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[lammps-users] Issues with CNT Thermal Conductivity Calculations


From: "Daksha, Chaitanya Mrityunjay" <daksha@...2437...>
Date: Tue, 29 Aug 2017 19:06:26 +0000

Dear LAMMPS Users,

 

I am trying to calculate the thermal conductivity of a (10,10) CNT that is 5 nm in length using the Green-Kubo formalism.  I modified the liquid Argon LAMMPS thermal conductivity example for CNT.  First, I equilibrated the CNT structure at 300K, and then I ran the simulation to get the heat flux, heat current auto correlation function (HCACF) and thermal conductivity. To plot the HCACF, I averaged columns 4, 5, and 6 in the ‘J0Jt.dat’ file for every 1000 timesteps (which is my dump interval). 

 

 

Currently I am having two problems -

  1. The HCACF does not decay to zero. I have tried running the simulation for up to 1200 ps, but the HCACF still did not decay to zero. 
  2. The thermal conductivity value I attain differs based on the correlation length parameter I use in the ‘fix ave/correlate’ command.  Should the conductivity be independent of correlation length? If not, then how should I determine the appropriate correlation length?

 

I checked the LAMMPS email archive, but I was not able to find anything specific to my issues. Attached is the LAMMPS script, as well as other input data files. There is also a graph of the HCACF over time attached.

 

I would appreciate any insights as to why the HCACF does not decay to zero. 

 

 

Thank you,

 

Chad Daksha

 


 # input script for SWNT simulation in LAMMPS
#-------10--------20--------30--------40--------50--------60--------70--------80

# Variables
variable input index coordi-cnt.txt

# INITIALIZATION
units		    metal
boundary            p p p 
atom_style          atomic

variable	T equal 300.0
variable 	dt equal 0.0002 		# ps
variable    p equal 100     		# correlation length
variable    s equal 10      		# sample interval
variable	d equal $p*$s 			# dump interval

thermo 1000
timestep ${dt}            # ps

# ATOM DEFINITION

read_data           ${input}

# FORCE FIELD

pair_style     airebo 3.0 1 1
pair_coeff     * * CH.airebo C
 
# SETTINGS

neighbor	    1.0 bin
neigh_modify	    delay 1


# Calculating Volume

variable 	diameter equal (sqrt(3)*1.42*sqrt(10^2+10*10+10^2))/PI			#(10,10) armchair CNT; assuming C-C bond distance of 1.42
variable 	radius equal ${diameter}/2
variable 	height equal "lz"												#Height is equal to z-dimension length
variable 	V equal 2*PI*${radius}*3.4*${height}							

# Convert from metal units to SI

variable    kB equal 1.3806504e-23    # [J/K] Boltzmann
variable    eV2J equal 1.602176565e-19
variable    A2m equal 1.0e-10
variable    ps2s equal 1.0e-12
variable    convert equal ${eV2J}*${eV2J}/${ps2s}/${A2m}

group Carbon type 1

# ------------------------------------------------------------------------------
variable temp equal temp

# output for VMD
dump 		1 all custom 10000 dump.uhmwpe-coord id type x y z
dump 		2 all xyz 10000 dump.uhmwpe-xyz-format
dump_modify 	2 element C 

## --- Relaxation ---
fix 51 all nvt temp $T $T 0.1
run 200000

## --- Thermal Conductivity Calculation ---
unfix 51
fix 51 all nve

reset_timestep 0
compute      myKE all ke/atom
compute      myPE all pe/atom
compute      myStress all stress/atom NULL virial
compute      flux all heat/flux myKE myPE myStress
variable     Jx equal c_flux[1]/$V
variable     Jy equal c_flux[2]/$V
variable     Jz equal c_flux[3]/$V
fix          JJ all ave/correlate $s $p $d &
             c_flux[1] c_flux[2] c_flux[3] type auto file J0Jt.dat ave running
variable     scale equal ${convert}/${kB}/$T/$T/$V*$s*${dt}
variable     k11 equal trap(f_JJ[3])*${scale}
variable     k22 equal trap(f_JJ[4])*${scale}
variable     k33 equal trap(f_JJ[5])*${scale}
thermo_style custom step temp cpu v_Jx v_Jy v_Jz v_k11 v_k22 v_k33

run          2000000

variable     k equal (v_k11+v_k22+v_k33)/3.0
print        "average conductivity: $k[W/mK] @ $T K"
unfix 51

print "Run is complete!"

