Identifying sections where the element aperture for V6.501 differs from the continuous model for V6.500

Develop the method first with just one aperture component.  Build a table

"index_95.gif"

LHCB1$START 0 0 0.029
IP1 0 0.029 0.029
MBAS.R1 2.65 0 0.029
TAS.1R1 20.915 0.017 0.0193214
BPMSW.1R1.B1 21.475 0.03 0.03
MQXA.1R1 29.335 0.01895 0.01895
MCBX.1R1 29.842 0.01895 0.01895
BPMS.2R1.B1 31.529 0.0301 0.0301
MQXB.A2R1 37.55 0.024 0.024
MCBX.2R1 38.019 0.024 0.024
MQXB.B2R1 44.05 0.024 0.024
TASB.3R1 45.942 0.027554 0.0275543
MQSX.3R1 46.7195 0.024 0.024
MQXA.3R1 53.335 0.024 0.024
MCBX.3R1 53.814 0.024 0.024
MCX3.3R1 53.814 0.024 0.024
MCSOX.3R1 54.297 0.024 0.024
DFBXB.3R1 57.972 0.0288 0.0357966
BPMSY.4R1.B1 58.3145 0.04 0.04
MBXW.A4R1 63.022 0.064 0.064

"index_96.gif"

LHCB1$START 0 0 0.029
IP1 0 0.029 0.029
MBAS.R1 2.65 0 0.029
TAS.1R1 20.915 0.017 0.0193214
BPMSW.1R1.B1 21.475 0.03 0.03
MQXA.1R1 29.335 0.01895 0.01895
MCBX.1R1 29.842 0.01895 0.01895
BPMS.2R1.B1 31.529 0.0301 0.0301
MQXB.A2R1 37.55 0.024 0.024
MCBX.2R1 38.019 0.024 0.024
MQXB.B2R1 44.05 0.024 0.024
TASB.3R1 45.942 0.027554 0.0275543
MQSX.3R1 46.7195 0.024 0.024
MQXA.3R1 53.335 0.024 0.024
MCBX.3R1 53.814 0.024 0.024
MCX3.3R1 53.814 0.024 0.024
MCSOX.3R1 54.297 0.024 0.024
DFBXB.3R1 57.972 0.0288 0.0357966
BPMSY.4R1.B1 58.3145 0.04 0.04
MBXW.A4R1 63.022 0.064 0.064
MBXW.B4R1 67.288 0.064 0.064
MBXW.C4R1 71.554 0.064 0.064
MBXW.D4R1 75.82 0.064 0.064
MBXW.E4R1 80.086 0.064 0.064
MBXW.F4R1 84.352 0.064 0.064
X1FCR.4R1 141.168 0 0.02728
BRANA.4R1 141.368 0 0.026
TANAR.4R1 142.75 0 0.026
BPMWB.4R1.B1 151.095 0.03 0.03
MBRC.4R1.B1 162.625 0.0313 0.0313
MCBYV.A4R1.B1 164.889 0.0289 0.0289
MCBYH.4R1.B1 166.185 0.0289 0.0289
MCBYV.B4R1.B1 167.481 0.0289 0.0289
MQY.4R1.B1 171.253 0.0289 0.0289
BPMYA.4R1.B1 172.227 0.03 0.03
TCL.5R1.B1 184.857 0.04 0.04
MCBCH.5R1.B1 193.898 0.02255 0.02255
MQML.5R1.B1 198.89 0.02255 0.02255
BPM.5R1.B1 199.635 0.024 0.024
MCBCV.6R1.B1 225.798 0.01765 0.01765
MQML.6R1.B1 230.79 0.01765 0.01765
BPMR.6R1.B1 231.535 0.024 0.024
XRPV.A7R1.B1 237.398 0 0.0289
BPMSA.7R1.B1 237.751 0 0.0289
XRPV.B7R1.B1 241.538 0 0.0289
DFBAB.7R1.B1 258.784 0.027633 0.0276335
BPM_A.7R1.B1 259.259 0.024 0.024
MQM.A7R1.B1 263.404 0.022 0.022
MQM.B7R1.B1 267.171 0.022 0.022
MCBCH.7R1.B1 268.262 0.022 0.022
S.DS.R1.B1 268.904 0.022 0.022
MCDO.8R1.B1 269.245 0.022 0.022
MB.A8R1.B1 283.884 0.022 0.022
MCS.A8R1.B1 284.213 0.022 0.022
MB.B8R1.B1 299.545 0.022 0.022
MCS.B8R1.B1 299.874 0.022 0.022
BPM.8R1.B1 300.698 0.024 0.024
MQML.8R1.B1 306.243 0.022 0.022
MCBCV.8R1.B1 307.335 0.022 0.022
MCDO.9R1.B1 308.311 0.022 0.022
MB.A9R1.B1 322.95 0.022 0.022
MCS.A9R1.B1 323.279 0.022 0.022
MB.B9R1.B1 338.611 0.022 0.022
MCS.B9R1.B1 338.94 0.022 0.022
