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The Cambridge Cluster Database


Lowest minima located for the Thomson problem

on constant mean curvature surfaces

H. Kusumaatmaja and D.J. Wales

Phys. Rev. Lett., in press (2013).


We study a family of catenoids with different values of the waist parameter c, and adjust the height parameter zm so that the radius of the catenoid at zm, c cosh(zm/c) = 1. {x, y, z} = {c cosh(v/c) cos(u), c cosh(v/c) sin(u), v}. See the above paper for more details.


$ N$ Catenoid Waist Radius Energy Voronoi Image xyz coordinates
200 0.4 310.1840282232 0.40.200.gif 0.40.200.xyz
200 0.5 298.9844521195 0.50.200.gif 0.50.200.xyz
200 0.525 297.3429974210 0.525.200.gif 0.525.200.xyz
200 0.55 296.5580640382 0.55.200.gif 0.55.200.xyz
200 0.575 296.8748662833 0.575.200.gif 0.575.200.xyz
200 0.6 298.3923892628 0.60.200.gif 0.60.200.xyz
200 0.7 314.8179205095 0.70.200.gif 0.70.200.xyz
200 0.8 365.9623745284 0.80.200.gif 0.80.200.xyz
250 0.4 589.6974548017 0.40.250.gif 0.40.250.xyz
250 0.5 569.2970178471 0.50.250.gif 0.50.250.xyz
250 0.525 566.6214502325 0.525.250.gif 0.525.250.xyz
250 0.55 565.2960344127 0.55.250.gif 0.55.250.xyz
250 0.575 565.8026826038 0.575.250.gif 0.575.250.xyz
250 0.6 568.2940115469 0.60.250.gif 0.60.250.xyz
250 0.7 598.3301087872 0.70.250.gif 0.70.250.xyz
250 0.8 690.0182235714 0.80.250.gif 0.80.250.xyz
300 0.4 978.1011161716 0.40.300.gif 0.40.300.xyz
300 0.5 945.1600518684 0.50.300.gif 0.50.300.xyz
300 0.525 940.8172375342 0.525.300.gif 0.525.300.xyz
300 0.55 939.0740287443 0.55.300.gif 0.55.300.xyz
300 0.575 940.0877599738 0.575.300.gif 0.575.300.xyz
300 0.6 944.2628706056 0.60.300.gif 0.60.300.xyz
300 0.7 992.4317820413 0.70.300.gif 0.70.300.xyz
300 0.8 1139.1159969727 0.80.300.gif 0.80.300.xyz
325 0.4 1215.6605216986 0.40.325.gif 0.40.325.xyz
325 0.5 1174.6234531945 0.50.325.gif 0.50.325.xyz
325 0.525 1170.5232332801 0.525.325.gif 0.525.325.xyz
325 0.55 1168.6776417526 0.55.325.gif 0.55.325.xyz
325 0.575 1169.0344760119 0.575.325.gif 0.575.325.xyz
325 0.6 1172.7712686720 0.60.325.gif 0.60.325.xyz
325 0.625 1180.8707291936 0.625.325.gif 0.625.325.xyz
325 0.65 1193.8416003371 0.65.325.gif 0.65.325.xyz
325 0.7 1232.3990624878 0.70.325.gif 0.70.325.xyz
325 0.8 1411.0813958049 0.80.325.gif 0.80.325.xyz
340 0.4 1372.2505964905 0.40.340.gif 0.40.340.xyz
340 0.5 1326.2064561462 0.50.340.gif 0.50.340.xyz
340 0.525 1321.0470761887 0.525.340.gif 0.525.340.xyz
340 0.55 1319.2455674904 0.55.340.gif 0.55.340.xyz
340 0.575 1320.9961624419 0.575.340.gif 0.575.340.xyz
340 0.6 1324.8948948968 0.60.340.gif 0.60.340.xyz
340 0.625 1333.1747377458 0.625.340.gif 0.625.340.xyz
340 0.7 1392.1467160449 0.70.340.gif 0.70.340.xyz
340 0.8 1591.5959377868 0.80.340.gif 0.80.340.xyz
350 0.4 1482.5142453843 0.40.350.gif 0.40.350.xyz
350 0.5 1433.5696499242 0.50.350.gif 0.50.350.xyz
350 0.525 1427.6816442941 0.525.350.gif 0.525.350.xyz
350 0.55 1425.3565655534 0.55.350.gif 0.55.350.xyz
350 0.575 1427.1543633480 0.575.350.gif 0.575.350.xyz
350 0.6 1432.6782438599 0.60.350.gif 0.60.350.xyz
350 0.625 1441.0756148463 0.625.350.gif 0.625.350.xyz
350 0.65 1455.2637289808 0.65.350.gif 0.65.350.xyz
