diff --git a/examples/VISCOSITY/README b/examples/VISCOSITY/README new file mode 100644 index 0000000000..92340ae849 --- /dev/null +++ b/examples/VISCOSITY/README @@ -0,0 +1,76 @@ +This directory has 4 scripts that compute the viscosity (eta) of a +Lennard-Jones fluid using 4 different methods. See the discussion in +Section 6.21 of the manual for an overview of the methods and pointers +to doc pages for the commands which implement them. Citations for the +various methods can also be found in the manaul. + +These scripts are provided for illustration purposes. No guarantee is +made that the systems are fully equilibrated or that the runs are long +enough to generate good statistics and highly accurate results. + +------------- + +These are the 4 methods for compute viscosity. The first 3 are +non-equilibrium methods; the last is an equilibrium method. + +in.wall = move a wall to shear the fluid between two walls +in.nemd = use fix deform and fix nvt/sllod to perform a NEMD shear simulation +in.mp = use fix viscosity and the Muller-Plathe method +in.gk = use the Green-Kubo method + +All the systems have around 800 atoms. The NEMD methods run for short +times; the G-K system needs to run longer to generate good statistics. + +The scripts were all run on a single processor. They all run in a +minute or so and produce the accompanying log files and profile files +(for velocity or momemtum flux). + +The state point of the LJ fluid is rho* = 0.6, T* = 1.0, and Rcut = +2.5 sigma. This system should have a shear viscosity of about 1.0. + +------------- + +Here is how to extract viscosity from the log file output for each +method. + +The NEMD methods use the formula eta = - dM / Velocity-gradient, where +dM = momentum flux in the y-direction, and Vel gradient = dVelX / dY = +the change in x-velocity over a distance dY in the y-direction. + +(1) in.wall.2d + +mom flux = pxy +dVelX = Srate = 2.7 +dY = Y box length = 41.99 + +eta = 0.946 = running average output as last log file column + +(2) in.nemd.2d + +mom flux = pxy +dVelX = velocity of top box edge = Srate = 2.7 +dY = Y box length = 36.51 + +eta = 1.18 = running average output as last log file column + +(3) in.mp.2d + +mom flux = dMom in Y / 2 / Area-perp-to-Y / dTime +dMom = -1370.2 from log file, tallied by MP + factor of 2 since system is periodic and dMom goes 2 ways + Area for 2d = lx + dTime = elapsed time in tau for accumulating dMom +dVelX = 4th column of log output, from fix ave/spatial +dY = 1/2 of Y box length + +eta = 1.09 = running average output as last log file column + +(4) in.gk.2d + +eta is computed directly within the script, by performing a time +integration of the formula discussed in Section 6.21 of the manual, +analagous to the formula for thermal conductivity given on the compute +heat/flux doc page - the resulting value prints at the end of the run +and is in the log file + +eta = 1.07 diff --git a/examples/VISCOSITY/in.gk.2d b/examples/VISCOSITY/in.gk.2d new file mode 100644 index 0000000000..1438be5341 --- /dev/null +++ b/examples/VISCOSITY/in.gk.2d @@ -0,0 +1,65 @@ +# sample LAMMPS input script for viscosity of 2d LJ liquid +# Green-Kubo method via fix ave/correlate + +# settings + +variable x equal 20 +variable y equal 20 + +variable rho equal 0.6 +variable t equal 1.0 +variable rc equal 2.5 + +variable p equal 400 # correlation length +variable s equal 5 # sample interval +variable d equal $p*$s # dump interval + +# problem setup + +units lj +dimension 2 +atom_style atomic +neigh_modify delay 0 every 1 + +lattice sq2 ${rho} +region simbox block 0 $x 0 $y -0.1 0.1 +create_box 1 simbox +create_atoms 1 box + +pair_style lj/cut ${rc} +pair_coeff * * 1 1 + +mass * 1.0 +velocity all create $t 97287 + +# equilibration run + +fix 1 all nve +fix 2 all langevin $t $t 0.1 498094 +fix 3 all enforce2d + +thermo $d +run 10000 + +velocity all scale $t + +unfix 2 + +# Green-Kubo viscosity calculation + +reset_timestep 0 + +variable pxy equal pxy + +fix SS all ave/correlate $s $p $d & + v_pxy type auto file profile.gk.2d ave running + +variable scale equal 1.0/$t*vol*$s*dt +variable v11 equal trap(f_SS[3])*${scale} + +thermo_style custom step temp press pxy v_v11 + +run 500000 + +variable eta equal v_v11 +print "running average viscosity: ${eta}" diff --git a/examples/VISCOSITY/in.mp.2d b/examples/VISCOSITY/in.mp.2d new file mode 100644 index 0000000000..890d2fb89a --- /dev/null +++ b/examples/VISCOSITY/in.mp.2d @@ -0,0 +1,71 @@ +# sample LAMMPS input script for viscosity of 2d LJ liquid +# Muller-Plathe via fix viscosity + +# settings + +variable x equal 20 +variable y equal 20 + +variable rho equal 0.6 +variable t equal 1.0 +variable rc equal 2.5 + +# problem setup + +units lj +dimension 2 +atom_style atomic +neigh_modify delay 0 every 1 + +lattice sq2 ${rho} +region simbox block 0 $x 0 $y -0.1 0.1 +create_box 1 simbox +create_atoms 1 box + +pair_style lj/cut ${rc} +pair_coeff * * 1 1 + +mass * 1.0 +velocity all create $t 97287 + +fix 1 all nve +fix 2 all langevin $t $t 0.1 498094 +fix 3 all enforce2d + +# equilibration run + +thermo 1000 +run 5000 + +unfix 2 + +# turn on Muller-Plathe driving force and equilibrate some more + +velocity all scale $t + +fix 4 all viscosity 100 x y 20 +fix 5 all ave/spatial 20 50 1000 y center 0.05 vx & + units reduced file profile.mp.2d + +# equilibration run + +variable dVx equal f_5[10][3]-f_5[1][3] + +thermo 1000 +thermo_style custom step temp epair etotal press f_4 v_dVx +run 20000 + +# data gathering run +# reset fix viscosity to zero flux accumulation + +unfix 4 +fix 4 all viscosity 100 x y 20 + +variable visc equal -(f_4/(2*(step*0.005-125)*lx+1.0e-10))/(v_dVx/(ly/2)) +fix vave all ave/time 1000 1 1000 v_visc ave running start 26000 + +thermo_style custom step temp f_4 v_dVx v_visc f_vave + +#dump 1 all custom 100 dump.mp.2d id type x y z vx + +run 50000 diff --git a/examples/VISCOSITY/in.nemd.2d b/examples/VISCOSITY/in.nemd.2d new file mode 100644 index 0000000000..810943b184 --- /dev/null +++ b/examples/VISCOSITY/in.nemd.2d @@ -0,0 +1,76 @@ +# sample LAMMPS input script for viscosity of 2d LJ liquid +# NEMD via fix deform and fix nvt/sllod + +# settings + +variable x equal 20 +variable y equal 20 + +variable rho equal 0.6 +variable t equal 1.0 +variable rc equal 2.5 + +variable srate equal 2.7 + +# problem setup + +units lj +dimension 2 +atom_style atomic +neigh_modify delay 0 every 1 + +# problem setup + +lattice sq2 ${rho} +region simbox prism 0 $y 0 $y -0.1 0.1 0.0 0.0 0.0 +create_box 1 simbox +create_atoms 1 box + +pair_style lj/cut ${rc} +pair_coeff * * 1 1 + +mass * 1.0 +velocity all create $t 97287 + +fix 1 all nve +fix 2 all langevin $t $t 0.1 498094 +fix 3 all enforce2d + +# equilibration run + +thermo 1000 +run 5000 + +unfix 1 +unfix 2 + +# turn on NEMD shear and equilibrate some more + +velocity all scale $t + +variable xyrate equal ${srate}/lx + +fix 1 all nvt/sllod temp $t $t 0.1 +fix 2 all deform 1 xy erate ${xyrate} remap v +fix 4 all ave/spatial 20 250 5000 y center 0.05 vx & + units reduced file profile.nemd.2d + +compute usual all