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[lammps-users] Granular package: gran/hooke
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[lammps-users] Granular package: gran/hooke


From: Vinay Vaibhav <vinayv@...6701...>
Date: Wed, 18 Apr 2018 05:40:51 +0530


Hi,

I am doing some testing with the granular package. I take a bunch of spherical particles in a box.


atom_style	sphere
boundary	p p p
newton		off
comm_modify	vel yes

region		box block 0 81 0 81 0 81 units lattice
create_box	1 box
create_atoms	1 random 200000 35418 box

set             group all diameter 1
set		group all mass 1


Then I use gran/'hooke pair style but I keep only spring part of the normal force, others are set to zero.

pair_style      gran/hooke 200000 NULL 0.0 NULL 0.0 0
pair_coeff	* *

I run it with nve/sphere and expect the energy of the system to be fluctuating around some mean value because the dissipative part of the force is zero. But I observe a systematic increase in the energy of the system.

timestep	0.0001
fix		1 all nve/sphere
thermo          1000
run	        10000000

Can anyone give me some explanation for this? Am I making any mistake somewhere?

logfile and plot of the energy are attached.


With thanks and regards,

Vinay Vaibhav
Ph.D. Student, Theoretical Physics
The Institute of Mathematical Sciences Chennai, India

Attachment: energy.pdf
Description: Adobe PDF document

LAMMPS (11 Aug 2017)
# granular particles

atom_style	sphere
boundary	p p p
newton		off
comm_modify	vel yes


region		box block 0 81 0 81 0 81 units lattice
create_box	1 box
Created orthogonal box = (0 0 0) to (81 81 81)
  2 by 3 by 4 MPI processor grid
create_atoms	1 random 200000 35418 box
Created 200000 atoms

set             group all diameter 1
  200000 settings made for diameter
set		group all mass 1
  200000 settings made for mass