Attachment: CH.airebo
Description: CH.airebo

 840  atoms
        
 1  atom types
        
 -25.00    25.000    xlo xhi
 -25.00    25.000    ylo yhi
 -0.615    51.035    zlo zhi
        
 Masses
        
 1   12.080000
                            
 Atoms      
 
1	1	-6.7428590	-0.7087030	0.0000000
2	1	-6.7428590	0.7087030	0.0000000
3	1	-5.8716527	3.3900003	0.0000000
4	1	-5.0385223	4.5367059	0.0000000
5	1	-2.7576747	6.1938387	0.0000000
6	1	-1.4096414	6.6318413	0.0000000
7	1	1.4096414	6.6318413	0.0000000
8	1	2.7576747	6.1938387	0.0000000
9	1	5.0385223	4.5367059	0.0000000
10	1	5.8716527	3.3900003	0.0000000
11	1	6.7428590	0.7087030	0.0000000
12	1	6.7428590	-0.7087030	0.0000000
13	1	5.8716527	-3.3900003	0.0000000
14	1	5.0385223	-4.5367059	0.0000000
15	1	2.7576747	-6.1938387	0.0000000
16	1	1.4096414	-6.6318413	0.0000000
17	1	-1.4096414	-6.6318413	0.0000000
18	1	-2.7576747	-6.1938387	0.0000000
19	1	-5.0385223	-4.5367059	0.0000000
20	1	-5.8716527	-3.3900003	0.0000000
21	1	-6.6318413	-1.4096414	1.2297561
22	1	-6.6318413	1.4096414	1.2297561
23	1	-6.1938387	2.7576747	1.2297561
24	1	-4.5367059	5.0385223	1.2297561
25	1	-3.3900003	5.8716527	1.2297561
26	1	-0.7087030	6.7428590	1.2297561
27	1	0.7087030	6.7428590	1.2297561
28	1	3.3900003	5.8716527	1.2297561
29	1	4.5367059	5.0385223	1.2297561
30	1	6.1938387	2.7576747	1.2297561
31	1	6.6318413	1.4096414	1.2297561
32	1	6.6318413	-1.4096414	1.2297561
33	1	6.1938387	-2.7576747	1.2297561
34	1	4.5367059	-5.0385223	1.2297561
35	1	3.3900003	-5.8716527	1.2297561
36	1	0.7087030	-6.7428590	1.2297561
37	1	-0.7087030	-6.7428590	1.2297561
38	1	-3.3900003	-5.8716527	1.2297561
39	1	-4.5367059	-5.0385223	1.2297561
40	1	-6.1938387	-2.7576747	1.2297561
41	1	-6.7428590	-0.7087030	2.4595121
42	1	-6.7428590	0.7087030	2.4595121
43	1	-5.8716527	3.3900003	2.4595121
44	1	-5.0385223	4.5367059	2.4595121
45	1	-2.7576747	6.1938387	2.4595121
46	1	-1.4096414	6.6318413	2.4595121
47	1	1.4096414	6.6318413	2.4595121
48	1	2.7576747	6.1938387	2.4595121
49	1	5.0385223	4.5367059	2.4595121
50	1	5.8716527	3.3900003	2.4595121
51	1	6.7428590	0.7087030	2.4595121
52	1	6.7428590	-0.7087030	2.4595121
53	1	5.8716527	-3.3900003	2.4595121
54	1	5.0385223	-4.5367059	2.4595121
55	1	2.7576747	-6.1938387	2.4595121
56	1	1.4096414	-6.6318413	2.4595121
57	1	-1.4096414	-6.6318413	2.4595121
58	1	-2.7576747	-6.1938387	2.4595121
59	1	-5.0385223	-4.5367059	2.4595121
60	1	-5.8716527	-3.3900003	2.4595121
61	1	-6.6318413	-1.4096414	3.6892682
62	1	-6.6318413	1.4096414	3.6892682
63	1	-6.1938387	2.7576747	3.6892682
64	1	-4.5367059	5.0385223	3.6892682
65	1	-3.3900003	5.8716527	3.6892682
66	1	-0.7087030	6.7428590	3.6892682
67	1	0.7087030	6.7428590	3.6892682
68	1	3.3900003	5.8716527	3.6892682
69	1	4.5367059	5.0385223	3.6892682
70	1	6.1938387	2.7576747	3.6892682
