj 29.520000 0.0 Td (for ) Tj 15.360000 0.0 Td (the ) Tj 16.800000 0.0 Td (same ) Tj 24.960000 0.0 Td (data ) Tj 22.560000 0.0 Td (in ) Tj 12.480000 0.0 Td (Chapman ) Tj 43.920000 0.0 Td (et ) Tj 11.400000 0.0 Td (al. ) Tj ET BT 1.000000 0 0 1 300.720000 598.800000 Tm 3 Tr 0 0 0 rg /F0 10.440000 Tf 0.000000 0.0 Td ([1999]; ) Tj 31.080000 0.0 Td (we ) Tj 14.520000 0.0 Td (see ) Tj 16.320000 0.0 Td (that ) Tj 22.080000 0.0 Td (P\234 ) Tj 15.480000 0.0 Td (exhibits ) Tj 38.160000 0.0 Td (a ) Tj 8.280000 0.0 Td (power ) Tj 29.280000 0.0 Td (law ) Tj 18.000000 0.0 Td (with ) Tj 22.800000 0.0 Td (index ) Tj ET BT 1.000000 0 0 1 300.480000 588.840000 Tm 3 Tr 0 0 0 rg /F0 9.360000 Tf 0.000000 0.0 Td (-1 ) Tj 15.840000 0.0 Td (at ) Tj 12.120000 0.0 Td (large ) Tj 24.480000 0.0 Td (L. ) Tj ET BT 1.000000 0 0 1 310.200000 578.280000 Tm 3 Tr 0 0 0 rg /F0 9.960000 Tf 0.000000 0.0 Td (A ) Tj 11.880000 0.0 Td (special ) Tj 33.720000 0.0 Td (case ) Tj 22.680000 0.0 Td (of ) Tj 12.720000 0.0 Td (the ) Tj 18.720000 0.0 Td (model ) Tj 31.200000 0.0 Td (has ) Tj 19.080000 0.0 Td (been ) Tj 24.960000 0.0 Td (discussed ) Tj 44.520000 0.0 Td (by ) Tj ET BT 1.000000 0 0 1 300.360000 567.480000 Tm 3 Tr 0 0 0 rg /F0 10.440000 Tf 0.000000 0.0 Td (Helander ) Tj 44.880000 0.0 Td (et ) Tj 13.080000 0.0 Td (al. ) Tj 20.640000 0.0 Td ([1999]. ) Tj 37.800000 0.0 Td (These ) Tj 31.320000 0.0 Td (authors ) Tj 37.560000 0.0 Td (showed ) Tj 36.360000 0.0 Td (that ) Tj ET BT 1.000000 0 0 1 300.240000 557.400000 Tm 3 Tr 0 0 0 rg /F0 9.960000 Tf 0.000000 0.0 Td (the ) Tj 16.560000 0.0 Td (problem ) Tj 38.760000 0.0 Td (is ) Tj 9.600000 0.0 Td (exactly ) Tj 34.440000 0.0 Td (solvable ) Tj 37.560000 0.0 Td (analytically ) Tj 53.280000 0.0 Td (for ) Tj 15.240000 0.0 Td (the ) Tj 16.560000 0.0 Td (case ) Tj ET BT 1.000000 0 0 1 300.360000 544.680000 Tm 3 Tr 0 0 0 rg /F0 12.000000 Tf 0.000000 0.0 Td (P\(z\177\) ) Tj 31.320000 0.0 Td (= ) Tj 13.440000 0.0 Td (5\(z\177 ) Tj 22.440000 0.0 Td (- ) Tj 10.800000 0.0 Td (zo\). ) Tj 25.920000 0.0 Td (The ) Tj 22.800000 0.0 Td (system ) Tj 35.040000 0.0 Td (exhibits ) Tj 39.360000 0.0 Td (only ) Tj 23.760000 0.0 Td (one ) Tj ET BT 1.000000 0 0 1 300.240000 531.840000 Tm 3 Tr 0 0 0 rg /F0 12.600000 Tf 0.000000 0.0 Td (regime: ) Tj 39.840000 0.0 Td (Pz ) Tj 18.600000 0.0 Td (cr ) Tj 14.400000 0.0 Td (\(AXE\) ) Tj 24.000000 0.0 Td (-\177. ) Tj 22.800000 0.0 Td (It ) Tj 12.600000 0.0 Td (can ) Tj 20.520000 0.0 Td (also ) Tj 21.840000 0.0 Td (be ) Tj 15.120000 0.0 Td (shown ) Tj 32.160000 0.0 Td (that ) Tj ET BT 1.000000 0 0 1 300.600000 522.000000 Tm 3 Tr 0 0 0 rg /F0 9.600000 Tf 0.000000 0.0 Td (AE ) Tj 20.880000 0.0 Td (cr ) Tj 12.720000 0.0 Td (L ) Tj 11.040000 0.0 Td (for ) Tj 16.800000 0.0 Td (L ) Tj 11.760000 0.0 Td (>> ) Tj 15.600000 0.0 Td (1, ) Tj 12.120000 0.0 Td (although ) Tj 43.200000 0.0 Td (it ) Tj 11.160000 0.0 Td (was ) Tj 20.400000 0.0 Td (not ) Tj 18.960000 0.0 Td (mentioned ) Tj ET BT 1.000000 0 0 1 300.360000 511.320000 Tm 3 Tr 0 0 0 rg 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1.000000 0 0 1 44.760000 174.720000 Tm 3 Tr 0 0 0 rg /F0 9.840000 Tf 0.000000 0.0 Td (upper ) Tj 28.920000 0.0 Td (bound ) Tj 30.960000 0.0 Td (for ) Tj 15.840000 0.0 Td (the ) Tj 17.640000 0.0 Td (range ) Tj 27.480000 0.0 Td (of ) Tj 12.000000 0.0 Td (z\177 ) Tj 12.840000 0.0 Td (that ) Tj 21.840000 0.0 Td (satisfies ) Tj 37.320000 0.0 Td (the ) Tj 17.280000 0.0 Td (con- ) Tj ET BT 1.000000 0 0 1 44.520000 163.200000 Tm 3 Tr 0 0 0 rg /F0 10.920000 Tf 0.000000 0.0 Td (dition. ) Tj 36.000000 0.0 Td (This ) Tj 24.000000 0.0 Td (estimated ) Tj 47.160000 0.0 Td (upper ) Tj 29.520000 0.0 Td (bound ) Tj 31.800000 0.0 Td (is ) Tj 11.640000 0.0 Td ({z*l/k ) Tj 28.440000 0.0 Td (, ) Tj 6.480000 0.0 Td (where ) Tj ET BT 1.000000 0 0 1 45.120000 153.000000 Tm 3 Tr 0 0 0 rg /F0 10.920000 Tf 0.000000 0.0 Td (\(z*\) ) Tj 20.760000 0.0 Td (= ) Tj 11.520000 0.0 Td (\(z\177\) ) Tj 20.760000 0.0 Td (= ) Tj 11.520000 0.0 Td (\(z\177_\177\). ) Tj 35.760000 0.0 Td (Thus, ) Tj 28.920000 0.0 Td (the ) Tj 17.520000 0.0 Td (range ) Tj 27.720000 0.0 Td (of ) Tj 11.880000 0.0 Td (z\177 ) Tj 13.320000 0.0 Td (that ) Tj 22.080000 0.0 Td (con- ) Tj ET BT 1.000000 0 0 1 44.640000 141.960000 Tm 3 Tr 0 0 0 rg /F0 9.840000 Tf 0.000000 0.0 Td (tributes ) Tj 37.800000 0.0 Td (to ) Tj 12.960000 0.0 Td (the ) Tj 18.120000 0.0 Td (probability ) Tj 52.200000 0.0 Td (Qk ) Tj 16.440000 0.0 Td (decreases ) Tj 44.280000 0.0 Td (as ) Tj 13.080000 0.0 Td (k ) Tj 9.240000 0.0 Td (becomes ) Tj ET BT 1.000000 0 0 1 44.520000 130.920000 Tm 3 Tr 0 0 0 rg /F0 10.560000 Tf 0.000000 0.0 Td (larger. ) Tj 32.040000 0.0 Td (We ) Tj 16.800000 0.0 Td (therefore ) Tj 42.120000 0.0 Td (conclude ) Tj 40.800000 0.0 Td (that ) Tj 21.600000 0.0 Td (Q\177 ) Tj 15.480000 0.0 Td (is ) Tj 9.480000 0.0 Td (small ) Tj 25.920000 0.0 Td (for ) Tj 15.360000 0.0 Td (large ) Tj ET BT 1.000000 0 0 1 44.760000 120.960000 Tm 3 Tr 0 0 0 rg /F0 9.840000 Tf 0.000000 0.0 Td (k. ) Tj 12.840000 0.0 Td (Based ) Tj 29.280000 0.0 Td (on ) Tj 14.520000 0.0 Td (this ) Tj 19.680000 0.0 Td (argument, ) Tj 47.760000 0.0 Td (we ) Tj 14.640000 0.0 Td (expect ) Tj 31.920000 0.0 Td (that ) Tj 21.840000 0.0 Td (if ) Tj 9.480000 0.0 Td (N ) Tj 12.240000 0.0 Td (is ) Tj 10.080000 0.0 Td (suf- ) Tj ET BT 1.000000 0 0 1 44.160000 110.520000 Tm 3 Tr 0 0 0 rg /F0 9.720000 Tf 0.000000 0.0 Td (ficiently ) Tj 38.400000 0.0 Td (large, ) Tj 27.960000 0.0 Td (there ) Tj 26.040000 0.0 Td (exists ) Tj 28.200000 0.0 Td (a ) Tj 8.520000 0.0 Td (cell ) Tj 18.360000 0.0 Td (K ) Tj 12.960000 0.0 Td (< ) Tj 10.920000 0.0 Td (N ) Tj 12.360000 0.0 Td (such ) Tj 23.160000 0.0 Td (that ) Tj 21.840000 0.0 Td (for ) Tj ET BT 1.000000 0 0 1 44.520000 99.720000 Tm 3 Tr 0 0 0 rg /F0 10.080000 Tf 0.000000 0.0 Td (k ) Tj 8.640000 0.0 Td (> ) Tj 10.320000 0.0 Td (K, ) Tj 15.000000 0.0 Td (Q\177 ) Tj 15.840000 