temp +compute tilt all temp/deform + +thermo 1000 +thermo_style custom step temp c_usual epair etotal press pxy +thermo_modify temp tilt +run 50000 + +# data gathering run + +variable visc equal -pxy/(v_srate/ly) +fix vave all ave/time 10 100 1000 v_visc ave running start 56000 + +thermo_style custom step temp press pxy v_visc f_vave xy +thermo_modify temp tilt + +#dump 1 all custom 10 dump.nemd.2d id type x y z vx + +run 50000 diff --git a/examples/VISCOSITY/in.wall.2d b/examples/VISCOSITY/in.wall.2d new file mode 100644 index 0000000000..6b2799705b --- /dev/null +++ b/examples/VISCOSITY/in.wall.2d @@ -0,0 +1,78 @@ +# sample LAMMPS input script for viscosity of 2d LJ liquid +# use shearing wall, thermostat via fix langevin + +# settings + +variable x equal 20 +variable y equal 20 +variable ylo equal -2.5 +variable yhi equal 23 + +variable rho equal 0.6 +variable t equal 1.0 +variable rc equal 2.5 + +variable srate equal 2.7 + +# problem setup + +units lj +dimension 2 +atom_style atomic +neigh_modify delay 0 every 1 + +lattice sq2 ${rho} +region simbox block 0 $x ${ylo} ${yhi} -0.1 0.1 +create_box 3 simbox +create_atoms 1 box + +mass * 1.0 + +pair_style lj/cut ${rc} +pair_coeff * * 1 1 + +region lower block INF INF INF 0.0 INF INF +region upper block INF INF $y INF INF INF +group lower region lower +group upper region upper +set group lower type 2 +set group upper type 3 +group wall union lower upper +group flow subtract all wall + +velocity flow create $t 97287 +velocity upper set ${srate} 0.0 0.0 units box + +compute thermal flow temp/partial 0 1 0 +compute flow flow temp + +fix 1 all nve +fix 2 flow langevin $t $t 0.1 498094 +fix_modify 2 temp thermal + +fix 3 wall setforce 0.0 0.0 0.0 +fix 4 flow ave/spatial 20 500 10000 y center 0.05 vx & + units reduced file profile.wall.2d +fix 5 all enforce2d + +# equilibration run + +variable ybox equal $y*ylat +compute tilt flow temp/ramp vx 0 ${srate} y 0 ${ybox} units box + +thermo 1000 +thermo_style custom step temp c_tilt epair etotal press pxy + +run 20000 + +# data gathering run + +variable visc equal -pxy/(v_srate/ly) +fix vave all ave/time 1000 1 1000 v_visc ave running + +thermo_style custom step temp pxy v_visc f_vave +thermo_modify temp tilt + +#dump 1 all custom 1000 dump.wall.2d id type x y z + +run 50000 diff --git a/examples/VISCOSITY/log.gk.2d.12Sep13 b/examples/VISCOSITY/log.gk.2d.12Sep13 new file mode 100644 index 0000000000..a98e3fe7f0 --- /dev/null +++ b/examples/VISCOSITY/log.gk.2d.12Sep13 @@ -0,0 +1,386 @@ +LAMMPS (10 Sep 2013) +# sample LAMMPS input script for viscosity of 2d LJ liquid +# Green-Kubo method via fix ave/correlate + +# settings + +variable x equal 20 +variable y equal 20 + +variable rho equal 0.6 +variable t equal 1.0 +variable rc equal 2.5 + +variable p equal 400 # correlation length +variable s equal 5 # sample interval +variable d equal $p*$s # dump interval +variable d equal 400*$s +variable d equal 400*5 + +# problem setup + +units lj +dimension 2 +atom_style atomic +neigh_modify delay 0 every 1 + +lattice sq2 ${rho} +lattice sq2 0.5999999999999999778 +Lattice spacing in x,y,z = 1.82574 1.82574 1.82574 +region simbox block 0 $x 0 $y -0.1 0.1 +region simbox block 0 20 0 $y -0.1 0.1 +region simbox block 0 20 0 20 -0.1 0.1 +create_box 1 simbox +Created orthogonal box = (0 0 -0.182574) to (36.5148 36.5148 0.182574) + 1 by 1 by 1 MPI processor grid +create_atoms 1 box +Created 800 atoms + +pair_style lj/cut ${rc} +pair_style lj/cut 2.5 +pair_coeff * * 1 1 + +mass * 1.0 +velocity all create $t 