71	1	6.6318413	1.4096414	3.6892682
72	1	6.6318413	-1.4096414	3.6892682
73	1	6.1938387	-2.7576747	3.6892682
74	1	4.5367059	-5.0385223	3.6892682
75	1	3.3900003	-5.8716527	3.6892682
76	1	0.7087030	-6.7428590	3.6892682
77	1	-0.7087030	-6.7428590	3.6892682
78	1	-3.3900003	-5.8716527	3.6892682
79	1	-4.5367059	-5.0385223	3.6892682
80	1	-6.1938387	-2.7576747	3.6892682
81	1	-6.7428590	-0.7087030	4.9190243
82	1	-6.7428590	0.7087030	4.9190243
83	1	-5.8716527	3.3900003	4.9190243
84	1	-5.0385223	4.5367059	4.9190243
85	1	-2.7576747	6.1938387	4.9190243
86	1	-1.4096414	6.6318413	4.9190243
87	1	1.4096414	6.6318413	4.9190243
88	1	2.7576747	6.1938387	4.9190243
89	1	5.0385223	4.5367059	4.9190243
90	1	5.8716527	3.3900003	4.9190243
91	1	6.7428590	0.7087030	4.9190243
92	1	6.7428590	-0.7087030	4.9190243
93	1	5.8716527	-3.3900003	4.9190243
94	1	5.0385223	-4.5367059	4.9190243
95	1	2.7576747	-6.1938387	4.9190243
96	1	1.4096414	-6.6318413	4.9190243
97	1	-1.4096414	-6.6318413	4.9190243
98	1	-2.7576747	-6.1938387	4.9190243
99	1	-5.0385223	-4.5367059	4.9190243
100	1	-5.8716527	-3.3900003	4.9190243
101	1	-6.6318413	-1.4096414	6.1487804
102	1	-6.6318413	1.4096414	6.1487804
103	1	-6.1938387	2.7576747	6.1487804
104	1	-4.5367059	5.0385223	6.1487804
105	1	-3.3900003	5.8716527	6.1487804
106	1	-0.7087030	6.7428590	6.1487804
107	1	0.7087030	6.7428590	6.1487804
108	1	3.3900003	5.8716527	6.1487804
109	1	4.5367059	5.0385223	6.1487804
110	1	6.1938387	2.7576747	6.1487804
111	1	6.6318413	1.4096414	6.1487804
112	1	6.6318413	-1.4096414	6.1487804
113	1	6.1938387	-2.7576747	6.1487804
114	1	4.5367059	-5.0385223	6.1487804
115	1	3.3900003	-5.8716527	6.1487804
116	1	0.7087030	-6.7428590	6.1487804
117	1	-0.7087030	-6.7428590	6.1487804
118	1	-3.3900003	-5.8716527	6.1487804
119	1	-4.5367059	-5.0385223	6.1487804
120	1	-6.1938387	-2.7576747	6.1487804
121	1	-6.7428590	-0.7087030	7.3785364
122	1	-6.7428590	0.7087030	7.3785364
123	1	-5.8716527	3.3900003	7.3785364
124	1	-5.0385223	4.5367059	7.3785364
125	1	-2.7576747	6.1938387	7.3785364
126	1	-1.4096414	6.6318413	7.3785364
127	1	1.4096414	6.6318413	7.3785364
128	1	2.7576747	6.1938387	7.3785364
129	1	5.0385223	4.5367059	7.3785364
130	1	5.8716527	3.3900003	7.3785364
131	1	6.7428590	0.7087030	7.3785364
132	1	6.7428590	-0.7087030	7.3785364
133	1	5.8716527	-3.3900003	7.3785364
134	1	5.0385223	-4.5367059	7.3785364
135	1	2.7576747	-6.1938387	7.3785364
136	1	1.4096414	-6.6318413	7.3785364
137	1	-1.4096414	-6.6318413	7.3785364
138	1	-2.7576747	-6.1938387	7.3785364
139	1	-5.0385223	-4.5367059	7.3785364
140	1	-5.8716527	-3.3900003	7.3785364
141	1	-6.6318413	-1.4096414	8.6082925
142	1	-6.6318413	1.4096414	8.6082925
143	1	-6.1938387	2.7576747	8.6082925
144	1	-4.5367059	5.0385223	8.6082925
145	1	-3.3900003	5.8716527	8.6082925