0.0 Td (is ) Tj 10.200000 0.0 Td (in ) Tj 11.760000 0.0 Td (the ) Tj 16.920000 0.0 Td (regime ) Tj 32.280000 0.0 Td (governed ) Tj 41.640000 0.0 Td (by ) Tj 13.920000 0.0 Td (the ) Tj 16.800000 0.0 Td (fixed ) Tj 24.480000 0.0 Td (point ) Tj ET BT 1.000000 0 0 1 54.480000 78.720000 Tm 3 Tr 0 0 0 rg /F0 9.960000 Tf 0.000000 0.0 Td (Now ) Tj 23.520000 0.0 Td (we ) Tj 15.600000 0.0 Td (renormalize ) Tj 55.440000 0.0 Td (the ) Tj 17.880000 0.0 Td (system, ) Tj 37.440000 0.0 Td (and ) Tj 19.920000 0.0 Td (study ) Tj 28.800000 0.0 Td (the ) Tj 18.120000 0.0 Td (be- ) Tj ET BT 1.000000 0 0 1 44.280000 68.280000 Tm 3 Tr 0 0 0 rg /F0 9.840000 Tf 0.000000 0.0 Td (havior ) Tj 30.840000 0.0 Td (near ) Tj 22.560000 0.0 Td (Q ) Tj 11.400000 0.0 Td (= ) Tj 10.800000 0.0 Td (0. ) Tj 13.080000 0.0 Td (For ) Tj 17.880000 0.0 Td (each ) Tj 22.560000 0.0 Td (step ) Tj 21.480000 0.0 Td (of ) Tj 11.760000 0.0 Td (transformation, ) Tj 71.520000 0.0 Td (L ) Tj ET BT 1.000000 0 0 1 44.280000 58.440000 Tm 3 Tr 0 0 0 rg /F0 9.240000 Tf 0.000000 0.0 Td (and ) Tj 19.560000 0.0 Td (Q ) Tj 10.800000 0.0 Td (evolve ) Tj 30.600000 0.0 Td (as: ) Tj ET BT 1.000000 0 0 1 351.600000 736.920000 Tm 3 Tr 0 0 0 rg /F0 11.640000 Tf 0.000000 0.0 Td (L'=L/2, ) Tj 51.240000 0.0 Td (and ) Tj 22.800000 0.0 Td (Q'=2Q-Q2. ) Tj 103.680000 0.0 Td (\(7\) ) Tj ET BT 1.000000 0 0 1 300.000000 716.760000 Tm 3 Tr 0 0 0 rg /F0 10.320000 Tf 0.000000 0.0 Td (Near ) Tj 25.320000 0.0 Td (Q ) Tj 11.880000 0.0 Td (= ) Tj 12.120000 0.0 Td (0, ) Tj 12.000000 0.0 Td (the ) Tj 18.240000 0.0 Td (last ) Tj 19.680000 0.0 Td (term ) Tj 24.960000 0.0 Td (in ) Tj 13.320000 0.0 Td (\(7\) ) Tj 16.200000 0.0 Td (is ) Tj 10.800000 0.0 Td (small. ) Tj 32.520000 0.0 Td (Thus, ) Tj 29.400000 0.0 Td (one ) Tj ET BT 1.000000 0 0 1 299.880000 706.920000 Tm 3 Tr 0 0 0 rg /F0 9.240000 Tf 0.000000 0.0 Td (can ) Tj 18.240000 0.0 Td (show ) Tj 25.200000 0.0 Td (that ) Tj 21.840000 0.0 Td (under ) Tj 28.680000 0.0 Td (the ) Tj 17.280000 0.0 Td (transformation, ) Tj ET BT 1.000000 0 0 1 375.360000 684.840000 Tm 3 Tr 0 0 0 rg /F0 11.640000 Tf 0.000000 0.0 Td (Q ) Tj 10.680000 0.0 Td (-\177 ) Tj 11.280000 0.0 Td (1/L ) Tj 18.720000 0.0 Td (+ ) Tj 9.960000 0.0 Td (0\(1/L2\). ) Tj ET BT 1.000000 0 0 1 529.200000 684.480000 Tm 3 Tr 0 0 0 rg /F0 10.200000 Tf 0.000000 0.0 Td (\(8\) ) Tj ET BT 1.000000 0 0 1 300.000000 665.280000 Tm 3 Tr 0 0 0 rg /F0 9.360000 Tf 0.000000 0.0 Td (Or ) Tj 14.760000 0.0 Td (QL ) Tj 17.640000 0.0 Td (is ) Tj 9.840000 0.0 Td (an ) Tj 13.440000 0.0 Td (invariant ) Tj 42.120000 0.0 Td (under ) Tj 28.200000 0.0 Td (the ) Tj 17.400000 0.0 Td (RG ) Tj 17.760000 0.0 Td (transformation ) Tj 67.920000 0.0 Td (for ) Tj ET BT 1.000000 0 0 1 299.760000 654.600000 Tm 3 Tr 0 0 0 rg /F0 9.720000 Tf 0.000000 0.0 Td (large ) Tj 24.960000 0.0 Td (L ) Tj 10.200000 0.0 Td (and ) Tj 19.320000 0.0 Td (small ) Tj 26.760000 0.0 Td (Q. ) Tj 15.480000 0.0 Td (Note ) Tj 24.600000 0.0 Td (that ) Tj 22.080000 0.0 Td (this ) Tj 19.560000 0.0 Td (result ) Tj 27.960000 0.0 Td (is ) Tj 10.560000 0.0 Td (true ) Tj 21.240000 0.0 Td (only ) Tj ET BT 1.000000 0 0 1 299.400000 644.040000 Tm 3 Tr 0 0 0 rg /F0 9.600000 Tf 0.000000 0.0 Td (for ) Tj 15.840000 0.0 Td (avalanches ) Tj 49.680000 0.0 Td (of ) Tj 11.760000 0.0 Td (large ) Tj 25.200000 0.0 Td (L, ) Tj 13.080000 0.0 Td (where ) Tj 29.400000 0.0 Td (Q ) Tj 11.160000 0.0 Td (is ) Tj 10.440000 0.0 Td (close ) Tj 24.360000 0.0 Td (to ) Tj 12.360000 0.0 Td (the ) Tj 17.400000 0.0 Td (fixed ) Tj ET BT 1.000000 0 0 1 299.760000 633.720000 Tm 3 Tr 0 0 0 rg /F0 9.480000 Tf 0.000000 0.0 Td (point. ) Tj 30.000000 0.0 Td (In ) Tj 12.120000 0.0 Td (this ) Tj 19.080000 0.0 Td (regime, ) Tj 35.280000 0.0 Td (the ) Tj 16.800000 0.0 Td (probability ) Tj 51.120000 0.0 Td (that ) Tj 21.480000 0.0 Td (an ) Tj 13.440000 0.0 Td (avalanche ) Tj ET BT 1.000000 0 0 1 299.520000 623.040000 Tm 3 Tr 0 0 0 rg /F0 9.600000 Tf 0.000000 0.0 Td (which ) Tj 28.440000 0.0 Td (has ) Tj 17.400000 0.0 Td (reached ) Tj 36.240000 0.0 Td (a ) Tj 7.680000 0.0 Td (cell ) Tj 17.760000 0.0 Td (k ) Tj 8.280000 0.0 Td (will ) Tj 18.360000 0.0 Td (go ) Tj 12.960000 0.0 Td (no ) Tj 13.200000 0.0 Td (further ) Tj 33.360000 0.0 Td (is ) Tj 9.720000 0.0 Td (inversely ) Tj ET BT 1.000000 0 0 1 299.640000 612.480000 Tm 3 Tr 0 0 0 rg /F0 9.480000 Tf 0.000000 0.0 Td (proportional ) Tj 58.800000 0.0 Td (to ) Tj 13.440000 0.0 Td (the ) Tj 18.240000 0.0 Td (length ) Tj 31.800000 0.0 Td (of ) Tj 12.480000 0.0 Td (the ) Tj 18.480000 0.0 Td (avalanche ) Tj 46.200000 0.0 Td (itself. ) Tj 31.320000 0.0 Td (Of ) Tj ET BT 1.000000 0 0 1 299.520000 601.920000 Tm 3 Tr 0 0 0 rg /F0 9.600000 Tf 0.000000 0.0 Td (course, ) Tj 33.120000 0.0 Td (if ) Tj 8.880000 0.0 Td (the ) Tj 16.680000 0.0 Td (avalanche ) Tj 44.760000 0.0 Td (stops ) Tj 25.560000 0.0 Td (at ) Tj 11.760000 0.0 Td (cell ) Tj 17.400000 0.0 Td (k, ) Tj 11.040000 0.0 Td (its ) Tj 13.440000 0.0 Td (!ength ) Tj 30.240000 0.0 Td (will ) Tj 18.480000 0.0 Td (be ) Tj ET BT 1.000000 0 0 1 300.240000 589.560000 Tm 3 Tr 0 0 0 rg /F0 11.160000 Tf 0.000000 0.0 Td (k. ) Tj 12.240000 0.0 Td (We ) Tj 16.200000 0.0 Td (can ) Tj 17.520000 0.0 Td (thus ) Tj 21.000000 0.0 Td (express ) Tj 34.200000 0.0 Td (the ) Tj 16.320000 0.0 Td (result ) Tj 26.880000 0.0 Td (as ) Tj 11.400000 0.0 Td (Q\177 ) Tj 15.720000 0.0 Td (cr ) Tj 10.440000 0.0 Td (k ) Tj 5.880000 0.0 Td (-\177 ) Tj 10.680000 0.0 Td (+O\(k-2\). ) Tj ET BT 1.000000 0 0 1 300.120000 580.080000 Tm 3 Tr 0 0 0 rg /F0 9.360000 Tf 0.000000 0.0 Td (Now ) Tj 21.840000 0.0 Td (let ) Tj 13.560000 0.0 Td (us ) Tj 11.760000 0.0 Td (consider ) Tj 38.400000 0.0 Td (not ) Tj 17.040000 0.0 Td (only ) Tj 21.240000 0.0 Td (those ) Tj 25.200000 0.0 Td (avalanches ) Tj 48.480000 0.0 Td (that ) Tj 20.760000 0.0 Td (reach ) Tj ET BT 1.000000 0 0 1 300.240000 569.400000 Tm 3 Tr 0 0 0 rg /F0 9.600000 Tf 0.000000 