BPM.9R1.B1 339.765 0.024 0.024
MQMC.9R1.B1 342.941 0.022 0.022
MQM.9R1.B1 346.707 0.022 0.022
MCBCH.9R1.B1 347.798 0.022 0.022
MCDO.10R1.B1 348.777 0.022 0.022
MB.A10R1.B1 363.416 0.022 0.022
MCS.A10R1.B1 363.745 0.022 0.022
MB.B10R1.B1 379.077 0.022 0.022
MCS.B10R1.B1 379.406 0.022 0.022
BPM.10R1.B1 380.23 0.024 0.024
MQML.10R1.B1 385.775 0.022 0.022
MCBCV.10R1.B1 386.867 0.022 0.022
MCDO.11R1.B1 387.843 0.022 0.022
MB.A11R1.B1 402.482 0.022 0.022
MCS.A11R1.B1 402.811 0.022 0.022
MB.B11R1.B1 418.143 0.022 0.022
MCS.B11R1.B1 418.472 0.022 0.022
BPM.11R1.B1 433.013 0.024 0.024
MQ.11R1.B1 437.11 0.022 0.022
MQTLI.11R1.B1 438.579 0.022 0.022
MS.11R1.B1 439.125 0.022 0.022
MCBH.11R1.B1 439.857 0.022 0.022
S.ARC.12.B1 440.285 0.022 0.022
MCDO.A12R1.B1 440.626 0.022 0.022
MB.A12R1.B1 455.265 0.022 0.022
MCS.A12R1.B1 455.594 0.022 0.022
MB.B12R1.B1 470.925 0.022 0.022
MCS.B12R1.B1 471.255 0.022 0.022
MCDO.B12R1.B1 471.947 0.022 0.022
MB.C12R1.B1 486.586 0.022 0.022
MCS.C12R1.B1 486.915 0.022 0.022
BPM.12R1.B1 487.739 0.024 0.024
MQT.12R1.B1 488.653 0.022 0.022
MQ.12R1.B1 492.051 0.022 0.022
MS.12R1.B1 492.581 0.022 0.022
MCBV.12R1.B1 493.313 0.022 0.022
MB.A13R1.B1 508.716 0.022 0.022
MCS.A13R1.B1 509.046 0.022 0.022
MCDO.13R1.B1 509.738 0.022 0.022
MB.B13R1.B1 524.377 0.022 0.022
MCS.B13R1.B1 524.706 0.022 0.022
MB.C13R1.B1 540.037 0.022 0.022
MCS.C13R1.B1 540.367 0.022 0.022
BPM.13R1.B1 541.191 0.024 0.024
MQT.13R1.B1 542.105 0.022 0.022
MQ.13R1.B1 545.503 0.022 0.022
MS.13R1.B1 546.032 0.022 0.022
MCBH.13R1.B1 546.764 0.022 0.022
E.DS.R1.B1 547.188 0.022 0.022
MCDO.A14R1.B1 547.529 0.022 0.022
MB.A14R1.B1 562.168 0.022 0.022
MCS.A14R1.B1 562.497 0.022 0.022
MB.B14R1.B1 577.828 0.022 0.022
MCS.B14R1.B1 578.158 0.022 0.022
MCDO.B14R1.B1 578.85 0.022 0.022
MB.C14R1.B1 593.489 0.022 0.022
MCS.C14R1.B1 593.818 0.022 0.022
BPM.14R1.B1 594.642 0.024 0.024
MQT.14R1.B1 595.556 0.022 0.022
MQ.14R1.B1 598.954 0.022 0.022
MS.14R1.B1 599.484 0.022 0.022
MCBV.14R1.B1 600.216 0.022 0.022
MB.A15R1.B1 615.619 0.022 0.022
MCS.A15R1.B1 615.949 0.022 0.022
MCDO.15R1.B1 616.641 0.022 0.022
MB.B15R1.B1 631.28 0.022 0.022
MCS.B15R1.B1 631.609 0.022 0.022
MB.C15R1.B1 646.94 0.022 0.022
MCS.C15R1.B1 647.27 0.022 0.022
BPM.15R1.B1 648.094 0.024 0.024
MQT.15R1.B1 649.008 0.022 0.022
MQ.15R1.B1 652.406 0.022 0.022
MS.15R1.B1 652.935 0.022 0.022
MCBH.15R1.B1 653.667 0.022 0.022
MCDO.A16R1.B1 654.432 0.022 0.022
MB.A16R1.B1 669.071 0.022 0.022
MCS.A16R1.B1 669.4 0.022 0.022
MB.B16R1.B1 684.731 0.022 0.022
MCS.B16R1.B1 685.061 0.022 0.022
MCDO.B16R1.B1 685.753 0.022 0.022
MB.C16R1.B1 700.392 0.022 0.022
MCS.C16R1.B1 700.721 0.022 0.022
BPM.16R1.B1 701.545 0.024 0.024
MQT.16R1.B1 702.459 0.022 0.022
MQ.16R1.B1 705.857 0.022 0.022
MS.16R1.B1 706.387 0.022 0.022