146	1	-0.7087030	6.7428590	8.6082925
147	1	0.7087030	6.7428590	8.6082925
148	1	3.3900003	5.8716527	8.6082925
149	1	4.5367059	5.0385223	8.6082925
150	1	6.1938387	2.7576747	8.6082925
151	1	6.6318413	1.4096414	8.6082925
152	1	6.6318413	-1.4096414	8.6082925
153	1	6.1938387	-2.7576747	8.6082925
154	1	4.5367059	-5.0385223	8.6082925
155	1	3.3900003	-5.8716527	8.6082925
156	1	0.7087030	-6.7428590	8.6082925
157	1	-0.7087030	-6.7428590	8.6082925
158	1	-3.3900003	-5.8716527	8.6082925
159	1	-4.5367059	-5.0385223	8.6082925
160	1	-6.1938387	-2.7576747	8.6082925
161	1	-6.7428590	-0.7087030	9.8380486
162	1	-6.7428590	0.7087030	9.8380486
163	1	-5.8716527	3.3900003	9.8380486
164	1	-5.0385223	4.5367059	9.8380486
165	1	-2.7576747	6.1938387	9.8380486
166	1	-1.4096414	6.6318413	9.8380486
167	1	1.4096414	6.6318413	9.8380486
168	1	2.7576747	6.1938387	9.8380486
169	1	5.0385223	4.5367059	9.8380486
170	1	5.8716527	3.3900003	9.8380486
171	1	6.7428590	0.7087030	9.8380486
172	1	6.7428590	-0.7087030	9.8380486
173	1	5.8716527	-3.3900003	9.8380486
174	1	5.0385223	-4.5367059	9.8380486
175	1	2.7576747	-6.1938387	9.8380486
176	1	1.4096414	-6.6318413	9.8380486
177	1	-1.4096414	-6.6318413	9.8380486
178	1	-2.7576747	-6.1938387	9.8380486
179	1	-5.0385223	-4.5367059	9.8380486
180	1	-5.8716527	-3.3900003	9.8380486
181	1	-6.6318413	-1.4096414	11.0678047
182	1	-6.6318413	1.4096414	11.0678047
183	1	-6.1938387	2.7576747	11.0678047
184	1	-4.5367059	5.0385223	11.0678047
185	1	-3.3900003	5.8716527	11.0678047
186	1	-0.7087030	6.7428590	11.0678047
187	1	0.7087030	6.7428590	11.0678047
188	1	3.3900003	5.8716527	11.0678047
189	1	4.5367059	5.0385223	11.0678047
190	1	6.1938387	2.7576747	11.0678047
191	1	6.6318413	1.4096414	11.0678047
192	1	6.6318413	-1.4096414	11.0678047
193	1	6.1938387	-2.7576747	11.0678047
194	1	4.5367059	-5.0385223	11.0678047
195	1	3.3900003	-5.8716527	11.0678047
196	1	0.7087030	-6.7428590	11.0678047
197	1	-0.7087030	-6.7428590	11.0678047
198	1	-3.3900003	-5.8716527	11.0678047
199	1	-4.5367059	-5.0385223	11.0678047
200	1	-6.1938387	-2.7576747	11.0678047
201	1	-6.7428590	-0.7087030	12.2975607
202	1	-6.7428590	0.7087030	12.2975607
203	1	-5.8716527	3.3900003	12.2975607
204	1	-5.0385223	4.5367059	12.2975607
205	1	-2.7576747	6.1938387	12.2975607
206	1	-1.4096414	6.6318413	12.2975607
207	1	1.4096414	6.6318413	12.2975607
208	1	2.7576747	6.1938387	12.2975607
209	1	5.0385223	4.5367059	12.2975607
210	1	5.8716527	3.3900003	12.2975607
211	1	6.7428590	0.7087030	12.2975607
212	1	6.7428590	-0.7087030	12.2975607
213	1	5.8716527	-3.3900003	12.2975607
214	1	5.0385223	-4.5367059	12.2975607
215	1	2.7576747	-6.1938387	12.2975607
216	1	1.4096414	-6.6318413	12.2975607
217	1	-1.4096414	-6.6318413	12.2975607
218	1	-2.7576747	-6.1938387	12.2975607