0.0 Td (k, ) Tj 11.160000 0.0 Td (but ) Tj 17.880000 0.0 Td (avalanches ) Tj 48.960000 0.0 Td (of ) Tj 11.160000 0.0 Td (all ) Tj 13.320000 0.0 Td (lengths. ) Tj 38.520000 0.0 Td (An ) Tj 16.080000 0.0 Td (arbitrary ) Tj 42.120000 0.0 Td (avalanche ) Tj ET BT 1.000000 0 0 1 300.120000 558.720000 Tm 3 Tr 0 0 0 rg /F0 9.720000 Tf 0.000000 0.0 Td (that ) Tj 23.040000 0.0 Td (stops ) Tj 27.480000 0.0 Td (at ) Tj 13.800000 0.0 Td (k ) Tj 11.040000 0.0 Td (> ) Tj 12.720000 0.0 Td (K ) Tj 13.800000 0.0 Td (must ) Tj 26.520000 0.0 Td (have ) Tj 24.480000 0.0 Td (propagated ) Tj 54.000000 0.0 Td (through ) Tj ET BT 1.000000 0 0 1 300.360000 548.520000 Tm 3 Tr 0 0 0 rg /F0 9.360000 Tf 0.000000 0.0 Td (K, ) Tj 13.320000 0.0 Td (K+i,..., ) Tj 45.840000 0.0 Td (k-1. ) Tj 27.000000 0.0 Td (Hence, ) Tj 31.920000 0.0 Td (for ) Tj 15.240000 0.0 Td (k ) Tj 8.520000 0.0 Td (> ) Tj 10.560000 0.0 Td (K, ) Tj 14.280000 0.0 Td (we ) Tj 14.280000 0.0 Td (can ) Tj 17.760000 0.0 Td (normalize ) Tj ET BT 1.000000 0 0 1 300.240000 537.120000 Tm 3 Tr 0 0 0 rg /F0 10.440000 Tf 0.000000 0.0 Td (PL ) Tj 15.480000 0.0 Td (by ) Tj 14.160000 0.0 Td (the ) Tj 16.800000 0.0 Td (factor ) Tj 29.880000 0.0 Td (\(1- ) Tj 20.880000 0.0 Td (Q\177\)... ) Tj 32.040000 0.0 Td (\(1- ) Tj 20.520000 0.0 Td (QK-\177\), ) Tj 36.120000 0.0 Td (and ) Tj 19.440000 0.0 Td (write: ) Tj ET BT 1.000000 0 0 1 306.480000 516.600000 Tm 3 Tr 0 0 0 rg /F0 10.560000 Tf 0.000000 0.0 Td (PL\(L ) Tj 25.920000 0.0 Td (= ) Tj 10.680000 0.0 Td (k\) ) Tj 12.720000 0.0 Td (cr ) Tj 11.640000 0.0 Td (\(1 ) Tj 11.040000 0.0 Td (- ) Tj 9.960000 0.0 Td (QK\)\(1 ) Tj 31.200000 0.0 Td (- ) Tj 9.600000 0.0 Td (QK+\177\) ) Tj 32.040000 0.0 Td (. ) Tj 4.560000 0.0 Td (. ) Tj 4.560000 0.0 Td (. ) Tj 4.320000 0.0 Td (\(1 ) Tj 10.920000 0.0 Td (- ) Tj 9.600000 0.0 Td (Q\177_\177\)Qk ) Tj ET BT 1.000000 0 0 1 355.800000 501.720000 Tm 3 Tr 0 0 0 rg /F0 11.760000 Tf 26.520000 0.0 Td (+ ) Tj 9.960000 0.0 Td (O\(Q ) Tj ET BT 1.000000 0 0 1 355.800000 486.480000 Tm 3 Tr 0 0 0 rg /F0 11.880000 Tf 0.000000 0.0 Td (oc ) Tj 11.160000 0.0 Td (k ) Tj 5.880000 0.0 Td (-\177 ) Tj 12.960000 0.0 Td (+ ) Tj 9.960000 0.0 Td (O\(k-2\), ) Tj 133.440000 0.0 Td (\(9\) ) Tj ET BT 1.000000 0 0 1 300.240000 465.960000 Tm 3 Tr 0 0 0 rg /F0 10.200000 Tf 0.000000 0.0 Td (as ) Tj 13.080000 0.0 Td (all ) Tj 14.400000 0.0 Td (the ) Tj 17.880000 0.0 Td (Q's ) Tj 18.480000 0.0 Td (in ) Tj 12.720000 0.0 Td (Eq. ) Tj 19.320000 0.0 Td (\(9\) ) Tj 16.320000 0.0 Td (are ) Tj 17.400000 0.0 Td (much ) Tj 27.120000 0.0 Td (smaller ) Tj 35.520000 0.0 Td (than ) Tj 24.240000 0.0 Td (unity. ) Tj ET BT 1.000000 0 0 1 299.880000 456.240000 Tm 3 Tr 0 0 0 rg /F0 9.480000 Tf 0.000000 0.0 Td (This ) Tj 23.160000 0.0 Td (result ) Tj 27.720000 0.0 Td (is ) Tj 10.200000 0.0 Td (equivalent ) Tj 48.000000 0.0 Td (to ) Tj ET BT 1.000000 0 0 1 367.320000 433.800000 Tm 3 Tr 0 0 0 rg /F0 11.760000 Tf 0.000000 0.0 Td (PL\(L\) ) Tj 30.120000 0.0 Td (cr ) Tj 10.800000 0.0 Td (L-\177 ) Tj 19.800000 0.0 Td (+ ) Tj 9.960000 0.0 Td (O\(L-2\). ) Tj ET BT 1.000000 0 0 1 524.160000 433.800000 Tm 3 Tr 0 0 0 rg /F0 10.320000 Tf 0.000000 0.0 Td (\(10\) ) Tj ET BT 1.000000 0 0 1 299.760000 413.280000 Tm 3 Tr 0 0 0 rg /F0 10.440000 Tf 0.000000 0.0 Td (Therefore, ) Tj 48.000000 0.0 Td (for ) Tj 15.240000 0.0 Td (small ) Tj 26.280000 0.0 Td (Q\177 ) Tj 16.560000 0.0 Td (\(or ) Tj 15.240000 0.0 Td (large ) Tj 24.360000 0.0 Td (L, ) Tj 12.360000 0.0 Td (see ) Tj 16.080000 0.0 Td (Fig. ) Tj 20.880000 0.0 Td (1\), ) Tj 14.040000 0.0 Td (our ) Tj 17.640000 0.0 Td (RG ) Tj ET BT 1.000000 0 0 1 300.120000 403.560000 Tm 3 Tr 0 0 0 rg /F0 9.720000 Tf 0.000000 0.0 Td (analysis ) Tj 38.400000 0.0 Td (has ) Tj 18.600000 0.0 Td (reproduced ) Tj 53.280000 0.0 Td (to ) Tj 13.080000 0.0 Td (the ) Tj 17.880000 0.0 Td (leading ) Tj 35.280000 0.0 Td (order ) Tj 27.120000 0.0 Td (the ) Tj 17.880000 0.0 Td (scal- ) Tj ET BT 1.000000 0 0 1 299.880000 393.120000 Tm 3 Tr 0 0 0 rg /F0 9.600000 Tf 0.000000 0.0 Td (ing ) Tj 17.040000 0.0 Td (law ) Tj 18.360000 0.0 Td (obtained ) Tj 41.520000 0.0 Td (by ) Tj 14.280000 0.0 Td (large-scale ) Tj 48.960000 0.0 Td (avalanche ) Tj 45.480000 0.0 Td (model ) Tj 30.120000 0.0 Td (calcu- ) Tj ET BT 1.000000 0 0 1 299.880000 384.720000 Tm 3 Tr 0 0 0 rg /F0 7.440000 Tf 0.000000 0.0 Td (lations. ) Tj ET BT 1.000000 0 0 1 310.080000 372.120000 Tm 3 Tr 0 0 0 rg /F0 9.600000 Tf 0.000000 0.0 Td (The ) Tj 21.240000 0.0 Td (analysis ) Tj 38.280000 0.0 Td (above, ) Tj 32.040000 0.0 Td (however, ) Tj 41.880000 0.0 Td (has ) Tj 18.240000 0.0 Td (yet ) Tj 17.640000 0.0 Td (to ) Tj 12.360000 0.0 Td (explain ) Tj 35.760000 0.0 Td (the ) Tj ET BT 1.000000 0 0 1 300.000000 361.800000 Tm 3 Tr 0 0 0 rg /F0 9.360000 Tf 0.000000 0.0 Td (power ) Tj 30.480000 0.0 Td (law ) Tj 19.080000 0.0 Td (behavior ) Tj 42.000000 0.0 Td (for ) Tj 17.040000 0.0 Td (PE. ) Tj 23.640000 0.0 Td (Here ) Tj 24.720000 0.0 Td (we ) Tj 16.080000 0.0 Td (look ) Tj 22.320000 0.0 Td (for ) Tj 16.920000 0.0 Td (a ) Tj 9.360000 0.0 Td (rela- ) Tj ET BT 1.000000 0 0 1 300.000000 351.120000 Tm 3 Tr 0 0 0 rg /F0 9.600000 Tf 0.000000 0.0 Td (tionship ) Tj 38.640000 0.0 Td (between ) Tj 39.240000 0.0 Td (AE ) Tj 20.160000 0.0 Td (and ) Tj 19.800000 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(system, ) Tj 35.520000 0.0 Td (given ) Tj 25.440000 0.0 Td (by ) Tj 13.200000 0.0 Td (Eq. ) Tj 17.640000 0.0 Td (\(1\), ) Tj 17.400000 0.0 Td (scales ) Tj 27.120000 0.0 Td (as ) Tj 11.280000 0.0 Td (the ) Tj 15.960000 0.0 Td (system ) Tj ET BT 1.000000 0 0 1 299.640000 308.760000 Tm 3 Tr 0 0 0 rg /F0 9.720000 Tf 0.000000 0.0 Td (size ) Tj 19.320000 0.0 Td (N. ) Tj 15.960000 0.0 Td (When ) Tj 28.920000 0.0 Td (we ) Tj 14.760000 0.0 Td (renormalize, ) Tj 57.120000 0.0 Td (the ) Tj 16.920000 0.0 Td (length ) Tj 30.360000 0.0 Td (of ) Tj 11.160000 0.0 Td (the ) Tj 16.800000 0.0 Td (system ) Tj ET BT 1.000000 0 0 1 299.760000 298.440000 Tm 3 Tr 0 0 0 rg /F0 9.720000 Tf 0.000000 0.0 Td (is ) Tj 10.560000 0.0 Td (halved. ) Tj 36.480000 0.0 Td (One ) Tj 21.000000 0.0 Td (can ) Tj 18.840000 0.0 Td (thus ) Tj 22.320000 0.0 Td (write ) Tj 26.040000 0.0 Td (the ) Tj 17.640000 0.0 Td (renormalized ) Tj 59.640000 0.0 Td (energy ) Tj ET BT 1.000000 0 0 1 300.000000 287.880000 Tm 3 Tr 0 0 0 rg /F0 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BT 1.000000 0 0 1 46.560000 499.680000 Tm 3 Tr 0 0 0 rg /F0 10.320000 Tf 0.000000 0.0 Td (The ) Tj 21.120000 0.0 Td (FSOC ) Tj 30.360000 0.0 Td (behavior ) Tj 41.040000 0.0 Td (demonstrated ) Tj 63.360000 0.0 Td (by ) Tj 13.920000 0.0 Td (this ) Tj 19.560000 0.0 Td (class ) Tj 23.280000 0.0 Td (of ) Tj 11.520000 0.0 Td (sys- ) Tj ET BT 1.000000 0 0 1 46.560000 489.000000 Tm 3 Tr 0 0 0 rg /F0 10.440000 Tf 0.000000 0.0 Td (tems ) Tj 24.720000 0.0 Td (is ) Tj 10.560000 0.0 Td (of ) Tj 12.120000 0.0 Td (particular ) Tj 47.160000 0.0 Td (interest ) Tj 36.720000 0.0 Td (in ) Tj 12.240000 0.0 Td (the ) Tj 17.640000 0.0 Td (study ) Tj 28.080000 0.0 Td (of ) Tj 12.000000 0.0 Td (the ) Tj 17.640000 0.0 Td (mag- ) Tj ET BT 1.000000 0 0 1 46.440000 479.400000 Tm 3 Tr 0 0 0 rg /F0 9.480000 Tf 0.000000 0.0 Td (netospheric ) Tj 53.880000 0.0 Td (dynamics; ) Tj 48.360000 0.0 Td (statistics ) Tj 42.960000 0.0 Td (of ) Tj 12.240000 0.0 Td (internal ) Tj 37.800000 0.0 Td (avalanches ) Tj ET BT 1.000000 0 0 1 46.560000 467.880000 Tm 3 Tr 0 0 0 rg /F0 10.440000 Tf 0.000000 0.0 Td (in ) Tj 12.600000 0.0 Td (the ) Tj 18.120000 0.0 Td (models ) Tj 34.680000 0.0 Td (exhibits ) Tj 39.000000 0.0 Td (two ) Tj 19.800000 0.0 Td (scale-free ) Tj 44.280000 0.0 Td (regions, ) Tj 37.560000 0.0 Td (whereas ) Tj ET BT 1.000000 0 0 1 46.440000 458.640000 Tm 3 Tr 0 0 0 rg /F0 9.360000 Tf 0.000000 0.0 Td (that ) Tj 21.120000 0.0 Td (of ) Tj 11.160000 0.0 Td (systemwide ) Tj 52.920000 0.0 Td (events ) Tj 30.480000 0.0 Td (has ) Tj 17.640000 0.0 Td (a ) Tj 7.800000 0.0 Td (well-defined ) Tj 54.240000 0.0 Td (mean. ) Tj 30.480000 0.0 Td (RG ) Tj ET BT 1.000000 0 0 1 46.680000 447.360000 Tm 3 Tr 0 0 0 rg /F0 9.960000 Tf 0.000000 0.0 Td (analysis ) Tj 38.160000 0.0 Td (has ) Tj 18.960000 0.0 Td (allowed ) Tj 36.240000 0.0 Td (us ) Tj 13.560000 0.0 Td (to ) Tj 12.720000 0.0 Td (explain ) Tj 35.760000 0.0 Td (the ) Tj 17.760000 0.0 Td (power-law ) Tj 47.640000 0.0 Td (rela- ) Tj ET BT 1.000000 0 0 1 46.440000 436.800000 Tm 3 Tr 0 0 0 rg /F0 10.080000 Tf 0.000000 0.0 Td (tions ) Tj 25.320000 0.0 Td (that ) Tj 22.440000 0.0 Td (characterize ) Tj 56.640000 0.0 Td (the ) Tj 18.120000 0.0 Td (large-scale ) Tj 49.320000 0.0 Td (regime ) Tj 32.880000 0.0 Td (of ) Tj 12.240000 0.0 Td (inter- ) Tj ET BT 1.000000 0 0 1 46.200000 426.120000 Tm 3 Tr 0 0 0 rg /F0 10.200000 Tf 0.000000 0.0 Td (nal ) Tj 17.040000 0.0 Td (avalanches ) Tj 49.440000 0.0 Td (in ) Tj 11.640000 0.0 Td (the ) Tj 17.280000 0.0 Td (sandpile ) Tj 39.360000 0.0 Td (systems. ) Tj 41.160000 0.0 Td (The ) Tj 20.760000 0.0 Td (analysis ) Tj 37.320000 0.0 Td (is ) Tj ET BT 1.000000 0 0 1 46.200000 415.560000 Tm 3 Tr 0 0 0 rg /F0 10.080000 Tf 0.000000 0.0 Td (quite ) Tj 25.440000 0.0 Td (general, ) Tj 38.040000 0.0 Td (and ) Tj 19.440000 0.0 Td (is ) Tj 10.440000 0.0 Td (applicable ) Tj 47.640000 0.0 Td (to ) Tj 12.120000 0.0 Td (other ) Tj 26.040000 0.0 Td (sandpile ) Tj 39.120000 0.0 Td (mod- ) Tj ET BT 1.000000 0 0 1 46.080000 405.240000 Tm 3 Tr 0 0 0 rg /F0 10.200000 Tf 0.000000 0.0 Td (els, ) Tj 18.600000 0.0 Td (or ) Tj 13.680000 0.0 Td (perhaps ) Tj 38.640000 0.0 Td (even ) Tj 24.120000 0.0 Td (more ) Tj 26.280000 0.0 Td (complicated ) Tj 56.880000 0.0 Td (avalanche ) Tj 45.960000 0.0 Td (sys- ) Tj ET BT 1.000000 0 0 1 46.200000 394.560000 Tm 3 Tr 0 0 0 rg /F0 10.200000 Tf 0.000000 0.0 Td (tems ) Tj 24.240000 0.0 Td (that ) Tj 21.600000 0.0 Td (exhibit ) Tj 34.320000 0.0 Td (FSOC. ) Tj 33.240000 0.0 Td (In ) Tj 12.600000 0.0 Td (more ) Tj 25.080000 0.0 Td (general ) Tj 34.920000 0.0 Td (applications, ) Tj ET BT 1.000000 0 0 1 46.080000 383.640000 Tm 3 Tr 0 0 0 rg /F0 10.560000 Tf 0.000000 0.0 Td (recursion ) Tj 44.040000 0.0 Td (equations ) Tj 45.960000 0.0 Td (such ) Tj 24.240000 0.0 Td (as ) Tj 13.680000 0.0 Td (\(3\) ) Tj 16.800000 0.0 Td (and ) Tj 20.880000 0.0 Td (\(12\)may ) Tj 44.040000 0.0 Td (include ) Tj ET BT 1.000000 0 0 1 46.080000 373.680000 Tm 3 Tr 0 0 0 rg /F0 9.960000 Tf 0.000000 0.0 Td (more ) Tj 24.840000 0.0 Td (than ) Tj 23.040000 0.0 Td (one ) Tj 18.120000 0.0 Td (parameter ) Tj 48.120000 0.0 Td (and ) Tj 19.200000 0.0 Td (more ) Tj 24.720000 0.0 Td (complex ) Tj 38.760000 0.0 Td (nonlinear- ) Tj ET BT 1.000000 0 0 1 45.960000 363.360000 Tm 3 Tr 0 0 0 rg /F0 9.720000 Tf 0.000000 0.0 Td (ity, ) Tj 16.920000 0.0 Td (leading ) Tj 34.680000 0.0 Td (to ) Tj 12.360000 0.0 Td (power-law ) Tj 47.640000 0.0 Td (relations ) Tj 40.800000 0.0 Td (other ) Tj 26.040000 0.0 Td (than ) Tj 23.640000 0.0 Td (-1. ) Tj ET BT 1.000000 0 0 1 55.920000 341.640000 Tm 3 Tr 0 0 0 rg /F0 8.640000 Tf 0.000000 0.0 Td (Acknowledgments. ) Tj 96.960000 0.0 Td (The ) Tj 19.800000 0.0 Td (authors ) Tj 34.080000 0.0 Td (would ) Tj 26.880000 0.0 Td (like ) Tj 17.640000 0.0 Td (to ) Tj 11.760000 0.0 Td (thank ) Tj ET BT 1.000000 0 0 1 45.720000 331.560000 Tm 3 Tr 0 0 0 rg /F0 8.880000 Tf 0.000000 0.0 Td (Henrik ) Tj 32.160000 0.0 Td (Jensen ) Tj 31.560000 0.0 Td (and ) Tj 19.800000 0.0 Td (George ) Tj 33.000000 0.0 Td (Rowlands ) Tj 43.440000 0.0 Td (for ) Tj 15.720000 0.0 Td (valuable ) Tj 37.560000 0.0 Td (discus- ) Tj ET BT 1.000000 0 0 1 45.480000 321.000000 Tm 3 Tr 0 0 0 rg /F0 9.240000 Tf 0.000000 0.0 Td (sions. ) Tj 30.120000 0.0 Td (SCC ) Tj 23.040000 0.0 Td (was ) Tj 18.480000 0.0 Td (funded ) Tj 32.160000 0.0 Td (by ) Tj 14.160000 0.0 Td (PPARC. ) Tj 39.000000 0.0 Td (NWW ) Tj 29.640000 0.0 Td (is ) Tj 10.560000 0.0 