neighbor	0.2 bin
neigh_modify	delay 0

pair_style      gran/hooke 200000 NULL 0.0 NULL 0.0 0
pair_coeff	* *

timestep	0.0001

fix		1 all nve/sphere

thermo          1000

run	        10000000
Neighbor list info ...
  update every 1 steps, delay 0 steps, check yes
  max neighbors/atom: 2000, page size: 100000
  master list distance cutoff = 1.2
  ghost atom cutoff = 1.2
  binsize = 0.6, bins = 135 135 135
  1 neighbor lists, perpetual/occasional/extra = 1 0 0
  (1) pair gran/hooke, perpetual
      attributes: half, newton off, size
      pair build: half/size/bin/newtoff
      stencil: half/bin/3d/newtoff
      bin: standard
Per MPI rank memory allocation (min/avg/max) = 5.12 | 5.144 | 5.186 Mbytes
Step Temp E_pair E_mol TotEng Press 
       0            0            0            0            0    2961.8596 
    1000    4676.1758            0            0    7014.2287    2750.9773 
    2000    4674.1056            0            0    7011.1234    2750.6781 
    3000    4668.9034            0            0    7003.3201    2751.4394 
    4000    4678.8971            0            0    7018.3106    2750.0185 
    5000    4670.6268            0            0    7005.9051    2752.6411 
    6000    4672.8624            0            0    7009.2585     2754.747 
    7000    4679.9884            0            0    7019.9474    2747.6953 
    8000    4673.2883            0            0    7009.8975    2752.3536 
    9000    4672.9302            0            0    7009.3602    2752.5642 
   10000    4677.1446            0            0    7015.6818    2752.6908 
   11000    4670.7903            0            0    7006.1504    2753.7525 
   12000    4675.5014            0            0    7013.2171    2752.1183 
   13000    4675.1155            0            0    7012.6382    2749.5253 
   14000     4675.676            0            0     7013.479    2747.6247 
   15000    4676.9044            0            0    7015.3216    2751.0179 
   16000    4673.6994            0            0    7010.5141    2749.9554 
   17000    4673.9814            0            0     7010.937    2750.0426 
   18000    4677.1509            0            0    7015.6913    2746.5182 
   19000    4675.7631            0            0    7013.6096    2753.7589 
   20000    4679.9542            0            0    7019.8961    2748.0128 
   21000    4677.6198            0            0    7016.3946    2753.5346 
   22000    4674.1464            0            0    7011.1846    2750.8479 
   23000     4670.786            0            0     7006.144    2753.0364 
   24000    4678.5008            0            0    7017.7162    2750.3466 
   25000    4675.5494            0            0     7013.289     2747.888 
   26000    4672.7174            0            0    7009.0411    2752.2308 
   27000    4676.8809            0            0    7015.2862    2753.7696 
   28000    4672.2196            0            0    7008.2943    2747.2241 
   29000    4673.6877            0            0    7010.4964    2752.4695 
   30000    4675.7101            0            0      7013.53     2753.871 
   31000    4673.2679            0            0    7009.8668    2752.3266 
   32000    4677.1264            0            0    7015.6545    2750.5005 
   33000    4675.2716            0            0    7012.8724     2749.968 
   34000    4679.4565            0            0    7019.1496    2749.6647 
   35000    4675.1858            0            0    7012.7437     2750.404 
   36000    4673.4998            0            0    7010.2146    2752.5102 
   37000    4673.4901            0            0    7010.2001    2753.3561 
   38000    4674.0824            0            0    7011.0886    2753.0825 
   39000    4674.6541            0            0    7011.9461    2753.4603 
   40000    4671.4634            0            0      7007.16    2750.6671 
   41000    4676.4856            0            0    7014.6934    2745.2454 
   42000     4674.269            0            0    7011.3684    2753.5753 
   43000    4673.9001            0            0    7010.8152    2754.1641 
   44000     4675.396            0            0    7013.0589     2746.487 
   45000    4676.2719            0            0    7014.3728    2752.1804 
   46000    4676.7598            0            0    7015.1047     2751.353 
   47000    4673.6844            0            0    7010.4915    2749.2886 
   48000    4674.8689            0            0    7012.2683    2750.7051 
   49000     4679.521            0            0    7019.2464    2745.5591 
   50000    4677.0295            0            0    7015.5091     2746.379 
   51000    4679.5426            0            0    7019.2789    2750.2446 
   52000    4674.8602            0            0    7012.2552    2753.9414 
   53000    4677.1255            0            0    7015.6531    2749.2643 
   54000    4673.6649            0            0    7010.4622    2753.5209 
   55000    4675.1243            0            0    7012.6514    2751.8034 
   56000    4673.5178            0            0    7010.2417    2750.2926 
   57000    4677.4763            0            0    7016.1794    2751.7709 
   58000    4678.9643            0            0    7018.4113    2749.7924 
   59000    4679.7014            0            0     7019.517    2749.6623 
   60000     4670.348            0            0     7005.487     2756.247 
   61000    4672.0257            0            0    7008.0035    2751.0027 
   62000    4679.8819            0            0    7019.7878    2746.9342 
   63000    4675.8249            0            0    7013.7022    2750.6211 
   64000    4675.8976            0            0    7013.8114    2751.8212 
   65000    4676.8738            0            0    7015.2756    2749.7796 
   66000    4677.6851            0            0    7016.4925    2752.1591 
   67000    4673.4517            0            0    7010.1425    2753.3787 
   68000    4675.2514            0            0     7012.842    2749.3326 
   69000    4674.6571            0            0    7011.9505    2748.7698 
   70000    4671.5277            0            0    7007.2565    2754.8662 
   71000    4677.8908            0            0    7016.8011    2753.8678 
   72000    4672.4548            0            0    7008.6472    2752.0085 
   73000    4675.8665            0            0    7013.7648    2751.9341 
   74000    4672.0939            0            0    7008.1058    2752.8328 
   75000    4671.2062            0            0    7006.7743    2754.5338 
   76000     4676.053            0            0    7014.0444    2751.2663 
   77000    4674.4521            0            0     7011.643    2752.6384 
   78000    4681.1921            0            0     7021.753    2749.4237 
   79000    4669.3798            0            0    7004.0346    2755.2089 
   80000    4677.1972            0            0    7015.7607    2745.5509 
   81000     4675.734            0            0    7013.5659     2751.249 
   82000    4675.0789            0            0    7012.5833    2749.8478 
   83000    4678.7005            0            0    7018.0156     2747.276 
   84000    4673.8211            0            0    7010.6966     2751.897 
   85000    4682.3198            0            0    7023.4445    2744.1213 
   86000    4672.9821            0            0    7009.4381    2750.4545 
   87000    4674.0249            0            0    7011.0024    2750.1916 
   88000    4666.5737            0            0    6999.8256    2751.7546 
   89000    4678.2665            0            0    7017.3646    2748.9182 