"index_97.gif"

"index_98.gif"

Simple plot of the differences between the two versions of the APER_1 component

"index_99.gif"

"index_100.gif"

"index_101.gif"

"index_102.gif"

A number of the difference occur because the V6.501 element aperture is unassigned (zero after we processed it) for elements whose names did not appear in the V6.500 sequence.  Create a list of elements where the difference is significant but excluding those.

"index_104.gif"

Plotting the s values, we see that they cluster in a few regions.

"index_105.gif"

"index_106.gif"

We can try to separate the clusters using a length scale of 200 m

"index_107.gif"

"index_108.gif"

"index_109.gif"

"index_110.gif"

But is that the right scale?  Let's look at varying the scale d:

"index_111.gif"

"index_112.gif"

Looks like d=240m would be a good choice.  Or maybe 100 m.

But we need to do this for all 4 aperture components.  Anbd then again for LHCB2.   Here is a program which defines an array appdiffs[seq] for any sequence and a trial value of the distance scale.

"index_113.gif"

Here we choose our length scale for clustering:

"index_114.gif"

Graphics:LHCB1

Graphics:LHCB2

"index_117.gif"

"index_118.gif"

"index_119.gif"

TAS.1R1 20.915 0.017 0.017 0.017 0.017 0.0193214 0.0193214 0.0193214 0.0193214

"index_120.gif"

"index_121.gif"

"index_122.gif"

"index_123.gif"

"index_124.gif"

Created by Wolfram Mathematica 6.0  (30 August 2007) Valid XHTML 1.1!