350 0.7 1505.1815697812 0.70.350.gif 0.70.350.xyz
350 0.8 1719.6074294923 0.80.350.gif 0.80.350.xyz
360 0.4 1597.8502159301 0.40.360.gif 0.40.360.xyz
360 0.5 1545.4991827993 0.50.360.gif 0.50.360.xyz
360 0.525 1539.4580014841 0.525.360.gif 0.525.360.xyz
360 0.55 1536.5398952011 0.55.360.gif 0.55.360.xyz
360 0.575 1537.8536450551 0.575.360.gif 0.575.360.xyz
360 0.6 1544.2274166233 0.60.360.gif 0.60.360.xyz
360 0.625 1554.2635749919 0.625.360.gif 0.625.360.xyz
360 0.7 1620.8810253338 0.70.360.gif 0.70.360.xyz
360 0.8 1852.8202382723 0.80.360.gif 0.80.360.xyz
375 0.4 1780.3276763691 0.40.375.gif 0.40.375.xyz
375 0.5 1722.2476495635 0.50.375.gif 0.50.375.xyz
375 0.525 1715.7448966261 0.525.375.gif 0.525.375.xyz
375 0.55 1712.7108300767 0.55.375.gif 0.55.375.xyz
375 0.575 1713.5334743002 0.575.375.gif 0.575.375.xyz
375 0.6 1719.8507388565 0.60.375.gif 0.60.375.xyz
375 0.625 1732.0404992798 0.625.375.gif 0.625.375.xyz
375 0.65 1749.1326544803 0.65.375.gif 0.65.375.xyz
375 0.7 1804.4871267995 0.70.375.gif 0.70.375.xyz
375 0.8 2060.4375911209 0.80.375.gif 0.80.375.xyz
400 0.4 2108.8244109929 0.40.400.gif 0.40.400.xyz
400 0.5 2040.5781353982 0.50.400.gif 0.50.400.xyz
400 0.525 2032.8982276200 0.525.400.gif 0.525.400.xyz
400 0.55 2030.2903592698 0.55.400.gif 0.55.400.xyz
400 0.575 2032.1885031903 0.575.400.gif 0.575.400.xyz
400 0.6 2038.1631306315 0.60.400.gif 0.60.400.xyz
400 0.625 2051.0557983980 0.625.400.gif 0.625.400.xyz
400 0.7 2137.5514675269 0.70.400.gif 0.70.400.xyz
400 0.8 2435.2613990312 0.80.400.gif 0.80.400.xyz
450 0.4 2861.7886392029 0.40.450.gif 0.40.450.xyz
450 0.5 2771.1611059660 0.50.450.gif 0.50.450.xyz
450 0.525 2761.2981958223 0.525.450.gif 0.525.450.xyz
450 0.55 2757.0963312529 0.55.450.gif 0.55.450.xyz
450 0.575 2758.5735485158 0.575.450.gif 0.575.450.xyz
450 0.6 2767.6595291897 0.60.450.gif 0.60.450.xyz
450 0.7 2899.9808416481 0.70.450.gif 0.70.450.xyz
450 0.8 3298.4191791529 0.80.450.gif 0.80.450.xyz
500 0.4 3745.1871683800 0.40.500.gif 0.40.500.xyz
500 0.5 3628.8900201337 0.50.500.gif 0.50.500.xyz
500 0.525 3615.9331131675 0.525.500.gif 0.525.500.xyz
500 0.55 3609.7382782770 0.55.500.gif 0.55.500.xyz
500 0.575 3612.3707237274 0.575.500.gif 0.575.500.xyz
500 0.6 3625.7108031839 0.60.500.gif 0.60.500.xyz
500 0.7 3797.3088467369 0.70.500.gif 0.70.500.xyz
500 0.8 4303.1024464806 0.80.500.gif 0.80.500.xyz
550 0.4 4762.6309446034 0.40.550.gif 0.40.550.xyz
550 0.5 4616.7981295410 0.50.550.gif 0.50.550.xyz
550 0.525 4600.1780500792 0.525.550.gif 0.525.550.xyz
550 0.55 4593.3641571444 0.55.550.gif 0.55.550.xyz
550 0.575 4597.8720316505 0.575.550.gif 0.575.550.xyz
550 0.6 4612.1681607311 0.60.550.gif 0.60.550.xyz
550 0.7 4824.9876536970 0.70.550.gif 0.70.550.xyz
550 0.8 5463.5477761936 0.80.550.gif 0.80.550.xyz
600 0.4 5916.7537164376 0.40.600.gif 0.40.600.xyz
600 0.5 5738.1130727151 0.50.600.gif 0.50.600.xyz
600 0.525 5718.1547773799 0.525.600.gif 0.525.600.xyz
600 0.55 5709.9161373612 0.55.600.gif 0.55.600.xyz
600 0.575 5713.6553066387 0.575.600.gif 0.575.600.xyz
600 0.6 5731.6982124241 0.60.600.gif 0.60.600.xyz
600 0.7 5994.8063773555 0.70.600.gif 0.70.600.xyz
600 0.8 6773.5652411633 0.80.600.gif 0.80.600.xyz