   90000    4672.8366            0            0    7009.2199    2754.1396 
   91000    4675.6994            0            0     7013.514    2752.5935 
   92000    4676.9354            0            0     7015.368    2748.0193 
   93000    4678.1934            0            0     7017.255    2747.8091 
   94000    4673.5134            0            0    7010.2351    2750.6687 
   95000    4671.2603            0            0    7006.8554    2752.3081 
   96000    4674.9165            0            0    7012.3396    2748.6134 
   97000    4671.0777            0            0    7006.5815    2754.3695 
   98000    4672.8048            0            0    7009.1722     2753.307 
   99000    4674.4148            0            0    7011.5871    2752.6581 
  100000    4674.9302            0            0    7012.3603     2753.149 
  101000    4677.9949            0            0    7016.9573    2749.4557 
  102000    4674.3998            0            0    7011.5647    2750.8995 
  103000    4674.3131            0            0    7011.4346     2752.642 
  104000    4677.3501            0            0    7015.9901    2753.2487 
  105000    4676.9447            0            0    7015.3819    2752.7476 
  106000    4673.2616            0            0    7009.8573    2748.8755 
  107000     4674.869            0            0    7012.2684    2753.6329 
  108000    4674.1505            0            0    7011.1906    2752.8016 
  109000    4673.4322            0            0    7010.1133    2753.3162 
  110000    4670.8448            0            0    7006.2322    2755.4032 
  111000    4672.7271            0            0    7009.0556    2753.6645 
  112000    4674.4541            0            0    7011.6461     2753.104 
  113000     4672.934            0            0    7009.3659    2752.4506 
  114000    4681.4388            0            0    7022.1231    2746.6518 
  115000     4672.876            0            0    7009.2789    2754.4575 
  116000    4675.8326            0            0    7013.7138    2750.4311 
  117000     4675.018            0            0    7012.4919    2749.1641 
  118000    4673.4657            0            0    7010.1635    2755.1059 
  119000    4684.1113            0            0    7026.1318    2749.8486 
  120000    4675.3347            0            0    7012.9669     2754.799 
  121000    4669.1088            0            0    7003.6281     2756.078 
  122000    4675.2021            0            0     7012.768     2754.585 
  123000    4674.7742            0            0    7012.1262    2748.8551 
  124000    4673.0406            0            0    7009.5259    2752.0848 
  125000    4677.2903            0            0    7015.9004    2748.7568 
  126000    4675.0825            0            0    7012.5887    2750.9507 
  127000    4671.3228            0            0    7006.9492    2754.7645 
  128000    4676.2135            0            0    7014.2851    2751.5777 
  129000    4677.9135            0            0    7016.8352    2747.4233 
  130000    4672.2049            0            0    7008.2723    2753.4937 
  131000    4674.7388            0            0    7012.0732    2752.0539 
  132000    4675.6165            0            0    7013.3897    2753.6096 
  133000    4672.3664            0            0    7008.5145    2752.4296 
  134000    4675.1252            0            0    7012.6527    2755.0416 
  135000    4674.5638            0            0    7011.8106    2755.2134 
  136000    4676.9041            0            0     7015.321    2753.5061 
  137000    4670.3637            0            0    7005.5105    2754.6871 
  138000    4673.6449            0            0    7010.4323    2750.8552 
  139000    4679.3992            0            0    7019.0638    2747.5848 
  140000    4680.6254            0            0     7020.903    2750.2738 
  141000     4682.132            0            0    7023.1628     2746.507 
  142000    4676.4558            0            0    7014.6486    2751.3114 
  143000    4673.7701            0            0    7010.6201     2751.891 
  144000    4674.1356            0            0    7011.1684    2750.9154 
  145000    4678.8916            0            0    7018.3023    2749.9323 
  146000    4673.9251            0            0    7010.8527    2751.2665 
  147000    4678.4495            0            0    7017.6391    2750.0063 
  148000    4679.5735            0            0    7019.3252     2750.767 
  149000    4672.0242            0            0    7008.0013    2752.2237 
  150000    4678.7678            0            0    7018.1167     2752.142 
  151000    4677.2379            0            0    7015.8218    2753.9367 
  152000    4677.2247            0            0     7015.802    2753.9443 
  153000     4675.917            0            0    7013.8404    2747.5483 
  154000    4673.4956            0            0    7010.2084    2750.1962 
  155000    4676.9482            0            0    7015.3872    2748.4554 
  156000    4676.3285            0            0    7014.4577     2756.232 
  157000    4676.9293            0            0    7015.3589    2747.4942 
  158000    4672.8996            0            0    7009.3143    2752.3644 
  159000    4676.3473            0            0    7014.4859    2749.9006 
  160000    4674.7287            0            0     7012.058    2752.3899 
  161000    4681.3906            0            0    7022.0508    2746.4547 
  162000    4674.1866            0            0    7011.2448    2752.3761 
  163000    4677.7132            0            0    7016.5347     2749.315 
  164000    4673.7532            0            0    7010.5948    2752.9647 
  165000     4677.237            0            0    7015.8204    2751.1002 
  166000    4682.6346            0            0    7023.9168    2741.4326 
  167000     4674.058            0            0     7011.052    2753.7206 
  168000    4675.9691            0            0    7013.9186    2750.6142 
  169000    4672.0026            0            0    7007.9689    2752.3051 
  170000    4673.7488            0            0    7010.5882    2752.7791 
  171000    4679.5814            0            0     7019.337    2751.2202 
  172000    4674.4498            0            0    7011.6397    2753.6184 
  173000    4674.1399            0            0    7011.1749    2752.1217 
  174000    4674.7881            0            0    7012.1471    2751.7094 
  175000    4677.0767            0            0    7015.5799    2748.4355 
  176000     4675.488            0            0     7013.197    2752.8424 
  177000     4677.007            0            0    7015.4755     2749.491 
  178000    4676.0306            0            0    7014.0108    2750.6065 
  179000    4674.2978            0            0    7011.4116    2750.9816 
  180000    4673.6394            0            0    7010.4241    2749.0876 
  181000    4675.5715            0            0    7013.3221    2753.0798 
  182000     4674.619            0            0    7011.8934    2754.0837 
  183000    4676.6994            0            0    7015.0141    2749.3164 
  184000    4678.1777            0            0    7017.2315    2750.2108 
  185000    4680.4484            0            0    7020.6374    2748.3024 
  186000    4673.9411            0            0    7010.8766    2752.7747 
  187000    4679.2973            0            0    7018.9109    2748.5306 
  188000     4669.384            0            0     7004.041    2755.3733 
  189000    4676.2935            0            0    7014.4052    2755.4803 