219	1	-5.0385223	-4.5367059	12.2975607
220	1	-5.8716527	-3.3900003	12.2975607
221	1	-6.6318413	-1.4096414	13.5273168
222	1	-6.6318413	1.4096414	13.5273168
223	1	-6.1938387	2.7576747	13.5273168
224	1	-4.5367059	5.0385223	13.5273168
225	1	-3.3900003	5.8716527	13.5273168
226	1	-0.7087030	6.7428590	13.5273168
227	1	0.7087030	6.7428590	13.5273168
228	1	3.3900003	5.8716527	13.5273168
229	1	4.5367059	5.0385223	13.5273168
230	1	6.1938387	2.7576747	13.5273168
231	1	6.6318413	1.4096414	13.5273168
232	1	6.6318413	-1.4096414	13.5273168
233	1	6.1938387	-2.7576747	13.5273168
234	1	4.5367059	-5.0385223	13.5273168
235	1	3.3900003	-5.8716527	13.5273168
236	1	0.7087030	-6.7428590	13.5273168
237	1	-0.7087030	-6.7428590	13.5273168
238	1	-3.3900003	-5.8716527	13.5273168
239	1	-4.5367059	-5.0385223	13.5273168
240	1	-6.1938387	-2.7576747	13.5273168
241	1	-6.7428590	-0.7087030	14.7570729
242	1	-6.7428590	0.7087030	14.7570729
243	1	-5.8716527	3.3900003	14.7570729
244	1	-5.0385223	4.5367059	14.7570729
245	1	-2.7576747	6.1938387	14.7570729
246	1	-1.4096414	6.6318413	14.7570729
247	1	1.4096414	6.6318413	14.7570729
248	1	2.7576747	6.1938387	14.7570729
249	1	5.0385223	4.5367059	14.7570729
250	1	5.8716527	3.3900003	14.7570729
251	1	6.7428590	0.7087030	14.7570729
252	1	6.7428590	-0.7087030	14.7570729
253	1	5.8716527	-3.3900003	14.7570729
254	1	5.0385223	-4.5367059	14.7570729
255	1	2.7576747	-6.1938387	14.7570729
256	1	1.4096414	-6.6318413	14.7570729
257	1	-1.4096414	-6.6318413	14.7570729
258	1	-2.7576747	-6.1938387	14.7570729
259	1	-5.0385223	-4.5367059	14.7570729
260	1	-5.8716527	-3.3900003	14.7570729
261	1	-6.6318413	-1.4096414	15.9868290
262	1	-6.6318413	1.4096414	15.9868290
263	1	-6.1938387	2.7576747	15.9868290
264	1	-4.5367059	5.0385223	15.9868290
265	1	-3.3900003	5.8716527	15.9868290
266	1	-0.7087030	6.7428590	15.9868290
267	1	0.7087030	6.7428590	15.9868290
268	1	3.3900003	5.8716527	15.9868290
269	1	4.5367059	5.0385223	15.9868290
270	1	6.1938387	2.7576747	15.9868290
271	1	6.6318413	1.4096414	15.9868290
272	1	6.6318413	-1.4096414	15.9868290
273	1	6.1938387	-2.7576747	15.9868290
274	1	4.5367059	-5.0385223	15.9868290
275	1	3.3900003	-5.8716527	15.9868290
276	1	0.7087030	-6.7428590	15.9868290
277	1	-0.7087030	-6.7428590	15.9868290
278	1	-3.3900003	-5.8716527	15.9868290
279	1	-4.5367059	-5.0385223	15.9868290
280	1	-6.1938387	-2.7576747	15.9868290
281	1	-6.7428590	-0.7087030	17.2165850
282	1	-6.7428590	0.7087030	17.2165850
283	1	-5.8716527	3.3900003	17.2165850
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619	1	-5.0385223	-4.5367059	36.8926822
620	1	-5.8716527	-3.3900003	36.8926822
621	1	-6.6318413	-1.4096414	38.1224383
622	1	-6.6318413	1.4096414	38.1224383
623	1	-6.1938387	2.7576747	38.1224383
624	1	-4.5367059	5.0385223	38.1224383