In addition, we also study the arrangement of charges on unduloids. See the paper for our parameterizations of the unduloids.


$ N$ Unduloid [a, c] Energy Voronoi Image xyz coordinates
200 [0.50, 885.89] 169.8434357915 U0.50.200.gif U0.50.200.xyz
200 [0.55, 55.99] 194.5944427479 U0.55.200.gif U0.55.200.xyz
200 [0.60, 8.75] 245.4875647822 U0.60.200.gif U0.60.200.xyz
200 [0.65, 3.38] 295.7423974997 U0.65.200.gif U0.65.200.xyz
200 [0.70, 1.57] 337.2589134197 U0.70.200.gif U0.70.200.xyz
200 [0.75, 0.75] 362.1259920218 U0.75.200.gif U0.75.200.xyz
200 [0.4993, 0.775] 366.8859711826 U0.775.200.gif U0.775.200.xyz
200 [0.311, 0.80] 365.4230038825 U0.80.200.gif U0.80.200.xyz
200 [0.2345, 0.8125] 362.5749977393 U0.8125.200.gif U0.8125.200.xyz
200 [0.1674, 0.825] 358.4004545605 U0.825.200.gif U0.825.200.xyz
200 [0.1085, 0.8375] 352.5050273826 U0.8375.200.gif U0.8375.200.xyz
200 [0.06, 0.85] 343.9854237477 U0.85.200.gif U0.85.200.xyz
400 [0.50, 885.89] 1271.8640799533 U0.50.400.gif U0.50.400.xyz
400 [0.55, 55.99] 1422.8910383377 U0.55.400.gif U0.55.400.xyz
400 [0.60, 8.75] 1726.3997005679 U0.60.400.gif U0.60.400.xyz
400 [0.65, 3.38] 2015.1559015921 U0.65.400.gif U0.65.400.xyz
400 [0.70, 1.57] 2240.6729134395 U0.70.400.gif U0.70.400.xyz
400 [0.75, 0.75] 2366.5731636666 U0.75.400.gif U0.75.400.xyz
400 [0.311, 0.80] 2366.1792735346 U0.80.400.gif U0.80.400.xyz
400 [0.06, 0.85] 2214.6385787794 U0.85.400.gif U0.85.400.xyz
600 [0.50, 885.89] 3712.3503222968 U0.50.600.gif U0.50.600.xyz
600 [0.55, 55.99] 4111.8992007510 U0.55.600.gif U0.55.600.xyz
600 [0.60, 8.75] 4912.9418541828 U0.60.600.gif U0.60.600.xyz
600 [0.65, 3.38] 5656.1536032285 U0.65.600.gif U0.65.600.xyz
600 [0.70, 1.57] 6234.0347245611 U0.70.600.gif U0.70.600.xyz
600 [0.75, 0.75] 6542.1715280859 U0.75.600.gif U0.75.600.xyz
600 [0.311, 0.80] 6515.8794633966 U0.80.600.gif U0.80.600.xyz
600 [0.06, 0.85] 6095.8807359193 U0.85.600.gif U0.85.600.xyz




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Next: About this document ...
David Wales 2009-07-21