The Cambridge Cluster Database

Lowest minima located for the Thomson problem

on constant mean curvature surfaces

H. Kusumaatmaja and D.J. Wales

submitted (2012).

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	Point Group	Voronoi Image	xyz coordinates
200	0.4	310.1840282232	TBD	0.40.200.gif	0.40.200.xyz
200	0.5	298.9844521195	TBD	0.50.200.gif	0.50.200.xyz
200	0.525	297.3429974210	TBD	0.525.200.gif	0.525.200.xyz
200	0.55	296.5580640382	TBD	0.55.200.gif	0.55.200.xyz
200	0.575	296.8748662833	TBD	0.575.200.gif	0.575.200.xyz
200	0.6	298.3923892628	TBD	0.60.200.gif	0.60.200.xyz
200	0.7	314.8179205095	TBD	0.70.200.gif	0.70.200.xyz
200	0.8	365.9623745284	TBD	0.80.200.gif	0.80.200.xyz
250	0.4	589.6974548017	TBD	0.40.250.gif	0.40.250.xyz
250	0.5	569.2970178471	TBD	0.50.250.gif	0.50.250.xyz
250	0.525	566.6214502325	TBD	0.525.250.gif	0.525.250.xyz
250	0.55	565.2960344127	TBD	0.55.250.gif	0.55.250.xyz
250	0.575	565.8026826038	TBD	0.575.250.gif	0.575.250.xyz
250	0.6	568.2940115469	TBD	0.60.250.gif	0.60.250.xyz
250	0.7	598.3301087872	TBD	0.70.250.gif	0.70.250.xyz
250	0.8	690.0182235714	TBD	0.80.250.gif	0.80.250.xyz
300	0.4	978.1011161716	TBD	0.40.300.gif	0.40.300.xyz
300	0.5	945.1600518684	TBD	0.50.300.gif	0.50.300.xyz
300	0.525	940.8172375342	TBD	0.525.300.gif	0.525.300.xyz
300	0.55	939.0740287443	TBD	0.55.300.gif	0.55.300.xyz
300	0.575	940.0877599738	TBD	0.575.300.gif	0.575.300.xyz
300	0.6	944.2628706056	TBD	0.60.300.gif	0.60.300.xyz
300	0.7	992.4317820413	TBD	0.70.300.gif	0.70.300.xyz
300	0.8	1139.1159969727	TBD	0.80.300.gif	0.80.300.xyz
325	0.4	1215.6605216986	TBD	0.40.325.gif	0.40.325.xyz
325	0.5	1174.6234531945	TBD	0.50.325.gif	0.50.325.xyz
325	0.525	1170.5232332801	TBD	0.525.325.gif	0.525.325.xyz
325	0.55	1168.6776417526	TBD	0.55.325.gif	0.55.325.xyz
325	0.575	1169.0344760119	TBD	0.575.325.gif	0.575.325.xyz
325	0.6	1172.7712686720	TBD	0.60.325.gif	0.60.325.xyz
325	0.625	1180.8707291936	TBD	0.625.325.gif	0.625.325.xyz
325	0.65	1193.8416003371	TBD	0.65.325.gif	0.65.325.xyz
325	0.7	1232.3990624878	TBD	0.70.325.gif	0.70.325.xyz
325	0.8	1411.0813958049	TBD	0.80.325.gif	0.80.325.xyz
340	0.4	1372.2505964905	TBD	0.40.340.gif	0.40.340.xyz
340	0.5	1326.2064561462	TBD	0.50.340.gif	0.50.340.xyz
340	0.525	1321.0470761887	TBD	0.525.340.gif	0.525.340.xyz
340	0.55	1319.2455674904	TBD	0.55.340.gif	0.55.340.xyz
340	0.575	1320.9961624419	TBD	0.575.340.gif	0.575.340.xyz
340	0.6	1324.8948948968	TBD	0.60.340.gif	0.60.340.xyz
340	0.625	1333.1747377458	TBD	0.625.340.gif	0.625.340.xyz
340	0.7	1392.1467160449	TBD	0.70.340.gif	0.70.340.xyz
340	0.8	1591.5959377868	TBD	0.80.340.gif	0.80.340.xyz
350	0.4	1482.5142453843	TBD	0.40.350.gif	0.40.350.xyz
350	0.5	1433.5696499242	TBD	0.50.350.gif	0.50.350.xyz
350	0.525	1427.6816442941	TBD	0.525.350.gif	0.525.350.xyz