625	1	-3.3900003	5.8716527	38.1224383
626	1	-0.7087030	6.7428590	38.1224383
627	1	0.7087030	6.7428590	38.1224383
628	1	3.3900003	5.8716527	38.1224383
629	1	4.5367059	5.0385223	38.1224383
630	1	6.1938387	2.7576747	38.1224383
631	1	6.6318413	1.4096414	38.1224383
632	1	6.6318413	-1.4096414	38.1224383
633	1	6.1938387	-2.7576747	38.1224383
634	1	4.5367059	-5.0385223	38.1224383
635	1	3.3900003	-5.8716527	38.1224383
636	1	0.7087030	-6.7428590	38.1224383
637	1	-0.7087030	-6.7428590	38.1224383
638	1	-3.3900003	-5.8716527	38.1224383
639	1	-4.5367059	-5.0385223	38.1224383
640	1	-6.1938387	-2.7576747	38.1224383
641	1	-6.7428590	-0.7087030	39.3521943
642	1	-6.7428590	0.7087030	39.3521943
643	1	-5.8716527	3.3900003	39.3521943
644	1	-5.0385223	4.5367059	39.3521943
645	1	-2.7576747	6.1938387	39.3521943
646	1	-1.4096414	6.6318413	39.3521943
647	1	1.4096414	6.6318413	39.3521943
648	1	2.7576747	6.1938387	39.3521943
649	1	5.0385223	4.5367059	39.3521943
650	1	5.8716527	3.3900003	39.3521943
651	1	6.7428590	0.7087030	39.3521943
652	1	6.7428590	-0.7087030	39.3521943
653	1	5.8716527	-3.3900003	39.3521943
654	1	5.0385223	-4.5367059	39.3521943
655	1	2.7576747	-6.1938387	39.3521943
656	1	1.4096414	-6.6318413	39.3521943
657	1	-1.4096414	-6.6318413	39.3521943
658	1	-2.7576747	-6.1938387	39.3521943
659	1	-5.0385223	-4.5367059	39.3521943
660	1	-5.8716527	-3.3900003	39.3521943
661	1	-6.6318413	-1.4096414	40.5819504
662	1	-6.6318413	1.4096414	40.5819504
663	1	-6.1938387	2.7576747	40.5819504
664	1	-4.5367059	5.0385223	40.5819504
665	1	-3.3900003	5.8716527	40.5819504
666	1	-0.7087030	6.7428590	40.5819504
667	1	0.7087030	6.7428590	40.5819504
668	1	3.3900003	5.8716527	40.5819504
669	1	4.5367059	5.0385223	40.5819504
670	1	6.1938387	2.7576747	40.5819504
671	1	6.6318413	1.4096414	40.5819504
672	1	6.6318413	-1.4096414	40.5819504
673	1	6.1938387	-2.7576747	40.5819504
674	1	4.5367059	-5.0385223	40.5819504
675	1	3.3900003	-5.8716527	40.5819504
676	1	0.7087030	-6.7428590	40.5819504
677	1	-0.7087030	-6.7428590	40.5819504
678	1	-3.3900003	-5.8716527	40.5819504
679	1	-4.5367059	-5.0385223	40.5819504
680	1	-6.1938387	-2.7576747	40.5819504
681	1	-6.7428590	-0.7087030	41.8117065
682	1	-6.7428590	0.7087030	41.8117065
683	1	-5.8716527	3.3900003	41.8117065
684	1	-5.0385223	4.5367059	41.8117065
685	1	-2.7576747	6.1938387	41.8117065
686	1	-1.4096414	6.6318413	41.8117065
687	1	1.4096414	6.6318413	41.8117065
688	1	2.7576747	6.1938387	41.8117065
689	1	5.0385223	4.5367059	41.8117065
690	1	5.8716527	3.3900003	41.8117065
691	1	6.7428590	0.7087030	41.8117065
692	1	6.7428590	-0.7087030	41.8117065
693	1	5.8716527	-3.3900003	41.8117065
694	1	5.0385223	-4.5367059	41.8117065
695	1	2.7576747	-6.1938387	41.8117065
696	1	1.4096414	-6.6318413	41.8117065
697	1	-1.4096414	-6.6318413	41.8117065