Td (grateful ) Tj 35.520000 0.0 Td (to ) Tj ET BT 1.000000 0 0 1 45.600000 310.920000 Tm 3 Tr 0 0 0 rg /F0 9.720000 Tf 0.000000 0.0 Td (MIT/CSR ) Tj 44.280000 0.0 Td (for ) Tj 13.800000 0.0 Td (its ) Tj 12.480000 0.0 Td (hospitality. ) Tj 48.960000 0.0 Td (The ) Tj 18.720000 0.0 Td (work ) Tj 22.200000 0.0 Td (at ) Tj 10.680000 0.0 Td (MIT/CSR ) Tj 43.920000 0.0 Td (is ) Tj 8.880000 0.0 Td (par- ) Tj ET BT 1.000000 0 0 1 45.600000 301.200000 Tm 3 Tr 0 0 0 rg /F0 8.880000 Tf 0.000000 0.0 Td (tially ) Tj 23.760000 0.0 Td (supported ) Tj 43.800000 0.0 Td (by ) Tj 12.960000 0.0 Td (grants ) Tj 28.200000 0.0 Td (from ) Tj 22.200000 0.0 Td (AFOSR, ) Tj 37.560000 0.0 Td (NSF, ) Tj 23.640000 0.0 Td (and ) Tj 17.880000 0.0 Td (NASA. ) Tj ET BT 1.000000 0 0 1 45.600000 277.200000 Tm 3 Tr 0 0 0 rg /F0 9.000000 Tf 0.000000 0.0 Td (References ) Tj ET BT 1.000000 0 0 1 45.360000 258.240000 Tm 3 Tr 0 0 0 rg /F0 8.880000 Tf 0.000000 0.0 Td (Angelopoulos, ) Tj 59.280000 0.0 Td (V., ) Tj 14.400000 0.0 Td (et ) Tj 10.080000 0.0 Td (al., ) Tj 14.760000 0.0 Td (Multipoint ) Tj 46.080000 0.0 Td (analysis ) Tj 33.840000 0.0 Td (of ) Tj 9.600000 0.0 Td (a ) Tj 6.600000 0.0 Td (bursty ) Tj 28.080000 0.0 Td (bulk ) Tj ET BT 1.000000 0 0 1 54.240000 248.040000 Tm 3 Tr 0 0 0 rg /F0 9.000000 Tf 0.000000 0.0 Td (flow ) Tj 18.960000 0.0 Td (event ) Tj 24.000000 0.0 Td (on ) Tj 12.720000 0.0 Td (April ) Tj 24.000000 0.0 Td (11, ) Tj 14.640000 0.0 Td (1985, ) Tj 23.880000 0.0 Td (J. ) Tj 11.160000 0.0 Td (Geophys. ) Tj 38.400000 0.0 Td (Res., ) Tj 22.440000 0.0 Td (101, ) Tj 20.400000 0.0 Td (4967, ) Tj ET BT 1.000000 0 0 1 54.840000 240.480000 Tm 3 Tr 0 0 0 rg /F0 6.240000 Tf 0.000000 0.0 Td (1996. ) Tj ET BT 1.000000 0 0 1 45.120000 228.360000 Tm 3 Tr 0 0 0 rg /F0 8.760000 Tf 0.000000 0.0 Td (Angelopoulos, ) Tj 60.120000 0.0 Td (V., ) Tj 14.880000 0.0 Td (T. ) Tj 12.600000 0.0 Td (Mukai, ) Tj 30.960000 0.0 Td (and ) Tj 18.360000 0.0 Td (S. ) Tj 10.560000 0.0 Td (Kokubun, ) Tj 42.720000 0.0 Td (Evidence ) Tj 39.000000 0.0 Td (for ) Tj ET BT 1.000000 0 0 1 53.880000 218.280000 Tm 3 Tr 0 0 0 rg /F0 9.000000 Tf 0.000000 0.0 Td (intermittency ) Tj 57.120000 0.0 Td (in ) Tj 10.200000 0.0 Td (Earth's ) Tj 31.560000 0.0 Td (plasma ) Tj 30.960000 0.0 Td (sheet ) Tj 22.800000 0.0 Td (and ) Tj 16.800000 0.0 Td (implications ) Tj 50.880000 0.0 Td (for ) Tj ET BT 1.000000 0 0 1 54.000000 208.200000 Tm 3 Tr 0 0 0 rg /F0 8.880000 Tf 0.000000 0.0 Td (self-organized ) Tj 58.440000 0.0 Td (criticality, ) Tj 44.280000 0.0 Td (Phys. ) Tj 25.440000 0.0 Td (Plasmas, ) Tj 38.640000 0.0 Td (6, ) Tj 10.560000 0.0 Td (4161, ) Tj 24.600000 0.0 Td (1999. ) Tj ET BT 1.000000 0 0 1 44.880000 197.880000 Tm 3 Tr 0 0 0 rg /F0 9.120000 Tf 0.000000 0.0 Td (Bak, ) Tj 22.680000 0.0 Td (P., ) Tj 15.120000 0.0 Td (C. ) Tj 13.080000 0.0 Td (Tang, ) Tj 27.120000 0.0 Td (and ) Tj 18.840000 0.0 Td (K. ) Tj 13.800000 0.0 Td (Wiesenfeld, ) Tj 50.640000 0.0 Td (Self-organized ) Tj 59.760000 0.0 Td (criti- ) Tj ET BT 1.000000 0 0 1 54.000000 187.920000 Tm 3 Tr 0 0 0 rg /F0 9.120000 Tf 0.000000 0.0 Td (cality: ) Tj 29.280000 0.0 Td (An ) Tj 15.480000 0.0 Td (explanation ) Tj 50.400000 0.0 Td (of ) Tj 11.640000 0.0 Td (1/f ) Tj 14.520000 0.0 Td (noise, ) Tj 26.760000 0.0 Td (Phys. ) Tj 25.560000 0.0 Td (Rev. ) Tj 20.760000 0.0 Td (Lett., ) Tj 23.880000 0.0 Td (,59, ) Tj ET BT 1.000000 0 0 1 53.880000 178.800000 Tm 3 Tr 0 0 0 rg /F0 7.680000 Tf 0.000000 0.0 Td (381, ) Tj 20.160000 0.0 Td (1987. ) Tj ET BT 1.000000 0 0 1 45.000000 168.240000 Tm 3 Tr 0 0 0 rg /F0 9.000000 Tf 0.000000 0.0 Td (Chang, ) Tj 31.320000 0.0 Td (T., ) Tj 14.880000 0.0 Td (Low-dimensional ) Tj 70.680000 0.0 Td (behavior ) Tj 37.920000 0.0 Td (and ) Tj 17.400000 0.0 Td (symmetry ) Tj 42.720000 0.0 Td (break- ) Tj ET BT 1.000000 0 0 1 53.520000 158.160000 Tm 3 Tr 0 0 0 rg /F0 8.760000 Tf 0.000000 0.0 Td (ing ) Tj 16.200000 0.0 Td (of ) Tj 10.560000 0.0 Td (stochastic ) Tj 43.440000 0.0 Td (systems ) Tj 34.920000 0.0 Td (near ) Tj 21.000000 0.0 Td (criticality ) Tj 54.600000 0.0 Td (can ) Tj 17.040000 0.0 Td (these ) Tj 24.000000 0.0 Td (ef- ) Tj ET BT 1.000000 0 0 1 53.520000 148.080000 Tm 3 Tr 0 0 0 rg /F0 9.000000 Tf 0.000000 0.0 Td (fects ) Tj 22.200000 0.0 Td (be ) Tj 13.080000 0.0 Td (observed ) Tj 38.520000 0.0 Td (in ) Tj 11.280000 0.0 Td (space ) Tj 25.800000 0.0 Td (and ) Tj 18.120000 0.0 Td (in ) Tj 11.640000 0.0 Td (the ) Tj 15.960000 0.0 Td (laboratory?, ) Tj 53.160000 0.0 Td (IEEE ) Tj ET BT 1.000000 0 0 1 55.200000 138.120000 Tm 3 Tr 0 0 0 rg /F0 8.760000 Tf 0.000000 0.0 Td (Trans. ) Tj 28.440000 0.0 Td (on ) Tj 13.320000 0.0 Td (Plasma ) Tj 32.760000 0.0 Td (Science, ) Tj 35.520000 0.0 Td (20,691, ) Tj 36.360000 0.0 Td (1992. ) Tj ET BT 1.000000 0 0 1 44.880000 128.400000 Tm 3 Tr 0 0 0 rg /F0 8.640000 Tf 0.000000 0.0 Td (Chang, ) Tj 31.800000 0.0 Td (T., ) Tj 15.600000 0.0 Td (Sporadic ) Tj 38.160000 0.0 Td (localized ) Tj 38.160000 0.0 Td (reconnections ) Tj 58.080000 0.0 Td (and ) Tj 18.120000 0.0 Td (multiscale ) Tj ET BT 1.000000 0 0 1 53.400000 117.840000 Tm 3 Tr 0 0 0 rg /F0 8.880000 Tf 0.000000 0.0 Td (intermittent ) Tj 53.640000 0.0 Td (turbulence ) Tj 46.440000 0.0 Td (in ) Tj 12.240000 0.0 Td (the ) Tj 16.920000 0.0 Td (magnetotail, ) Tj 54.000000 0.0 Td (in ) Tj 13.200000 0.0 Td (Geospace ) Tj ET BT 1.000000 0 0 1 54.120000 108.240000 Tm 3 Tr 0 0 0 rg /F0 8.760000 Tf 0.000000 0.0 Td (Mass ) Tj 25.320000 0.0 Td (and ) Tj 19.200000 0.0 Td (Energy ) Tj 32.040000 0.0 Td (Flow, ) Tj 26.160000 0.0 Td (edited ) Tj 28.800000 0.0 Td (by ) Tj 14.280000 0.0 Td (J. ) Tj 11.280000 0.0 Td (L. ) Tj 12.600000 0.0 Td (Horwitz, ) Tj 39.000000 0.0 Td (D. ) Tj 14.040000 0.0 Td (L. ) Tj ET BT 1.000000 0 0 1 53.880000 97.920000 Tm 3 Tr 0 0 0 rg /F0 9.000000 Tf 0.000000 0.0 Td (Gallagher, ) Tj 46.080000 0.0 Td (and ) Tj 18.960000 0.0 Td (W. ) Tj 15.960000 0.0 Td (K. ) Tj 14.160000 0.0 