  190000     4676.986            0            0    7015.4439     2747.971 
  191000    4676.5196            0            0    7014.7444    2751.5764 
  192000    4677.0985            0            0    7015.6126    2751.0144 
  193000    4676.6654            0            0    7014.9631     2753.436 
  194000    4678.0505            0            0    7017.0407     2752.198 
  195000    4678.1412            0            0    7017.1768     2751.074 
  196000    4679.5008            0            0     7019.216    2750.8162 
  197000    4675.2006            0            0    7012.7659    2755.5537 
  198000    4678.8116            0            0    7018.1823    2753.0489 
  199000    4676.0377            0            0    7014.0215     2748.277 
  200000    4677.3028            0            0    7015.9192      2753.86 
  201000    4676.6114            0            0     7014.882    2751.7145 
  202000    4674.3398            0            0    7011.4746    2750.5365 
  203000    4670.2189            0            0    7005.2934    2759.7055 
  204000    4677.5756            0            0    7016.3283    2751.3008 
  205000    4676.4764            0            0    7014.6795    2755.8759 
  206000    4673.8342            0            0    7010.7162    2753.1317 
  207000     4677.645            0            0    7016.4325    2748.4197 
  208000    4676.2149            0            0    7014.2873    2754.3639 
  209000    4678.4767            0            0    7017.6799    2750.6749 
  210000    4673.4043            0            0    7010.0713    2750.8941 
  211000     4676.838            0            0    7015.2219    2750.8347 
  212000    4675.7596            0            0    7013.6043    2751.2838 
  213000    4681.4803            0            0    7022.1854    2748.7097 
  214000    4672.0391            0            0    7008.0236    2755.9334 
  215000    4674.7206            0            0    7012.0459    2754.0409 
  216000    4675.5616            0            0    7013.3073    2753.3131 
  217000    4675.6804            0            0    7013.4855    2753.5407 
  218000    4677.8918            0            0    7016.8026    2750.0612 
  219000    4675.0835            0            0    7012.5901      2753.03 
  220000    4674.5999            0            0    7011.8648    2749.7832 
  221000    4677.9351            0            0    7016.8676    2747.8782 
  222000    4679.6431            0            0    7019.4296    2750.9655 
  223000     4677.381            0            0    7016.0364    2749.9233 
  224000    4678.7299            0            0    7018.0598    2749.9213 
  225000    4678.2286            0            0    7017.3078    2749.4158 
  226000    4680.5286            0            0    7020.7577    2745.2066 
  227000    4677.8073            0            0    7016.6758    2750.6528 
  228000    4675.7737            0            0    7013.6255    2751.3831 
  229000    4681.5343            0            0    7022.2663    2745.1992 
  230000    4679.9599            0            0    7019.9047    2745.4698 
  231000    4681.6728            0            0    7022.4741    2747.3064 
  232000    4677.3639            0            0    7016.0108    2752.9318 
  233000    4678.7021            0            0     7018.018    2750.5382 
  234000    4677.3958            0            0    7016.0586    2749.0464 
  235000    4673.3946            0            0    7010.0568     2752.637 
  236000    4674.4378            0            0    7011.6217    2752.8979 
  237000    4671.8672            0            0    7007.7658    2754.6176 
  238000    4674.7868            0            0    7012.1451     2752.482 
  239000    4678.9182            0            0    7018.3422     2750.727 
  240000    4677.2292            0            0    7015.8087    2748.8872 
  241000    4678.0585            0            0    7017.0527    2751.2655 
  242000    4675.2197            0            0    7012.7945    2755.7733 
  243000    4673.4652            0            0    7010.1627    2755.0617 
  244000    4678.5634            0            0    7017.8099    2751.3934 
  245000    4675.6869            0            0    7013.4953     2752.735 
  246000    4671.3105            0            0    7006.9307    2753.7562 
  247000     4675.414            0            0     7013.086    2750.9083 
  248000    4675.3514            0            0    7012.9921    2753.5952 
  249000    4678.3679            0            0    7017.5168    2749.9046 
  250000    4678.0184            0            0    7016.9926    2748.5805 
  251000    4675.2531            0            0    7012.8446    2753.1779 
  252000    4673.1138            0            0    7009.6357    2753.7165 
  253000     4675.972            0            0     7013.923    2752.5536 
  254000    4678.8577            0            0    7018.2515    2751.9295 
  255000    4676.9223            0            0    7015.3484    2751.6275 
  256000     4669.903            0            0    7004.8195    2757.3913 
  257000    4676.8691            0            0    7015.2685    2750.5835 
  258000    4676.3507            0            0    7014.4909    2748.5339 
  259000    4683.3712            0            0    7025.0217    2747.9183 
  260000    4676.6461            0            0    7014.9341    2750.9406 
  261000    4676.2673            0            0    7014.3659    2755.0629 
  262000    4677.1946            0            0    7015.7568    2750.8419 
  263000    4677.6737            0            0    7016.4755    2750.0274 
  264000    4677.6277            0            0    7016.4064    2751.3047 
  265000    4677.3866            0            0    7016.0448    2753.0354 
  266000    4680.9853            0            0    7021.4428    2750.1765 
  267000    4671.9611            0            0    7007.9067    2753.5216 
  268000    4676.0867            0            0     7014.095    2751.8856 
  269000    4686.3237            0            0    7029.4504     2746.024 
  270000    4675.3651            0            0    7013.0126    2751.1691 
  271000    4673.9226            0            0    7010.8488    2753.7539 
  272000    4676.4012            0            0    7014.5667    2752.8815 
  273000    4679.2635            0            0    7018.8602    2752.2876 
  274000    4677.1832            0            0    7015.7397    2750.5796 
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 1799000    4686.9058            0            0    7030.3236    2752.5579 
 1800000    4674.2621            0            0    7011.3581    2762.0633 
 1801000    4681.3396            0            0    7021.9743    2759.1976 
 1802000    4679.8218            0            0    7019.6975    2757.7666 
 1803000    4685.7094            0            0     7028.529    2752.9541 
 1804000    4681.9773            0            0    7022.9308    2756.9803 
 1805000    4684.1652            0            0    7026.2126    2753.9732 
 1806000    4679.9554            0            0     7019.898    2758.9989 
 1807000    4682.4661            0            0     7023.664    2759.6407 
 1808000    4685.2345            0            0    7027.8166    2757.5915 
 1809000    4683.7331            0            0    7025.5645    2756.6004 
 1810000    4681.6366            0            0    7022.4197    2756.8766 
 1811000    4682.8368            0            0    7024.2201    2755.6722 
 1812000    4686.3372            0            0    7029.4707    2751.9217 
 1813000     4687.549            0            0    7031.2884    2752.0907 