97287 +velocity all create 1 97287 + +# equilibration run + +fix 1 all nve +fix 2 all langevin $t $t 0.1 498094 +fix 2 all langevin 1 $t 0.1 498094 +fix 2 all langevin 1 1 0.1 498094 +fix 3 all enforce2d + +thermo $d +thermo 2000 +run 10000 +Memory usage per processor = 2.07097 Mbytes +Step Temp E_pair E_mol TotEng Press + 0 1 -1.56492 0 -0.56617 -1.535262 + 2000 1.0164992 -1.6006146 0 -0.58538603 0.88642098 + 4000 1.0955206 -1.6156387 0 -0.52148756 0.94410568 + 6000 1.0384034 -1.6029204 0 -0.56581499 0.82862864 + 8000 1.03126 -1.5776603 0 -0.54768937 1.122187 + 10000 1.0159313 -1.6063811 0 -0.59171973 0.9961884 +Loop time of 1.89357 on 1 procs for 10000 steps with 800 atoms + +Pair time (%) = 1.05965 (55.9602) +Neigh time (%) = 0.227317 (12.0047) +Comm time (%) = 0.0356276 (1.88151) +Outpt time (%) = 5.60284e-05 (0.00295888) +Other time (%) = 0.570923 (30.1506) + +Nlocal: 800 ave 800 max 800 min +Histogram: 1 0 0 0 0 0 0 0 0 0 +Nghost: 264 ave 264 max 264 min +Histogram: 1 0 0 0 0 0 0 0 0 0 +Neighs: 5614 ave 5614 max 5614 min +Histogram: 1 0 0 0 0 0 0 0 0 0 + +Total # of neighbors = 5614 +Ave neighs/atom = 7.0175 +Neighbor list builds = 1103 +Dangerous builds = 0 + +velocity all scale $t +velocity all scale 1 + +unfix 2 + +# Green-Kubo viscosity calculation + +reset_timestep 0 + +variable pxy equal pxy + +fix SS all ave/correlate $s $p $d v_pxy type auto file profile.gk.2d ave running +fix SS all ave/correlate 5 $p $d v_pxy type auto file profile.gk.2d ave running +fix SS all ave/correlate 5 400 $d v_pxy type auto file profile.gk.2d ave running +fix SS all ave/correlate 5 400 2000 v_pxy type auto file profile.gk.2d ave running + +variable scale equal 1.0/$t*vol*$s*dt +variable scale equal 1.0/1*vol*$s*dt +variable scale equal 1.0/1*vol*5*dt +variable v11 equal trap(f_SS[3])*${scale} +variable v11 equal trap(f_SS[3])*33.333333333333328596 + +thermo_style custom step temp press pxy v_v11 + +run 500000 +Memory usage per processor = 2.07097 Mbytes +Step Temp Press Pxy v11 + 0 1 0.98664157 0.1056765 0.18612539 + 2000 0.95291404 1.199872 0.16190354 6.3622865 + 4000 0.97035474 0.95019583 -0.028108952 -0.019331326 + 6000 0.99784792 1.0066466 0.0085549073 -0.12148778 + 8000 0.99816414 0.90521139 0.00095639386 0.0098644997 + 10000 0.9951641 0.96718253 0.090881095 0.50006024 + 12000 0.93744355 1.2391514 0.014185646 1.4928658 + 14000 1.000559 0.97734913 -0.096964014 1.3899184 + 16000 1.002721 1.1185539 0.026144411 1.0983068 + 18000 0.96861294 1.0439439 0.090245855 1.4107497 + 20000 0.98664185 0.97686008 -0.27549912 1.3394189 + 22000 0.97569716 1.0845656 -0.0734503 1.2870138 + 24000 0.98609865 1.0625182 -0.01142576 1.0253871 + 26000 0.988828 0.99456937 -0.019918137 0.9418664 + 28000 0.98671933 0.94373279 -0.21675597 0.94445052 + 30000 0.98778176 0.8446134 0.15106071 0.9681741 + 32000 0.97606274 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-0.076396538 1.1782589 + 224000 1.0105632 1.0136738 0.039008755 1.1848006 + 226000 1.0023731 0.8427875 -0.10734019 1.177471 + 228000 0.98752126 0.90957923 -0.050531743 1.3182698 + 230000 0.9810267 1.0784386 0.08508881 1.3092904 + 232000 1.0021266 0.93921109 -0.18635777 1.2973489 + 234000 0.99533025 0.91807335 0.16664865 1.2848923 + 236000 0.98011149 0.92896398 0.020234263 1.2941781 + 238000 1.0080589 1.0422206 0.080342493 1.2756861 + 240000 1.013769 0.91271642 0.10024033 1.2720643 + 242000 1.0084395 0.8645878 -0.014896263 1.2473047 + 244000 0.96637824 1.0817071 -0.16165169 1.2490751 + 246000 0.97629725 1.0768466 0.062453669 1.2348816 + 248000 0.97081168 