698	1	-2.7576747	-6.1938387	41.8117065
699	1	-5.0385223	-4.5367059	41.8117065
700	1	-5.8716527	-3.3900003	41.8117065
701	1	-6.6318413	-1.4096414	43.0414626
702	1	-6.6318413	1.4096414	43.0414626
703	1	-6.1938387	2.7576747	43.0414626
704	1	-4.5367059	5.0385223	43.0414626
705	1	-3.3900003	5.8716527	43.0414626
706	1	-0.7087030	6.7428590	43.0414626
707	1	0.7087030	6.7428590	43.0414626
708	1	3.3900003	5.8716527	43.0414626
709	1	4.5367059	5.0385223	43.0414626
710	1	6.1938387	2.7576747	43.0414626
711	1	6.6318413	1.4096414	43.0414626
712	1	6.6318413	-1.4096414	43.0414626
713	1	6.1938387	-2.7576747	43.0414626
714	1	4.5367059	-5.0385223	43.0414626
715	1	3.3900003	-5.8716527	43.0414626
716	1	0.7087030	-6.7428590	43.0414626
717	1	-0.7087030	-6.7428590	43.0414626
718	1	-3.3900003	-5.8716527	43.0414626
719	1	-4.5367059	-5.0385223	43.0414626
720	1	-6.1938387	-2.7576747	43.0414626
721	1	-6.7428590	-0.7087030	44.2712186
722	1	-6.7428590	0.7087030	44.2712186
723	1	-5.8716527	3.3900003	44.2712186
724	1	-5.0385223	4.5367059	44.2712186
725	1	-2.7576747	6.1938387	44.2712186
726	1	-1.4096414	6.6318413	44.2712186
727	1	1.4096414	6.6318413	44.2712186
728	1	2.7576747	6.1938387	44.2712186
729	1	5.0385223	4.5367059	44.2712186
730	1	5.8716527	3.3900003	44.2712186
731	1	6.7428590	0.7087030	44.2712186
732	1	6.7428590	-0.7087030	44.2712186
733	1	5.8716527	-3.3900003	44.2712186
734	1	5.0385223	-4.5367059	44.2712186
735	1	2.7576747	-6.1938387	44.2712186
736	1	1.4096414	-6.6318413	44.2712186
737	1	-1.4096414	-6.6318413	44.2712186
738	1	-2.7576747	-6.1938387	44.2712186
739	1	-5.0385223	-4.5367059	44.2712186
740	1	-5.8716527	-3.3900003	44.2712186
741	1	-6.6318413	-1.4096414	45.5009747
742	1	-6.6318413	1.4096414	45.5009747
743	1	-6.1938387	2.7576747	45.5009747
744	1	-4.5367059	5.0385223	45.5009747
745	1	-3.3900003	5.8716527	45.5009747
746	1	-0.7087030	6.7428590	45.5009747
747	1	0.7087030	6.7428590	45.5009747
748	1	3.3900003	5.8716527	45.5009747
749	1	4.5367059	5.0385223	45.5009747
750	1	6.1938387	2.7576747	45.5009747
751	1	6.6318413	1.4096414	45.5009747
752	1	6.6318413	-1.4096414	45.5009747
753	1	6.1938387	-2.7576747	45.5009747
754	1	4.5367059	-5.0385223	45.5009747
755	1	3.3900003	-5.8716527	45.5009747
756	1	0.7087030	-6.7428590	45.5009747
757	1	-0.7087030	-6.7428590	45.5009747
758	1	-3.3900003	-5.8716527	45.5009747
759	1	-4.5367059	-5.0385223	45.5009747
760	1	-6.1938387	-2.7576747	45.5009747
761	1	-6.7428590	-0.7087030	46.7307308
762	1	-6.7428590	0.7087030	46.7307308
763	1	-5.8716527	3.3900003	46.7307308
764	1	-5.0385223	4.5367059	46.7307308
765	1	-2.7576747	6.1938387	46.7307308
766	1	-1.4096414	6.6318413	46.7307308
767	1	1.4096414	6.6318413	46.7307308
768	1	2.7576747	6.1938387	46.7307308
769	1	5.0385223	4.5367059	46.7307308