 1814000    4681.3431            0            0    7021.9796    2757.7185 
 1815000    4681.0343            0            0    7021.5164    2758.0857 
 1816000    4683.1223            0            0    7024.6484    2758.2246 
 1817000    4684.9475            0            0    7027.3862    2756.5099 
 1818000    4681.1387            0            0    7021.6729    2754.0452 
 1819000    4682.9614            0            0    7024.4069    2757.3099 
 1820000    4683.3824            0            0    7025.0385    2754.8561 
 1821000    4687.4859            0            0    7031.1937    2754.2434 
 1822000    4682.3068            0            0    7023.4251    2754.0212 
 1823000    4681.0902            0            0    7021.6002    2755.0657 
 1824000     4687.463            0            0    7031.1593    2754.0118 
 1825000    4682.3397            0            0    7023.4745    2754.7825 
 1826000    4683.0069            0            0    7024.4752     2755.476 
 1827000    4685.9748            0            0    7028.9271    2755.8356 
 1828000    4678.9442            0            0    7018.3811    2756.7518 
 1829000    4683.4976            0            0    7025.2113    2756.0721 
 1830000    4686.5694            0            0     7029.819    2755.7192 
 1831000    4678.4542            0            0    7017.6462    2757.6089 
 1832000    4685.4838            0            0    7028.1905    2750.5796 
 1833000    4683.4916            0            0    7025.2022    2756.9989 
 1834000    4685.4497            0            0    7028.1395    2755.4353 
 1835000    4682.8356            0            0    7024.2182    2755.6117 
 1836000     4682.431            0            0    7023.6114    2754.4372 
 1837000    4683.2213            0            0    7024.7968    2755.6485 
 1838000    4678.6016            0            0    7017.8672    2762.8503 
 1839000    4684.1082            0            0    7026.1271    2755.3693 
 1840000    4683.8884            0            0    7025.7975    2756.0949 
 1841000    4685.9405            0            0    7028.8755    2751.2185 
 1842000    4681.0257            0            0    7021.5035    2759.5518 
 1843000    4686.2007            0            0    7029.2659    2751.6319 
 1844000    4686.3452            0            0    7029.4827     2758.797 
 1845000     4685.461            0            0    7028.1563    2753.6253 
 1846000    4682.4962            0            0    7023.7092    2757.7564 
 1847000     4683.473            0            0    7025.1744    2754.2484 
 1848000    4683.7515            0            0    7025.5921    2757.5761 
 1849000    4683.8278            0            0    7025.7066    2758.7343 
 1850000    4688.1775            0            0    7032.2311    2752.5923 
 1851000    4685.8946            0            0    7028.8068    2753.1004 
 1852000     4684.647            0            0    7026.9353    2755.3814 
 1853000    4683.2614            0            0    7024.8569    2758.9381 
 1854000    4682.2758            0            0    7023.3787    2760.7898 
 1855000      4684.46            0            0    7026.6548    2756.7835 
 1856000    4683.2174            0            0     7024.791    2754.7907 
 1857000    4684.9204            0            0    7027.3455    2756.3681 
 1858000    4683.0783            0            0    7024.5823    2755.4108 
 1859000    4686.8708            0            0     7030.271    2756.7204 
 1860000     4679.585            0            0    7019.3424    2759.5967 
 1861000    4681.8462            0            0    7022.7342    2753.6194 
 1862000    4681.9501            0            0    7022.8901    2759.6768 
 1863000    4689.2674            0            0     7033.866    2753.2075 
 1864000    4679.5759            0            0    7019.3288    2753.6401 
 1865000    4691.1603            0            0    7036.7053    2750.4281 
 1866000    4686.9356            0            0    7030.3683    2751.7813 
 1867000    4688.9974            0            0    7033.4609    2752.5943 
 1868000    4681.0829            0            0    7021.5892    2754.6695 
 1869000    4682.2962            0            0    7023.4092    2756.2621 
 1870000     4680.624            0            0     7020.901    2761.5361 
 1871000    4681.9218            0            0    7022.8477    2758.1066 
 1872000    4681.2677            0            0    7021.8664    2757.1862 
 1873000    4683.7728            0            0    7025.6241    2756.0083 
 1874000    4678.5185            0            0    7017.7427    2757.9973 
 1875000    4682.0347            0            0     7023.017     2758.076 
 1876000    4680.5972            0            0    7020.8607    2758.7992 
 1877000    4685.0259            0            0    7027.5037     2755.717 
 1878000    4683.4072            0            0    7025.0757    2756.9748 
 1879000      4683.79            0            0    7025.6499    2755.4593 
 1880000    4687.4052            0            0    7031.0726     2756.197 
 1881000    4689.3102            0            0    7033.9302    2752.7433 
 1882000    4685.9196            0            0    7028.8443    2754.7034 
 1883000     4682.698            0            0    7024.0119    2756.7264 
 1884000    4685.1177            0            0    7027.6415    2754.5377 
 1885000    4678.0423            0            0    7017.0284    2758.6704 
 1886000    4682.2342            0            0    7023.3162    2756.6391 
 1887000    4684.2586            0            0    7026.3527    2758.8874 
 1888000    4681.2162            0            0    7021.7891    2759.5287 
 1889000    4686.2788            0            0    7029.3831    2752.2825 
 1890000    4689.7419            0            0    7034.5776    2750.9573 
 1891000    4676.9427            0            0    7015.3789    2761.9224 
 1892000    4681.7452            0            0    7022.5826    2758.1455 
 1893000    4685.1431            0            0    7027.6794    2753.1787 
 1894000    4688.4259            0            0    7032.6037    2752.6991 
 1895000    4685.8864            0            0    7028.7945    2752.4046 
 1896000    4686.7578            0            0    7030.1016    2755.8037 
 1897000    4685.9414            0            0    7028.8769    2757.0285 
 1898000    4679.5326            0            0    7019.2638    2758.5287 
 1899000    4680.2608            0            0    7020.3562    2755.9056 
 1900000    4677.6324            0            0    7016.4135    2760.9254 
 1901000    4688.7335            0            0    7033.0651    2752.3545 
 1902000    4681.9975            0            0    7022.9611    2757.4525 
 1903000    4687.3289            0            0    7030.9581    2754.3381 
 1904000    4678.0607            0            0    7017.0559    2758.5919 
 1905000    4684.7912            0            0    7027.1517    2757.4412 
 1906000    4689.7777            0            0    7034.6314    2752.8246 
 1907000    4681.5411            0            0    7022.2765    2759.4952 
 1908000    4686.9832            0            0    7030.4397    2753.5054 
 1909000    4682.7306            0            0    7024.0608    2753.6531 
 1910000    4679.3803            0            0    7019.0354    2760.0601 
 1911000    4680.0365            0            0    7020.0197    2758.2685 
 1912000    4683.2952            0            0    7024.9077    2755.9129 
 1913000    4684.6896            0            0    7026.9993    2755.8189 
