Open Access
Table C.2
Eigenvalues of the SCHs with Neumann (SCHNs) or Dirichlet (SCHDs) boundary conditions for various angular radii of the supercontinent.
| θc (deg) | (0,0) | (1,0) | (1,1) | (2,0) | (2,1) | (2,2) |
|---|---|---|---|---|---|---|
| Neumann boundary conditions (SCHNs) | ||||||
| 0 | 0.000000 | 2.000000 | 2.000000 | 6.000000 | 6.000000 | 6.000000 |
| 10 | 0.000000 | 2.043810 | 1.954799 | 6.204319 | 5.787950 | 5.996589 |
| 20 | 0.000000 | 2.166257 | 1.838982 | 6.717744 | 5.460750 | 5.949235 |
| 30 | 0.000000 | 2.360311 | 1.711429 | 7.467118 | 5.441569 | 5.785407 |
| 40 | 0.000000 | 2.629208 | 1.619197 | 8.452903 | 5.746033 | 5.518966 |
| 50 | 0.000000 | 2.985569 | 1.577808 | 9.717446 | 6.317753 | 5.278194 |
| 60 | 0.000000 | 3.452250 | 1.589586 | 11.339534 | 7.153126 | 5.166990 |
| 70 | 0.000000 | 4.065883 | 1.656959 | 13.444194 | 8.299630 | 5.229035 |
| 80 | 0.000000 | 4.884195 | 1.787952 | 16.226814 | 9.857388 | 5.491887 |
| 90 | 0.000000 | 6.000000 | 2.000000 | 20.000000 | 12.000000 | 6.000000 |
| 100 | 0.000000 | 7.568523 | 2.326061 | 25.285246 | 15.024623 | 6.839299 |
| 110 | 0.000000 | 9.864090 | 2.827415 | 33.003048 | 19.460404 | 8.174357 |
| 120 | 0.000000 | 13.408133 | 3.622974 | 44.902072 | 26.315661 | 10.329330 |
| 130 | 0.000000 | 19.292626 | 4.963802 | 64.643464 | 37.703724 | 13.992842 |
| 140 | 0.000000 | 30.132199 | 7.452826 | 100.992648 | 58.686045 | 20.822406 |
| 150 | 0.000000 | 53.558065 | 12.851483 | 179.532083 | 104.036347 | 35.663952 |
| 160 | 0.000000 | 120.497214 | 28.300199 | 403.938705 | 233.629059 | 78.165464 |
| 170 | 0.000000 | 481.981173 | 111.760030 | 1615.747119 | 933.460872 | 307.821577 |
| Dirichlet boundary conditions (SCHDs) | ||||||
| 0 | 0.000000 | 2.000000 | 2.000000 | 6.000000 | 6.000000 | 6.000000 |
| 10 | 0.241710 | 2.942918 | 2.043810 | 7.928496 | 6.204319 | 6.003307 |
| 20 | 0.349854 | 3.454660 | 2.166257 | 9.122983 | 6.717744 | 6.045851 |
| 30 | 0.466027 | 4.027851 | 2.360311 | 10.493540 | 7.467118 | 6.190333 |
| 40 | 0.600603 | 4.707711 | 2.629208 | 12.138321 | 8.452903 | 6.485855 |
| 50 | 0.762626 | 5.538331 | 2.985569 | 14.160734 | 9.717446 | 6.968283 |
| 60 | 0.963323 | 6.577054 | 3.452250 | 16.699223 | 11.339534 | 7.678163 |
| 70 | 1.218462 | 7.905884 | 4.065883 | 19.953910 | 13.444194 | 8.676820 |
| 80 | 1.551642 | 9.648467 | 4.884195 | 24.227788 | 16.226814 | 10.063195 |
| 90 | 2.000000 | 12.000000 | 6.000000 | 30.000000 | 20.000000 | 12.000000 |
| 100 | 2.625081 | 15.284420 | 7.568523 | 38.066269 | 25.285246 | 14.762935 |
| 110 | 3.535228 | 20.072333 | 9.864090 | 49.828657 | 33.003048 | 18.842401 |
| 120 | 4.936042 | 27.446847 | 13.408133 | 67.948839 | 44.902072 | 25.173291 |
| 130 | 7.257803 | 39.674941 | 19.292626 | 97.998058 | 64.643464 | 35.715869 |
| 140 | 11.530519 | 62.183561 | 30.132199 | 153.313622 | 100.992648 | 55.166033 |
| 150 | 20.760187 | 110.811047 | 53.558065 | 272.820192 | 179.532083 | 97.231717 |
| 160 | 47.128920 | 249.744161 | 120.497214 | 614.264854 | 403.938705 | 217.469478 |
| 170 | 189.517352 | 999.979043 | 481.981173 | 2458.061916 | 1615.747119 | 866.830706 |
Notes. The values of λl are were computed from Eq. (C.20) for the doublets (n, |m|) such that n = 0,1, 2 and |m| ≤ n using the values of real degrees given by Table C.1.
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