350	0.55	1425.3565655534	TBD	0.55.350.gif	0.55.350.xyz
350	0.575	1427.1543633480	TBD	0.575.350.gif	0.575.350.xyz
350	0.6	1432.6782438599	TBD	0.60.350.gif	0.60.350.xyz
350	0.625	1441.0756148463	TBD	0.625.350.gif	0.625.350.xyz
350	0.65	1455.2637289808	TBD	0.65.350.gif	0.65.350.xyz
350	0.7	1505.1815697812	TBD	0.70.350.gif	0.70.350.xyz
350	0.8	1719.6074294923	TBD	0.80.350.gif	0.80.350.xyz
360	0.4	1597.8502159301	TBD	0.40.360.gif	0.40.360.xyz
360	0.5	1545.4991827993	TBD	0.50.360.gif	0.50.360.xyz
360	0.525	1539.4580014841	TBD	0.525.360.gif	0.525.360.xyz
360	0.55	1536.5398952011	TBD	0.55.360.gif	0.55.360.xyz
360	0.575	1537.8536450551	TBD	0.575.360.gif	0.575.360.xyz
360	0.6	1544.2274166233	TBD	0.60.360.gif	0.60.360.xyz
360	0.625	1554.2635749919	TBD	0.625.360.gif	0.625.360.xyz
360	0.7	1620.8810253338	TBD	0.70.360.gif	0.70.360.xyz
360	0.8	1852.8202382723	TBD	0.80.360.gif	0.80.360.xyz
375	0.4	1780.3276763691	TBD	0.40.375.gif	0.40.375.xyz
375	0.5	1722.2476495635	TBD	0.50.375.gif	0.50.375.xyz
375	0.525	1715.7448966261	TBD	0.525.375.gif	0.525.375.xyz
375	0.55	1712.7108300767	TBD	0.55.375.gif	0.55.375.xyz
375	0.575	1713.5334743002	TBD	0.575.375.gif	0.575.375.xyz
375	0.6	1719.8507388565	TBD	0.60.375.gif	0.60.375.xyz
375	0.625	1732.0404992798	TBD	0.625.375.gif	0.625.375.xyz
375	0.65	1749.1326544803	TBD	0.65.375.gif	0.65.375.xyz
375	0.7	1804.4871267995	TBD	0.70.375.gif	0.70.375.xyz
375	0.8	2060.4375911209	TBD	0.80.375.gif	0.80.375.xyz
400	0.4	2108.8244109929	TBD	0.40.400.gif	0.40.400.xyz
400	0.5	2040.5781353982	TBD	0.50.400.gif	0.50.400.xyz
400	0.525	2032.8982276200	TBD	0.525.400.gif	0.525.400.xyz
400	0.55	2030.2903592698	TBD	0.55.400.gif	0.55.400.xyz
400	0.575	2032.1885031903	TBD	0.575.400.gif	0.575.400.xyz
400	0.6	2038.1631306315	TBD	0.60.400.gif	0.60.400.xyz
400	0.625	2051.0557983980	TBD	0.625.400.gif	0.625.400.xyz
400	0.7	2137.5514675269	TBD	0.70.400.gif	0.70.400.xyz
400	0.8	2435.2613990312	TBD	0.80.400.gif	0.80.400.xyz
450	0.4	2861.7886392029	TBD	0.40.450.gif	0.40.450.xyz
450	0.5	2771.1611059660	TBD	0.50.450.gif	0.50.450.xyz
450	0.525	2761.2981958223	TBD	0.525.450.gif	0.525.450.xyz
450	0.55	2757.0963312529	TBD	0.55.450.gif	0.55.450.xyz
450	0.575	2758.5735485158	TBD	0.575.450.gif	0.575.450.xyz
450	0.6	2767.6595291897	TBD	0.60.450.gif	0.60.450.xyz
450	0.7	2899.9808416481	TBD	0.70.450.gif	0.70.450.xyz
450	0.8	3298.4191791529	TBD	0.80.450.gif	0.80.450.xyz
500	0.4	3745.1871683800	TBD	0.40.500.gif	0.40.500.xyz
500	0.5	3628.8900201337	TBD	0.50.500.gif	0.50.500.xyz
500	0.525	3615.9331131675	TBD	0.525.500.gif	0.525.500.xyz
500	0.55	3609.7382782770	TBD	0.55.500.gif	0.55.500.xyz
500	0.575	3612.3707237274	TBD	0.575.500.gif	0.575.500.xyz
500	0.6	3625.7108031839	TBD	0.60.500.gif	0.60.500.xyz
500	0.7	3797.3088467369	TBD	0.70.500.gif	0.70.500.xyz
500	0.8	4303.1024464806	TBD	0.80.500.gif	0.80.500.xyz