 1914000      4685.27            0            0    7027.8699    2754.7417 
 1915000    4684.6323            0            0    7026.9133    2757.2141 
 1916000    4683.9294            0            0    7025.8589    2755.4172 
 1917000    4687.5675            0            0    7031.3161    2753.8473 
 1918000    4682.2016            0            0    7023.2673    2754.5365 
 1919000    4683.8599            0            0    7025.7548    2754.7832 
 1920000    4684.2486            0            0    7026.3377    2758.3396 
 1921000    4678.0378            0            0    7017.0216    2761.8241 
 1922000    4682.5325            0            0    7023.7636    2755.3961 
 1923000    4679.4942            0            0    7019.2062    2756.3463 
 1924000    4689.4111            0            0    7034.0815    2749.8529 
 1925000    4682.2768            0            0    7023.3801    2754.5844 
 1926000    4683.3459            0            0    7024.9838    2754.3799 
 1927000    4682.7331            0            0    7024.0645    2755.9853 
 1928000    4685.9028            0            0    7028.8191    2754.9206 
 1929000     4681.829            0            0    7022.7084    2759.0351 
 1930000    4683.7699            0            0    7025.6197    2754.4167 
 1931000    4687.7857            0            0    7031.6434    2752.3199 
 1932000    4688.3577            0            0    7032.5013    2755.6477 
 1933000    4685.0664            0            0    7027.5645    2755.6874 
 1934000    4684.2249            0            0    7026.3022    2752.6731 
 1935000    4681.2035            0            0    7021.7702    2758.9901 
 1936000     4684.132            0            0    7026.1629    2754.6198 
 1937000    4685.6723            0            0    7028.4733    2755.1416 
 1938000    4685.3732            0            0    7028.0247    2755.6662 
 1939000    4680.7207            0            0    7021.0459    2756.7075 
 1940000    4682.7493            0            0    7024.0889    2755.4673 
 1941000     4681.135            0            0    7021.6673     2755.905 
 1942000    4682.0684            0            0    7023.0675    2756.2745 
 1943000    4686.1784            0            0    7029.2325    2756.4687 
 1944000     4688.126            0            0    7032.1539    2754.7096 
 1945000    4684.0101            0            0    7025.9801    2756.8964 
 1946000    4686.1743            0            0    7029.2264    2752.7262 
 1947000    4687.0501            0            0      7030.54    2751.1972 
 1948000     4686.811            0            0    7030.1814    2753.3288 
 1949000    4684.5973            0            0    7026.8609    2755.8637 
 1950000    4689.1922            0            0    7033.7532    2751.8798 
 1951000    4682.2526            0            0    7023.3438    2756.6904 
 1952000    4685.9701            0            0      7028.92    2757.0992 
 1953000     4685.168            0            0    7027.7169    2755.0485 
 1954000    4684.2125            0            0    7026.2837    2756.0824 
 1955000    4687.5506            0            0    7031.2907    2754.1021 
 1956000    4682.5245            0            0    7023.7517    2757.0593 
 1957000     4684.614            0            0    7026.8858    2754.1313 
 1958000    4682.8675            0            0    7024.2661     2757.085 
 1959000    4684.0546            0            0    7026.0468    2759.1965 
 1960000    4682.2076            0            0    7023.2763    2756.7441 
 1961000    4686.1173            0            0    7029.1408    2756.8589 
 1962000    4686.7889            0            0    7030.1482    2753.6381 
 1963000    4685.2751            0            0    7027.8775    2759.3321 
 1964000     4684.243            0            0    7026.3293    2756.7607 
 1965000    4683.9747            0            0    7025.9269    2753.1824 
 1966000    4685.6288            0            0    7028.4081    2756.2986 
 1967000    4686.1724            0            0    7029.2235    2754.5131 
 1968000    4684.5705            0            0    7026.8206    2755.5046 
 1969000    4684.3619            0            0    7026.5076    2755.3631 
 1970000    4684.4368            0            0    7026.6201    2751.7379 
 1971000    4685.2006            0            0    7027.7657     2755.544 
 1972000    4684.2656            0            0    7026.3633    2755.1462 
 1973000    4684.3907            0            0    7026.5509    2753.5052 
 1974000    4680.9554            0            0     7021.398    2761.8021 
 1975000    4686.3501            0            0      7029.49    2751.0204 
 1976000    4685.9256            0            0    7028.8532     2755.795 
 1977000     4685.744            0            0    7028.5808    2754.5021 
 1978000    4683.6715            0            0    7025.4721    2756.5962 
 1979000    4681.0352            0            0    7021.5177    2757.2525 
 1980000    4682.8497            0            0    7024.2394    2753.9834 
 1981000     4688.559            0            0    7032.8033    2754.4585 
 1982000    4687.8258            0            0    7031.7035    2755.3232 
 1983000    4688.8981            0            0     7033.312     2754.824 
 1984000    4687.6652            0            0    7031.4626    2754.6143 
 1985000    4682.7964            0            0    7024.1595    2755.3646 
 1986000    4686.0434            0            0      7029.03    2755.4089 
 1987000    4689.7086            0            0    7034.5277    2754.3677 
 1988000    4680.6286            0            0    7020.9079    2757.9648 
 1989000    4683.6447            0            0    7025.4319    2756.9284 
 1990000    4679.6663            0            0    7019.4643    2758.3528 
 1991000    4685.7965            0            0    7028.6595    2755.9149 
 1992000    4681.1738            0            0    7021.7256    2757.8046 
 1993000    4691.5369            0            0    7037.2702    2752.0832 
 1994000    4685.0105            0            0    7027.4807    2756.5715 
 1995000    4680.2887            0            0    7020.3979    2757.9494 
 1996000    4681.6805            0            0    7022.4856    2755.5167 
 1997000     4690.599            0            0    7035.8632    2753.9799 
 1998000    4681.1138            0            0    7021.6356    2760.8652 
 1999000    4683.1329            0            0    7024.6642    2757.1724 
 2000000    4687.2672            0            0    7030.8657    2754.7965 
 2001000    4683.8959            0            0    7025.8088    2755.5116 
 2002000    4684.3154            0            0     7026.438    2756.5326 
 2003000    4680.5605            0            0    7020.8057    2760.1431 
 2004000    4682.4262            0            0    7023.6042    2753.9558 
 2005000    4687.3816            0            0    7031.0373    2757.4862 
 2006000    4690.3811            0            0    7035.5364    2749.6486 
 2007000    4683.7448            0            0     7025.582    2753.7054 
 2008000    4687.9359            0            0    7031.8686    2753.7211 
 2009000    4682.1264            0            0    7023.1544    2758.5191 
 2010000    4688.7584            0            0    7033.1025    2750.6655 
 2011000    4680.8339            0            0    7021.2157    2757.6039 
 2012000    4686.5257            0            0    7029.7534    2755.7411 
 2013000    4687.3855            0            0    7031.0431    2752.6729 