Td (Peterson, ) Tj 41.760000 0.0 Td (no. ) Tj 16.800000 0.0 Td (104 ) Tj 17.160000 0.0 Td (in ) Tj 12.120000 0.0 Td (Geophysical ) Tj ET BT 1.000000 0 0 1 309.600000 734.280000 Tm 3 Tr 0 0 0 rg /F0 8.760000 Tf 0.000000 0.0 Td (Monograph, ) Tj 50.880000 0.0 Td (p. ) Tj 11.040000 0.0 Td (193, ) Tj 18.600000 0.0 Td (Washington ) Tj 50.280000 0.0 Td (D.C. ) Tj 21.600000 0.0 Td (American ) Tj 41.280000 0.0 Td (Geophys- ) Tj ET BT 1.000000 0 0 1 309.240000 724.440000 Tm 3 Tr 0 0 0 rg /F0 8.400000 Tf 0.000000 0.0 Td (ical ) Tj 17.400000 0.0 Td (Union, ) Tj 30.600000 0.0 Td (1998. ) Tj ET BT 1.000000 0 0 1 300.720000 714.240000 Tm 3 Tr 0 0 0 rg /F0 8.880000 Tf 0.000000 0.0 Td (Chang, ) Tj 32.520000 0.0 Td (T., ) Tj 16.320000 0.0 Td (Self-organized ) Tj 60.240000 0.0 Td (criticality, ) Tj 44.880000 0.0 Td (multi-fractal ) Tj 54.240000 0.0 Td (spectra, ) Tj ET BT 1.000000 0 0 1 309.360000 704.640000 Tm 3 Tr 0 0 0 rg /F0 8.280000 Tf 0.000000 0.0 Td (sporadic ) Tj 37.320000 0.0 Td (localized ) Tj 38.400000 0.0 Td (reconnections ) Tj 58.680000 0.0 Td (and ) Tj 18.600000 0.0 Td (intermittent ) Tj 52.680000 0.0 Td (turbu- ) Tj ET BT 1.000000 0 0 1 309.120000 694.320000 Tm 3 Tr 0 0 0 rg /F0 8.640000 Tf 0.000000 0.0 Td (lence ) Tj 23.040000 0.0 Td (in ) Tj 11.160000 0.0 Td (the ) Tj 15.840000 0.0 Td (magnetotail, ) Tj 54.360000 0.0 Td (Phys. ) Tj 25.680000 0.0 Td (Plasmas, ) Tj 38.520000 0.0 Td (6, ) Tj 10.560000 0.0 Td (4137, ) Tj 24.840000 0.0 Td (1999. ) Tj ET BT 1.000000 0 0 1 301.080000 683.280000 Tm 3 Tr 0 0 0 rg /F0 8.880000 Tf 0.000000 0.0 Td (Chang, ) Tj 30.840000 0.0 Td (T. ) Tj 12.000000 0.0 Td (S., ) Tj 12.600000 0.0 Td (D. ) Tj 12.360000 0.0 Td (D. ) Tj 12.120000 0.0 Td (Vvedensky, ) Tj 48.240000 0.0 Td (and ) Tj 17.640000 0.0 Td (J. ) Tj 9.480000 0.0 Td (F. ) Tj 11.160000 0.0 Td (Nicoll, ) Tj 28.440000 0.0 Td (Differential ) Tj ET BT 1.000000 0 0 1 309.600000 673.320000 Tm 3 Tr 0 0 0 rg /F0 8.760000 Tf 0.000000 0.0 Td (renormalization-group ) Tj 93.480000 0.0 Td (generators ) Tj 45.240000 0.0 Td (for ) Tj 14.640000 0.0 Td (static ) Tj 25.680000 0.0 Td (and ) Tj 18.000000 0.0 Td (dynamic ) Tj ET BT 1.000000 0 0 1 309.840000 663.360000 Tm 3 Tr 0 0 0 rg /F0 8.640000 Tf 0.000000 0.0 Td (critical ) Tj 30.600000 0.0 Td (phenomena, ) Tj 52.560000 0.0 Td (Phys. ) Tj 25.320000 0.0 Td (Reports, ) Tj 35.760000 0.0 Td (217, ) Tj 21.840000 0.0 Td (279, ) Tj 19.680000 0.0 Td (1992. ) Tj ET BT 1.000000 0 0 1 301.080000 653.400000 Tm 3 Tr 0 0 0 rg /F0 8.760000 Tf 0.000000 0.0 Td (Chapman, ) Tj 44.040000 0.0 Td (S.C., ) Tj 24.960000 0.0 Td (N. ) Tj 12.360000 0.0 Td (W. ) Tj 14.880000 0.0 Td (Watkins, ) Tj 38.640000 0.0 Td (R. ) Tj 12.240000 0.0 Td (O. ) Tj 12.360000 0.0 Td (Dendy, ) Tj 30.840000 0.0 Td (P. ) Tj 10.920000 0.0 Td (Helander, ) Tj ET BT 1.000000 0 0 1 309.840000 643.560000 Tm 3 Tr 0 0 0 rg /F0 8.520000 Tf 0.000000 0.0 Td (and ) Tj 18.720000 0.0 Td (G. ) Tj 13.320000 0.0 Td (Rowlands, ) Tj 45.600000 0.0 Td (A ) Tj 10.560000 0.0 Td (simple ) Tj 29.640000 0.0 Td (avalanche ) Tj 42.600000 0.0 Td (model ) Tj 27.840000 0.0 Td (as ) Tj 12.000000 0.0 Td (an ) Tj 13.560000 0.0 Td (ana- ) Tj ET BT 1.000000 0 0 1 309.600000 633.240000 Tm 3 Tr 0 0 0 rg /F0 8.760000 Tf 0.000000 0.0 Td (logue ) Tj 23.280000 0.0 Td (for ) Tj 13.320000 0.0 Td (magnetospheric ) Tj 65.280000 0.0 Td (activity, ) Tj 36.000000 0.0 Td (Geophys. ) Tj 38.040000 0.0 Td (Res. ) Tj 19.320000 0.0 Td (Lett., ) Tj 23.040000 0.0 Td (2,5, ) Tj ET BT 1.000000 0 0 1 309.960000 623.640000 Tm 3 Tr 0 0 0 rg /F0 8.040000 Tf 0.000000 0.0 Td (2397, ) Tj 24.720000 0.0 Td (1998. ) Tj ET BT 1.000000 0 0 1 301.080000 613.200000 Tm 3 Tr 0 0 0 rg /F0 9.000000 Tf 0.000000 0.0 Td (Chapman, ) Tj 43.920000 0.0 Td (S.C., ) Tj 24.600000 0.0 Td (R. ) Tj 11.880000 0.0 Td (O. ) Tj 12.240000 0.0 Td (Dendy, ) Tj 31.080000 0.0 Td (and ) Tj 17.640000 0.0 Td (G. ) Tj 12.240000 0.0 Td (Rowlands, ) Tj 43.920000 0.0 Td (A ) Tj 9.360000 0.0 Td (sandpile ) Tj ET BT 1.000000 0 0 1 309.720000 603.240000 Tm 3 Tr 0 0 0 rg /F0 8.640000 Tf 0.000000 0.0 Td (model ) Tj 27.360000 0.0 Td (with ) Tj 20.640000 0.0 Td (dual ) Tj 19.920000 0.0 Td (scaling ) Tj 30.120000 0.0 Td (regimes ) Tj 33.120000 0.0 Td (for ) Tj 13.800000 0.0 Td (laboratory, ) Tj 46.800000 0.0 Td (space ) Tj 24.480000 0.0 Td (and ) Tj ET BT 1.000000 0 0 1 309.840000 593.400000 Tm 3 Tr 0 0 0 rg /F0 8.640000 Tf 0.000000 0.0 Td (astrophysical ) Tj 55.320000 0.0 Td (plasmas, ) Tj 38.640000 0.0 Td (Phys. ) Tj 25.560000 0.0 Td (Plasmas, ) Tj 38.640000 0.0 Td (6, ) Tj 10.800000 0.0 Td (4169, ) Tj 24.600000 0.0 Td (1999. ) Tj ET BT 1.000000 0 0 1 300.960000 582.960000 Tm 3 Tr 0 0 0 rg /F0 9.000000 Tf 0.000000 0.0 Td (Consolini, ) Tj 45.840000 0.0 Td (G., ) Tj 18.000000 0.0 Td (Sandpile ) Tj 39.720000 0.0 Td (cellular ) Tj 34.920000 0.0 Td (automata ) Tj 43.920000 0.0 Td (and ) Tj 20.040000 0.0 Td (magneto- ) Tj ET BT 1.000000 0 0 1 309.600000 573.480000 Tm 3 Tr 0 0 0 rg /F0 8.520000 Tf 0.000000 0.0 Td (spheric ) Tj 31.920000 0.0 Td (dynamics, ) Tj 44.040000 0.0 Td (in ) Tj 12.240000 0.0 Td (Proc. ) Tj 26.880000 0.0 Td (\"Cosmic ) Tj 36.840000 0.0 Td (Physics ) Tj 33.720000 0.0 Td (in ) Tj 11.760000 0.0 Td (the ) Tj 17.040000 0.0 Td (Year ) Tj ET BT 1.000000 0 0 1 310.200000 563.040000 Tm 3 Tr 0 0 0 rg /F0 8.760000 Tf 0.000000 0.0 Td (2000\", ) Tj 28.680000 0.0 Td (edited ) Tj 27.720000 0.0 Td (by ) Tj 13.320000 0.0 Td (S. ) Tj 10.800000 0.0 Td (Aiello, ) Tj 29.160000 0.0 Td (N. ) Tj 12.720000 0.0 Td (Iucci, ) Tj 25.200000 0.0 Td (G. ) Tj 12.960000 0.0 Td (Sironi, ) Tj 28.800000 0.0 Td (A. ) Tj 12.720000 0.0 Td (Treves, ) Tj ET BT 1.000000 0 0 1 309.720000 553.200000 Tm 3 Tr 0 0 0 rg /F0 8.880000 Tf 0.000000 0.0 Td (and ) Tj 18.960000 0.0 Td (U. ) Tj 13.200000 0.0 Td (Villante, ) Tj 38.880000 0.0 Td (vol. ) Tj 18.600000 0.0 Td (58, ) Tj 15.600000 0.0 Td (p. ) Tj 12.360000 0.0 Td (123, ) Tj 20.280000 0.0 Td (Bologna, ) Tj 