550	0.4	4762.6309446034	TBD	0.40.550.gif	0.40.550.xyz
550	0.5	4616.7981295410	TBD	0.50.550.gif	0.50.550.xyz
550	0.525	4600.1780500792	TBD	0.525.550.gif	0.525.550.xyz
550	0.55	4593.3641571444	TBD	0.55.550.gif	0.55.550.xyz
550	0.575	4597.8720316505	TBD	0.575.550.gif	0.575.550.xyz
550	0.6	4612.1681607311	TBD	0.60.550.gif	0.60.550.xyz
550	0.7	4824.9876536970	TBD	0.70.550.gif	0.70.550.xyz
550	0.8	5463.5477761936	TBD	0.80.550.gif	0.80.550.xyz
600	0.4	5916.7537164376	TBD	0.40.600.gif	0.40.600.xyz
600	0.5	5738.1130727151	TBD	0.50.600.gif	0.50.600.xyz
600	0.525	5718.1547773799	TBD	0.525.600.gif	0.525.600.xyz
600	0.55	5709.9161373612	TBD	0.55.600.gif	0.55.600.xyz
600	0.575	5713.6553066387	TBD	0.575.600.gif	0.575.600.xyz
600	0.6	5731.6982124241	TBD	0.60.600.gif	0.60.600.xyz
600	0.7	5994.8063773555	TBD	0.70.600.gif	0.70.600.xyz
600	0.8	6773.5652411633	TBD	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	Point Group	Voronoi Image	xyz coordinates
200	[0.50, 885.89]	169.8434357915	TBD	U0.50.200.gif	U0.50.200.xyz
200	[0.55, 55.99]	194.5944427479	TBD	U0.55.200.gif	U0.55.200.xyz
200	[0.60, 8.75]	245.4875647822	TBD	U0.60.200.gif	U0.60.200.xyz
200	[0.65, 3.38]	295.7423974997	TBD	U0.65.200.gif	U0.65.200.xyz
200	[0.70, 1.57]	337.2589134197	TBD	U0.70.200.gif	U0.70.200.xyz
200	[0.75, 0.75]	362.1259920218	TBD	U0.75.200.gif	U0.75.200.xyz
200	[0.4993, 0.775]	366.8859711826	TBD	U0.775.200.gif	U0.775.200.xyz
200	[0.311, 0.80]	365.4230038825	TBD	U0.80.200.gif	U0.80.200.xyz
200	[0.2345, 0.8125]	362.5749977393	TBD	U0.8125.200.gif	U0.8125.200.xyz
200	[0.1674, 0.825]	358.4004545605	TBD	U0.825.200.gif	U0.825.200.xyz
200	[0.1085, 0.8375]	352.5050273826	TBD	U0.8375.200.gif	U0.8375.200.xyz
200	[0.06, 0.85]	343.9854237477	TBD	U0.85.200.gif	U0.85.200.xyz
400	[0.50, 885.89]	1271.8640799533	TBD	U0.50.400.gif	U0.50.400.xyz
400	[0.55, 55.99]	1422.8910383377	TBD	U0.55.400.gif	U0.55.400.xyz
400	[0.60, 8.75]	1726.3997005679	TBD	U0.60.400.gif	U0.60.400.xyz
400	[0.65, 3.38]	2015.1559015921	TBD	U0.65.400.gif	U0.65.400.xyz
400	[0.70, 1.57]	2240.6729134395	TBD	U0.70.400.gif	U0.70.400.xyz
400	[0.75, 0.75]	2366.5731636666	TBD	U0.75.400.gif	U0.75.400.xyz
400	[0.311, 0.80]	2366.1792735346	TBD	U0.80.400.gif	U0.80.400.xyz
400	[0.06, 0.85]	2214.6385787794	TBD	U0.85.400.gif	U0.85.400.xyz
600	[0.50, 885.89]	3712.3503222968	TBD	U0.50.600.gif	U0.50.600.xyz
600	[0.55, 55.99]	4111.8992007510	TBD	U0.55.600.gif	U0.55.600.xyz
600	[0.60, 8.75]	4912.9418541828	TBD	U0.60.600.gif	U0.60.600.xyz
600	[0.65, 3.38]	5656.1536032285	TBD	U0.65.600.gif	U0.65.600.xyz
600	[0.70, 1.57]	6234.0347245611	TBD	U0.70.600.gif	U0.70.600.xyz
600	[0.75, 0.75]	6542.1715280859	TBD	U0.75.600.gif	U0.75.600.xyz
600	[0.311, 0.80]	6515.8794633966	TBD	U0.80.600.gif	U0.80.600.xyz
600	[0.06, 0.85]	6095.8807359193	TBD	U0.85.600.gif	U0.85.600.xyz