 2014000    4682.8804            0            0    7024.2855      2755.14 
 2015000    4685.4475            0            0    7028.1361     2754.709 
 2016000    4684.4223            0            0    7026.5983    2754.6604 
 2017000    4681.9004            0            0    7022.8154    2757.9642 
 2018000    4680.6904            0            0    7021.0006     2756.867 
 2019000    4684.7305            0            0    7027.0605    2756.9563 
 2020000     4680.733            0            0    7021.0643    2755.0689 
 2021000    4687.6448            0            0     7031.432    2753.9605 
 2022000    4684.6876            0            0    7026.9962    2752.8402 
 2023000    4681.6461            0            0     7022.434    2755.6321 
 2024000    4687.2016            0            0    7030.7672    2756.9083 
 2025000    4684.6966            0            0    7027.0098    2758.7626 
 2026000    4685.0921            0            0    7027.6031    2756.5094 
 2027000    4683.6884            0            0    7025.4974    2756.3598 
 2028000    4682.9708            0            0    7024.4211    2761.6894 
 2029000    4685.4578            0            0    7028.1516     2757.548 
 2030000    4685.2366            0            0    7027.8198    2757.6751 
 2031000     4686.033            0            0    7029.0144    2758.6244 
 2032000    4690.7194            0            0    7036.0439    2754.2697 
 2033000     4685.189            0            0    7027.7483    2756.8441 
 2034000    4683.6255            0            0    7025.4031    2753.2737 
 2035000    4690.4902            0            0    7035.7001    2751.5335 
 2036000    4680.4056            0            0    7020.5732    2757.0494 
 2037000    4684.3523            0            0    7026.4933    2755.6926 
 2038000    4680.6167            0            0      7020.89     2758.341 
 2039000    4682.3984            0            0    7023.5625    2753.9926 
 2040000    4690.1333            0            0    7035.1648    2754.1292 
 2041000    4683.3703            0            0    7025.0203    2753.1561 
 2042000    4687.6534            0            0    7031.4449    2752.2132 
 2043000    4688.2873            0            0    7032.3959    2754.7892 
 2044000    4684.8813            0            0    7027.2868    2756.8052 
 2045000    4685.2335            0            0    7027.8151    2754.9621 
 2046000    4685.0675            0            0    7027.5662     2757.221 
 2047000     4686.862            0            0    7030.2578    2755.4766 
 2048000    4690.4699            0            0    7035.6696    2751.5911 
 2049000    4688.3153            0            0    7032.4377    2751.6573 
 2050000    4674.2109            0            0    7011.2813    2763.9032 
 2051000    4682.7962            0            0    7024.1592    2759.4277 
 2052000    4684.2139            0            0    7026.2857    2756.4872 
 2053000    4689.3105            0            0    7033.9306    2754.7147 
 2054000     4685.578            0            0    7028.3318    2752.3521 
 2055000    4685.0514            0            0     7027.542    2756.5302 
 2056000    4684.5363            0            0    7026.7693    2757.1482 
 2057000    4688.5363            0            0    7032.7694    2757.0991 
 2058000     4685.842            0            0    7028.7279    2759.3195 
 2059000    4685.7553            0            0    7028.5978    2754.5508 
 2060000    4687.1434            0            0      7030.68    2754.2375 
 2061000    4680.8059            0            0    7021.1737    2757.5743 
 2062000    4684.1758            0            0    7026.2286    2754.8991 
 2063000    4684.8135            0            0    7027.1852    2754.6784 
 2064000    4689.0251            0            0    7033.5024     2753.896 
 2065000    4689.7308            0            0     7034.561    2755.0474 
 2066000    4683.8259            0            0    7025.7038    2755.8292 
 2067000    4685.2622            0            0    7027.8582    2755.9089 
 2068000    4684.1219            0            0    7026.1477    2756.2667 
 2069000    4682.8547            0            0     7024.247    2757.8025 
 2070000    4682.4571            0            0    7023.6505    2758.4005 
 2071000    4677.9526            0            0    7016.8938    2761.2935 
 2072000    4681.0957            0            0    7021.6084    2760.2735 
 2073000    4680.3646            0            0    7020.5118    2758.3488 
 2074000    4675.6356            0            0    7013.4183     2762.843 
 2075000    4685.3818            0            0    7028.0376    2757.4636 
 2076000    4681.1219            0            0    7021.6477    2757.8143 
 2077000    4686.5822            0            0    7029.8382    2755.1081 
 2078000    4692.2408            0            0     7038.326    2751.1757 
 2079000    4684.9346            0            0    7027.3667    2752.5305 
 2080000    4680.9188            0            0    7021.3431     2757.067 
 2081000    4685.0819            0            0    7027.5876    2755.0924 
 2082000     4682.714            0            0    7024.0359    2757.8516 
 2083000    4682.7973            0            0    7024.1609    2753.2976 
 2084000    4687.6125            0            0    7031.3836    2756.3782 
 2085000    4681.4725            0            0    7022.1736     2756.895 
 2086000    4683.0782            0            0    7024.5821    2757.3587 
 2087000    4682.3009            0            0    7023.4162    2755.7462 
 2088000    4685.1543            0            0    7027.6963    2754.6344 
 2089000    4685.1021            0            0     7027.618    2756.8416 
 2090000    4685.1998            0            0    7027.7645    2755.9471 
 2091000    4684.0636            0            0    7026.0603     2756.627 
 2092000    4684.2781            0            0     7026.382     2756.914 
 2093000    4686.3356            0            0    7029.4683    2752.9502 
 2094000    4685.3272            0            0    7027.9557    2755.6533 
 2095000    4683.0359            0            0    7024.5187    2759.2355 
 2096000     4683.983            0            0    7025.9393    2758.6083 
 2097000    4678.7721            0            0    7018.1231    2760.5514 
 2098000    4682.1901            0            0      7023.25    2755.6284 
 2099000    4685.9451            0            0    7028.8825     2758.648 
 2100000     4685.704            0            0    7028.5209      2759.21 
 2101000    4683.8236            0            0    7025.7003    2757.5073 
 2102000     4687.147            0            0    7030.6853    2756.8262 
 2103000    4682.1628            0            0    7023.2091    2760.4045 
 2104000    4687.8451            0            0    7031.7325    2750.8906 
 2105000    4680.1221            0            0    7020.1481    2758.7761 
 2106000    4686.2758            0            0    7029.3785    2756.3739 
 2107000    4689.9392            0            0    7034.8736    2750.7426 
 2108000    4685.6945            0            0    7028.5066    2756.3185 
 2109000    4687.2255            0            0    7030.8032    2755.4896 
 2110000    4685.0577            0            0    7027.5514    2759.1749 
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 2450000    4686.3254            0            0     7029.453    2754.5194 
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 2468000    4685.0477            0            0    7027.5364     2761.809 