39.840000 0.0 Td (Italy. ) Tj 24.480000 0.0 Td (Societa ) Tj ET BT 1.000000 0 0 1 309.960000 543.360000 Tm 3 Tr 0 0 0 rg /F0 8.520000 Tf 0.000000 0.0 Td (Iraliana ) Tj 33.720000 0.0 Td (de ) Tj 12.480000 0.0 Td (Fisica, ) Tj 30.000000 0.0 Td (1997. ) Tj ET BT 1.000000 0 0 1 300.600000 533.280000 Tm 3 Tr 0 0 0 rg /F0 8.760000 Tf 0.000000 0.0 Td (Freeman, ) Tj 40.320000 0.0 Td (M.P., ) Tj 28.200000 0.0 Td (N. ) Tj 12.840000 0.0 Td (W. ) Tj 15.600000 0.0 Td (Watkins, ) Tj 39.120000 0.0 Td (and ) Tj 18.360000 0.0 Td (D. ) Tj 13.080000 0.0 Td (J. ) Tj 10.440000 0.0 Td (Riley, ) Tj 25.800000 0.0 Td (Evidence ) Tj ET BT 1.000000 0 0 1 309.360000 523.080000 Tm 3 Tr 0 0 0 rg /F0 8.640000 Tf 0.000000 0.0 Td (for ) Tj 15.840000 0.0 Td (a ) Tj 8.760000 0.0 Td (solar ) Tj 23.880000 0.0 Td (wind ) Tj 23.760000 0.0 Td (origin ) Tj 27.960000 0.0 Td (of ) Tj 11.880000 0.0 Td (the ) Tj 17.040000 0.0 Td (power ) Tj 28.320000 0.0 Td (law ) Tj 18.240000 0.0 Td (burst ) Tj 25.200000 0.0 Td (lifetime ) Tj ET BT 1.000000 0 0 1 309.600000 513.120000 Tm 3 Tr 0 0 0 rg /F0 8.760000 Tf 0.000000 0.0 Td (distribution ) Tj 51.960000 0.0 Td (of ) Tj 12.240000 0.0 Td (the ) Tj 17.520000 0.0 Td (AE ) Tj 17.640000 0.0 Td (indices, ) Tj 36.240000 0.0 Td (Geophys. ) Tj 40.560000 0.0 Td (Res. ) Tj 21.720000 0.0 Td (Lett., ) Tj 25.200000 0.0 Td (in ) Tj ET BT 1.000000 0 0 1 309.360000 503.400000 Tm 3 Tr 0 0 0 rg /F0 7.920000 Tf 0.000000 0.0 Td (press, ) Tj 26.400000 0.0 Td (2000. ) Tj ET BT 1.000000 0 0 1 300.600000 493.080000 Tm 3 Tr 0 0 0 rg /F0 8.880000 Tf 0.000000 0.0 Td (Helander, ) Tj 42.360000 0.0 Td (P., ) Tj 14.760000 0.0 Td (S.C. ) Tj 24.120000 0.0 Td (Chapman, ) Tj 45.720000 0.0 Td (R. ) Tj 12.960000 0.0 Td (O. ) Tj 13.320000 0.0 Td (Dendy, ) Tj 32.160000 0.0 Td (G. ) Tj 13.320000 0.0 Td (Rowlands, ) Tj ET BT 1.000000 0 0 1 309.600000 483.120000 Tm 3 Tr 0 0 0 rg /F0 8.640000 Tf 0.000000 0.0 Td (and ) Tj 17.280000 0.0 Td (N. ) Tj 11.880000 0.0 Td (W. ) Tj 14.520000 0.0 Td (Watkins, ) Tj 38.280000 0.0 Td (Exactly ) Tj 33.360000 0.0 Td (solvable ) Tj 34.080000 0.0 Td (sandpile ) Tj 35.520000 0.0 Td (with ) Tj 19.800000 0.0 Td (fractal ) Tj ET BT 1.000000 0 0 1 309.600000 473.280000 Tm 3 Tr 0 0 0 rg /F0 8.520000 Tf 0.000000 0.0 Td (avalanching, ) Tj 53.280000 0.0 Td (Phys. ) Tj 25.440000 0.0 Td (Rev. ) Tj 21.000000 0.0 Td (E, ) Tj 11.760000 0.0 Td (,59, ) Tj 15.960000 0.0 Td (6356, ) Tj 24.960000 0.0 Td (1999. ) Tj ET BT 1.000000 0 0 1 300.480000 463.200000 Tm 3 Tr 0 0 0 rg /F0 8.640000 Tf 0.000000 0.0 Td (Hoshino, ) Tj 38.880000 0.0 Td (M., ) Tj 17.640000 0.0 Td (A. ) Tj 13.200000 0.0 Td (Nishida, ) Tj 37.320000 0.0 Td (T. ) Tj 13.200000 0.0 Td (Yamamoto, ) Tj 50.280000 0.0 Td (and ) Tj 18.600000 0.0 Td (S. ) Tj 11.280000 0.0 Td (Kokubun, ) Tj ET BT 1.000000 0 0 1 309.480000 453.120000 Tm 3 Tr 0 0 0 rg /F0 8.880000 Tf 0.000000 0.0 Td (Turbulence ) Tj 50.520000 0.0 Td (magnetic ) Tj 42.240000 0.0 Td (field ) Tj 22.440000 0.0 Td (in ) Tj 13.560000 0.0 Td (the ) Tj 18.480000 0.0 Td (distant ) Tj 33.600000 0.0 Td (magnetotail: ) Tj ET BT 1.000000 0 0 1 309.360000 443.160000 Tm 3 Tr 0 0 0 rg /F0 8.640000 Tf 0.000000 0.0 Td (bottom-up ) Tj 45.360000 0.0 Td (process ) Tj 32.040000 0.0 Td (of ) Tj 9.840000 0.0 Td (plasmoid ) Tj 38.640000 0.0 Td (formation?, ) Tj 50.400000 0.0 Td (Geophys. ) Tj 38.400000 0.0 Td (Res. ) Tj ET BT 1.000000 0 0 1 310.080000 433.560000 Tm 3 Tr 0 0 0 rg /F0 8.400000 Tf 0.000000 0.0 Td (Lett., ) Tj 23.760000 0.0 Td (21, ) Tj 16.560000 0.0 Td (2935, ) Tj 24.480000 0.0 Td (1994. ) Tj ET BT 1.000000 0 0 1 300.720000 423.000000 Tm 3 Tr 0 0 0 rg /F0 8.760000 Tf 0.000000 0.0 Td (Jensen, ) Tj 31.680000 0.0 Td (H. ) Tj 12.120000 0.0 Td (J., ) Tj 12.840000 0.0 Td (Self-Organized ) Tj 61.560000 0.0 Td (Criticality: ) Tj 46.920000 0.0 Td (Emergent ) Tj 41.400000 0.0 Td (Complex ) Tj ET BT 1.000000 0 0 1 309.960000 412.920000 Tm 3 Tr 0 0 0 rg /F0 9.000000 Tf 0.000000 0.0 Td (Behaviour ) Tj 44.040000 0.0 Td (in ) Tj 10.680000 0.0 Td (Physical ) Tj 36.240000 0.0 Td (and ) Tj 17.520000 0.0 Td (Biological ) Tj 41.520000 0.0 Td (Systems. ) Tj 36.960000 0.0 Td (Cambridge ) Tj ET BT 1.000000 0 0 1 309.360000 403.200000 Tm 3 Tr 0 0 0 rg /F0 8.520000 Tf 0.000000 0.0 Td (University ) Tj 44.640000 0.0 Td (Press, ) Tj 27.120000 0.0 Td (UK, ) Tj 20.400000 0.0 Td (1998. ) Tj ET BT 1.000000 0 0 1 300.360000 392.760000 Tm 3 Tr 0 0 0 rg /F0 8.880000 Tf 0.000000 0.0 Td (Lui, ) Tj 18.600000 0.0 Td (A. ) Tj 12.000000 0.0 Td (T. ) Tj 11.760000 0.0 Td (Y., ) Tj 14.880000 0.0 Td (R. ) Tj 11.760000 0.0 Td (E. ) Tj 11.400000 0.0 Td (Lopez, ) Tj 29.640000 0.0 Td (S. ) Tj 10.200000 0.0 Td (M. ) Tj 13.440000 0.0 Td (Krimigis, ) Tj 39.960000 0.0 Td (R. ) Tj 12.000000 0.0 Td (W. ) Tj 14.280000 0.0 Td (McEntire, ) Tj ET BT 1.000000 0 0 1 309.360000 382.680000 Tm 3 Tr 0 0 0 rg /F0 9.000000 Tf 0.000000 0.0 Td (L. ) Tj 12.120000 0.0 Td (J. ) Tj 10.800000 0.0 Td (Zanetti, ) Tj 35.400000 0.0 Td (and ) Tj 18.480000 0.0 Td (T. ) Tj 12.960000 0.0 Td (A. ) Tj 13.080000 0.0 Td (Potemra, ) Tj 40.920000 0.0 Td (A ) Tj 10.320000 0.0 Td (case ) Tj 20.160000 0.0 Td (study ) Tj 25.680000 0.0 Td (of ) Tj 11.160000 0.0 Td (mag- ) Tj ET BT 1.000000 0 0 1 309.120000 372.840000 Tm 3 Tr 0 0 0 rg /F0 8.520000 Tf 0.000000 0.0 Td (netotail ) Tj 34.320000 0.0 Td (current ) Tj 32.280000 0.0 Td (sheet ) Tj 24.000000 0.0 Td (disruption ) Tj 44.640000 0.0 Td (and ) Tj 18.000000 0.0 Td (diversion, ) Tj 43.080000 0.0 Td (Geophys. ) Tj ET BT 1.000000 0 0 1 309.840000 363.120000 Tm 3 Tr 0 0 0 rg /F0 8.400000 Tf 0.000000 0.0 Td (Res. ) Tj 20.400000 0.0 Td (Lett., ) Tj 24.600000 0.0 Td (1,5,721, ) Tj 35.520000 0.0 Td (1988. ) Tj ET BT 1.000000 0 0 1 300.240000 353.040000 Tm 3 Tr 0 0 0 rg /F0 8.400000 Tf 0.000000 0.0 Td (Lui, ) Tj 18.480000 0.0 Td (A. ) Tj 12.360000 0.0 Td (T. ) Tj 12.240000 0.0 Td (Y., ) Tj 14.760000 0.0 Td (Multiscale ) Tj 44.640000 0.0 Td (and ) Tj 17.400000 0.0 Td (intermittent ) Tj 52.080000 0.0 Td (nature ) Tj 28.800000 0.0 Td (of ) Tj 10.440000 0.0 Td (current ) Tj ET BT 1.000000 0 0 1 309.000000 342.840000 Tm 3 Tr 0 0 0 rg /F0 8.640000 Tf 0.000000 0.0 Td (disruption ) Tj 43.320000 0.0 Td (in ) Tj 10.200000 0.0 Td (the ) Tj 14.880000 0.0 Td (magnetotail, ) Tj 52.560000 0.0 Td (in ) Tj 10.680000 0.0 Td (Physics ) Tj 32.760000 0.0 Td (of ) Tj 9.720000 0.0 Td (Space ) Tj 24.720000 0.0 Td (Plasmas ) Tj ET BT 1.000000 0 0 1 310.080000 332.400000 Tm 3 Tr 0 0 0 rg /F0 9.360000 Tf 0.000000 0.0 Td (\(1998\), ) Tj 30.720000 0.0 Td (edited ) Tj 27.240000 0.0 Td (by ) Tj 12.600000 0.0 Td (T. ) Tj 12.240000 0.0 Td (Chang, ) Tj 31.560000 0.0 Td (and ) Tj 17.760000 0.0 Td (J. ) Tj 9.840000 0.0 Td (R. ) Tj 12.240000 0.0 Td (Jasperse, ) Tj 38.760000 0.0 Td (no. ) Tj 15.600000 0.0 Td (15, ) Tj 13.560000 0.0 Td (p. ) Tj ET BT 1.000000 0 0 1 309.360000 322.440000 Tm 3 Tr 0 0 0 rg /F0 9.120000 Tf 0.000000 0.0 Td (233, ) Tj 18.960000 0.0 Td (Cambridge, ) Tj 48.840000 0.0 Td (Massachusetts. ) Tj 62.640000 0.0 Td (MIT ) Tj 21.000000 0.0 Td (Geo/Cosmo ) Tj 50.040000 0.0 Td (Plasma ) Tj ET BT 1.000000 0 0 1 309.000000 312.960000 Tm 3 Tr 0 0 0 rg /F0 8.280000 Tf 0.000000 0.0 Td (Physics, ) Tj 36.480000 0.0 Td (1998. ) Tj ET BT 1.000000 0 0 1 300.000000 302.760000 Tm 3 Tr 0 0 0 rg /F0 8.640000 Tf 0.000000 0.0 Td (Lui, ) Tj 19.080000 0.0 Td (A. ) Tj 12.720000 0.0 Td (T. ) Tj 12.840000 0.0 Td (Y., ) Tj 15.360000 0.0 Td (S.C. ) Tj 23.520000 0.0 Td (Chapman, ) Tj 45.120000 0.0 Td (K. ) Tj 12.960000 0.0 Td (Liou, ) Tj 24.000000 0.0 Td (P. ) Tj 11.280000 0.0 Td (T. ) Tj 12.480000 0.0 Td (Newell, ) Tj 33.000000 0.0 Td (C.-I. ) Tj ET BT 1.000000 0 0 1 309.000000 292.680000 Tm 3 Tr 0 0 0 rg /F0 8.520000 Tf 0.000000 0.0 Td (Meng, ) Tj 27.840000 0.0 Td (M. ) Tj 14.040000 0.0 Td (J. ) Tj 9.840000 0.0 Td (Brittnacher, ) Tj 52.200000 0.0 Td (and ) Tj 18.120000 0.0 Td (G. ) Tj 12.240000 0.0 Td (K. ) Tj 12.960000 0.0 Td (Parks, ) Tj 28.440000 0.0 Td (Is ) Tj 9.360000 0.0 Td (the ) Tj 15.360000 0.0 Td (dynam- ) Tj ET BT 1.000000 0 0 1 308.760000 282.720000 Tm 3 Tr 0 0 0 rg /F0 8.760000 Tf 0.000000 0.0 Td (ics ) Tj 13.080000 0.0 Td (magnetosphere ) Tj 62.880000 0.0 Td (an ) Tj 12.360000 0.0 Td (avalanching ) Tj 49.680000 0.0 Td (system?, ) Tj 38.520000 0.0 Td (Geophys. ) Tj 38.280000 0.0 Td (Res. ) Tj ET BT 1.000000 0 0 1 309.480000 272.880000 Tm 3 Tr 0 0 0 rg /F0 8.400000 Tf 0.000000 0.0 Td (Lett., ) Tj 23.400000 0.0 Td (in ) Tj 10.920000 0.0 Td (press, ) Tj 26.280000 0.0 Td (2000. ) Tj ET BT 1.000000 0 0 1 299.880000 262.800000 Tm 3 Tr 0 0 0 rg /F0 8.640000 Tf 0.000000 0.0 Td (Watkins, ) Tj 38.400000 0.0 Td (N. ) Tj 12.120000 0.0 Td (W., ) Tj 17.160000 0.0 Td (S.C. ) Tj 22.440000 0.0 Td (Chapman, ) Tj 44.280000 0.0 Td (R. ) Tj 12.000000 0.0 Td (O. ) Tj 12.360000 0.0 Td (Dendy, ) Tj 30.720000 0.0 Td (and ) Tj 17.640000 0.0 Td (G. ) Tj 12.120000 0.0 Td (Row- ) Tj ET BT 1.000000 0 0 1 308.640000 252.360000 Tm 3 Tr 0 0 0 rg /F0 9.000000 Tf 0.000000 0.0 Td (lands, ) Tj 30.840000 0.0 Td (Robustness ) Tj 51.600000 0.0 Td (of ) Tj 13.680000 0.0 Td (collective ) Tj 42.960000 0.0 Td (behaviour ) Tj 45.960000 0.0 Td (in ) Tj 13.680000 0.0 Td (strongly ) Tj ET BT 1.000000 0 0 1 308.640000 242.640000 Tm 3 Tr 0 0 0 rg /F0 8.640000 Tf 0.000000 0.0 Td (driven ) Tj 30.000000 0.0 Td (avalanche ) Tj 43.680000 0.0 Td (models: ) Tj 38.160000 0.0 Td (Magnetospheric ) Tj 67.920000 0.0 Td (implications, ) Tj ET BT 1.000000 0 0 1 309.960000 232.920000 Tm 3 Tr 0 0 0 rg /F0 8.280000 Tf 0.000000 0.0 Td (Geophys. ) Tj 39.000000 0.0 Td (Res. ) Tj 20.400000 0.0 Td (Lett., ) Tj 24.120000 0.0 Td (26, ) Tj 16.200000 0.0 Td (2617, ) Tj 24.840000 0.0 Td (1999. ) Tj ET BT 1.000000 0 0 1 299.760000 222.600000 Tm 3 Tr 0 0 0 rg /F0 8.880000 Tf 0.000000 0.0 Td (Wilson, ) Tj 34.920000 0.0 Td (K. ) Tj 14.280000 0.0 Td (G., ) Tj 16.920000 0.0 Td (and ) Tj 19.200000 0.0 Td (J. ) Tj 11.520000 0.0 Td (Kogut, ) Tj 32.520000 0.0 Td (The ) Tj 20.040000 0.0 Td (renormalization ) Tj 67.440000 0.0 Td (group ) Tj ET BT 1.000000 0 0 1 308.760000 212.880000 Tm 3 Tr 0 0 0 rg /F0 8.280000 Tf 0.000000 0.0 Td (and ) Tj 18.000000 0.0 Td (the ) Tj 15.840000 0.0 Td (e ) Tj 7.080000 0.0 Td (expansion, ) Tj 46.200000 0.0 Td (Phys. ) Tj 25.560000 0.0 Td (Reports, ) Tj 36.120000 0.0 Td (12, ) Tj 15.960000 0.0 Td (75, ) Tj 15.000000 0.0 Td (1974. ) Tj ET BT 1.000000 0 0 1 306.840000 185.880000 Tm 3 Tr 0 0 0 rg /F0 8.760000 Tf 0.000000 0.0 Td (S. ) Tj 10.560000 0.0 Td (W. ) Tj 15.240000 0.0 Td (Y. ) Tj 12.360000 0.0 Td (Tam ) Tj 21.360000 0.0 Td (and ) Tj 18.120000 0.0 Td (T. ) Tj 12.600000 0.0 Td (Chang, ) Tj 31.920000 0.0 Td (Center ) Tj 29.760000 0.0 Td (for ) Tj 14.760000 0.0 Td (Space ) Tj 25.680000 0.0 Td (Research, ) Tj ET BT 1.000000 0 0 1 297.480000 175.560000 Tm 3 Tr 0 0 0 rg /F0 9.000000 Tf 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dynamics; Space Plasma Physics: Experimental and mathematical techniques Analytical determination of power&#8208;law index for the Chapman et al. sandpile (FSOC) analog for magnetospheric activity &#8212; A renormalization&#8208;group analysis Sunny W. Y. Tam, Tom Chang, S. C. Chapman, N. W. Watkins http://dx.doi.org/10.1029/2000GL000030, doi:10.1029/2000GL000030 escape 1.1 2007-01-05T14:31:48Z www.PrincetonImaging.com 2012-07-18T14:11:50-04:00 2012-07-18T14:11:50-04:00 uuid:61d6060f-3146-4cf6-8eec-61a4d48273c5 uuid:1254c270-7da2-4d85-ab9f-a3af92324abc endstream endobj xref 0 19 0000000000 65535 f 0000112695 00000 n 0000112890 00000 n 0000214118 00000 n 0000214148 00000 n 0000214233 00000 n 0000250863 00000 n 0000251058 00000 n 0000339704 00000 n 0000339735 00000 n 0000339820 00000 n 0000376022 00000 n 0000376220 00000 n 0000477840 00000 n 0000477873 00000 n 0000477959 00000 n 0000514803 00000 n 0000514879 00000 n 0000515602 00000 n trailer << /Size 19 >> startxref 160 %%EOF