770	1	5.8716527	3.3900003	46.7307308
771	1	6.7428590	0.7087030	46.7307308
772	1	6.7428590	-0.7087030	46.7307308
773	1	5.8716527	-3.3900003	46.7307308
774	1	5.0385223	-4.5367059	46.7307308
775	1	2.7576747	-6.1938387	46.7307308
776	1	1.4096414	-6.6318413	46.7307308
777	1	-1.4096414	-6.6318413	46.7307308
778	1	-2.7576747	-6.1938387	46.7307308
779	1	-5.0385223	-4.5367059	46.7307308
780	1	-5.8716527	-3.3900003	46.7307308
781	1	-6.6318413	-1.4096414	47.9604869
782	1	-6.6318413	1.4096414	47.9604869
783	1	-6.1938387	2.7576747	47.9604869
784	1	-4.5367059	5.0385223	47.9604869
785	1	-3.3900003	5.8716527	47.9604869
786	1	-0.7087030	6.7428590	47.9604869
787	1	0.7087030	6.7428590	47.9604869
788	1	3.3900003	5.8716527	47.9604869
789	1	4.5367059	5.0385223	47.9604869
790	1	6.1938387	2.7576747	47.9604869
791	1	6.6318413	1.4096414	47.9604869
792	1	6.6318413	-1.4096414	47.9604869
793	1	6.1938387	-2.7576747	47.9604869
794	1	4.5367059	-5.0385223	47.9604869
795	1	3.3900003	-5.8716527	47.9604869
796	1	0.7087030	-6.7428590	47.9604869
797	1	-0.7087030	-6.7428590	47.9604869
798	1	-3.3900003	-5.8716527	47.9604869
799	1	-4.5367059	-5.0385223	47.9604869
800	1	-6.1938387	-2.7576747	47.9604869
801	1	-6.7428590	-0.7087030	49.1902429
802	1	-6.7428590	0.7087030	49.1902429
803	1	-5.8716527	3.3900003	49.1902429
804	1	-5.0385223	4.5367059	49.1902429
805	1	-2.7576747	6.1938387	49.1902429
806	1	-1.4096414	6.6318413	49.1902429
807	1	1.4096414	6.6318413	49.1902429
808	1	2.7576747	6.1938387	49.1902429
809	1	5.0385223	4.5367059	49.1902429
810	1	5.8716527	3.3900003	49.1902429
811	1	6.7428590	0.7087030	49.1902429
812	1	6.7428590	-0.7087030	49.1902429
813	1	5.8716527	-3.3900003	49.1902429
814	1	5.0385223	-4.5367059	49.1902429
815	1	2.7576747	-6.1938387	49.1902429
816	1	1.4096414	-6.6318413	49.1902429
817	1	-1.4096414	-6.6318413	49.1902429
818	1	-2.7576747	-6.1938387	49.1902429
819	1	-5.0385223	-4.5367059	49.1902429
820	1	-5.8716527	-3.3900003	49.1902429
821	1	-6.6318413	-1.4096414	50.4199990
822	1	-6.6318413	1.4096414	50.4199990
823	1	-6.1938387	2.7576747	50.4199990
824	1	-4.5367059	5.0385223	50.4199990
825	1	-3.3900003	5.8716527	50.4199990
826	1	-0.7087030	6.7428590	50.4199990
827	1	0.7087030	6.7428590	50.4199990
828	1	3.3900003	5.8716527	50.4199990
829	1	4.5367059	5.0385223	50.4199990
830	1	6.1938387	2.7576747	50.4199990
831	1	6.6318413	1.4096414	50.4199990
832	1	6.6318413	-1.4096414	50.4199990
833	1	6.1938387	-2.7576747	50.4199990
834	1	4.5367059	-5.0385223	50.4199990
835	1	3.3900003	-5.8716527	50.4199990
836	1	0.7087030	-6.7428590	50.4199990
837	1	-0.7087030	-6.7428590	50.4199990
838	1	-3.3900003	-5.8716527	50.4199990
839	1	-4.5367059	-5.0385223	50.4199990
840	1	-6.1938387	-2.7576747	50.4199990

 

Attachment: HCACF_graph.pptx
Description: HCACF_graph.pptx