 2469000    4688.9124            0            0    7033.3334    2760.9018 
 2470000    4685.2586            0            0    7027.8527    2760.0986 
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 2520000    4689.8133            0            0    7034.6847    2757.7936 
 2521000    4694.8795            0            0     7042.284    2755.0913 
 2522000    4688.6009            0            0    7032.8662      2754.32 
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 2550000    4689.4402            0            0    7034.1251    2758.1955 
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 2559000    4685.9952            0            0    7028.9576       2760.4 
 2560000    4688.1104            0            0    7032.1304    2761.4144 
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 2570000    4688.0194            0            0    7031.9939    2757.0411 
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 2580000     4686.004            0            0    7028.9709    2759.1469 
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 2583000    4688.6123            0            0    7032.8833     2760.571 
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 2600000     4683.911            0            0    7025.8313    2763.1786 
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 2602000    4694.2836            0            0    7041.3902     2749.744 
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 2627000    4687.7251            0            0    7031.5526      2761.75 
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 2630000    4685.3039            0            0    7027.9207    2760.2326 
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 2697000    4686.6912            0            0    7030.0016    2759.3063 
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 3650000     4697.218            0            0    7045.7918     2755.598 
 3651000    4689.5669            0            0    7034.3151    2762.9172 
 3652000    4697.4518            0            0    7046.1424    2759.2185 
 3653000    4691.2007            0            0    7036.7659     2762.164 
 3654000    4695.0206            0            0    7042.4957    2759.4118 
 3655000     4692.514            0            0    7038.7358    2762.4285 
 3656000    4691.9456            0            0    7037.8832    2763.8121 
 3657000    4693.8636            0            0    7040.7602    2759.6878 
 3658000    4692.4312            0            0    7038.6117    2761.3127 
 3659000     4695.596            0            0    7043.3588    2761.2668 
 3660000    4688.4539            0            0    7032.6457     2761.935 
 3661000    4694.4627            0            0    7041.6589    2759.0986 
 3662000    4691.3096            0            0    7036.9292    2763.3572 
 3663000    4695.2186            0            0    7042.7926    2760.6927 
 3664000    4695.2761            0            0     7042.879    2760.4087 
 3665000    4689.7583            0            0    7034.6022    2762.6075 
 3666000    4698.5414            0            0    7047.7769    2757.9398 
 3667000    4691.6974            0            0     7037.511    2762.5736 
 3668000    4693.2103            0            0    7039.7802    2761.4126 
 3669000    4687.6153            0            0    7031.3877    2763.5917 
 3670000    4693.3991            0            0    7040.0635    2757.6191 
 3671000    4695.7231            0            0    7043.5494     2761.577 
 3672000    4695.2896            0            0    7042.8992    2758.0622 
 3673000     4695.583            0            0    7043.3393    2759.2064 
 3674000    4692.9024            0            0    7039.3184    2763.8891 
 3675000     4696.093            0            0    7044.1044    2760.6436 
 3676000    4691.3166            0            0    7036.9397    2758.2547 
 3677000      4687.35            0            0    7030.9898    2767.1604 
 3678000       4697.2            0            0    7045.7648    2758.8441 
 3679000    4691.3405            0            0    7036.9756    2763.4708 
 3680000    4697.2974            0            0    7045.9109    2760.0288 
 3681000    4698.2803            0            0    7047.3852    2757.6069 
 3682000    4690.3791            0            0    7035.5335    2763.0725 
 3683000    4697.2232            0            0    7045.7996    2758.3858 
 3684000    4695.9287            0            0    7043.8578    2756.9019 
 3685000    4697.8969            0            0      7046.81    2758.5184 
 3686000    4697.2804            0            0    7045.8854    2758.8643 
 3687000    4689.9456            0            0    7034.8832    2764.9203 
 3688000    4699.1472            0            0    7048.6856    2757.5792 
 3689000    4692.0441            0            0     7038.031    2761.7842 
 3690000    4695.1732            0            0    7042.7247    2758.0553 
 3691000    4694.1148            0            0     7041.137    2757.7668 
 3692000    4691.9231            0            0    7037.8495    2760.9988 
 3693000    4695.1257            0            0    7042.6534    2760.3029 
 3694000    4695.2171            0            0    7042.7904    2758.2286 
 3695000    4692.6156            0            0    7038.8882    2764.8167 
 3696000    4697.7139            0            0    7046.5356    2758.7302 
 3697000    4696.2291            0            0    7044.3084    27