0.95332682 0.09584424 1.2232201 + 250000 1.001316 0.90207588 -0.045980098 1.2179401 + 252000 1.0107243 0.97832107 -0.14601722 1.2134106 + 254000 0.98659744 1.0943909 -0.088294528 1.2333875 + 256000 1.0123386 0.99162386 -0.039344985 1.2164364 + 258000 0.95762302 1.0676734 0.012199759 1.2076414 + 260000 0.99842463 0.99944454 -0.060917216 1.1988621 + 262000 0.97766994 1.0286325 -0.10141058 1.2395609 + 264000 0.97615582 0.90531751 0.18512981 1.2044769 + 266000 0.96241019 1.0566036 0.078113491 1.2005364 + 268000 1.0168176 0.81665569 -0.030349244 1.2025997 + 270000 0.99827104 1.0749573 -0.056801916 1.1962529 + 272000 0.9968558 0.94529972 0.028725191 1.1828897 + 274000 0.97566641 0.91457261 0.015049168 1.1902579 + 276000 0.99070015 0.94576384 0.025755724 1.1896323 + 278000 0.96895102 1.0397797 0.080651494 1.1763571 + 280000 1.0072996 0.89570696 -0.15542961 1.1652696 + 282000 1.0144016 0.77288242 -0.029784437 1.1582708 + 284000 1.0181351 0.7694665 -0.054640099 1.1544617 + 286000 0.98291392 0.9938831 -0.0062479011 1.1596522 + 288000 0.97279582 1.0358224 -0.13401081 1.1505486 + 290000 0.99909636 1.0213079 -0.0012162009 1.1399725 + 292000 0.98460352 0.94742548 -0.031343507 1.1581955 + 294000 0.99038521 0.98665849 0.051955637 1.1524198 + 296000 0.99556533 0.86180797 0.055142099 1.1523058 + 298000 0.97636077 0.98781403 0.013204553 1.129189 + 300000 0.97032776 1.0678134 0.11879155 1.1176141 + 302000 1.0003067 0.87686391 0.023979249 1.1210971 + 304000 1.0209877 0.82384059 -0.019162225 1.1201332 + 306000 0.98495148 0.97853853 0.0067884582 1.1146556 + 308000 1.0080456 0.89962394 -0.039014939 1.1072495 + 310000 0.98760314 1.0580182 -0.0084950963 1.1128641 + 312000 1.0163132 0.743878 -0.13381063 1.1072529 + 314000 0.97482482 0.93981262 0.1188583 1.1113744 + 316000 0.99642196 0.92559157 -0.076386258 1.1180406 + 318000 0.98668334 0.9960588 0.051851225 1.1282305 + 320000 1.018361 0.82279734 -0.033370883 1.1306313 + 322000 1.0101361 0.79697655 -0.0097104031 1.1269227 + 324000 0.98374012 0.89538164 0.072387631 1.1184602 + 326000 1.0005728 0.81698596 -0.097827025 1.1067008 + 328000 0.98296796 1.0888354 -0.00019150727 1.1026196 + 330000 0.97244323 1.1015085 0.047308269 1.0967215 + 332000 0.99301221 1.0908167 -0.12434045 1.0911357 + 334000 0.99279827 1.0192878 -0.030977699 1.0804029 + 336000 0.98580679 1.055276 0.11288823 1.0750277 + 338000 0.98757346 1.0072102 0.10201237 1.0933627 + 340000 1.0067327 0.87701361 0.067382458 1.0850067 + 342000 1.0154351 0.94291159 0.070059816 1.0801363 + 344000 0.9743083 1.1059353 0.066961003 1.1524185 + 346000 0.99814584 1.0356474 -0.016510209 1.1432772 + 348000 0.97641572 1.1686199 0.046528576 1.1496039 + 350000 0.99518846 1.0517486 0.13448583 1.1381818 + 352000 0.98588655 0.98536282 -0.060862396 1.1294455 + 354000 0.96615995 1.1110151 0.083719861 1.1256268 + 356000 1.0078606 0.78439358 -0.10603102 1.1362455 + 358000 0.99367549 1.0489552 0.07500459 1.1427616 + 360000 0.98811261 1.0329632 0.02037644 1.1456498 + 362000 0.99543973 0.89319851 0.071618522 1.1516636 + 364000 0.98165417 0.88412777 0.01496297 1.1479466 + 366000 0.97321522 1.1989343 0.12226461 1.1407247 + 368000 0.98226259 0.98513508 -0.032773905 1.145514 + 370000 0.98523554 0.99191598 0.048321875 1.1454723 + 372000 0.99757543 1.0704533 -0.044499362 1.1397563 + 374000 0.96826544 1.0155716 0.10537727 1.1380956 + 376000 0.97764036 0.91461704 -0.0071326471 1.1311759 + 378000 0.96197183 1.2654546 0.063772824 1.1342523 + 380000 0.9563135 0.92013089 0.14946354 1.122797 + 382000 0.99157671 1.1416454 -0.0020281283 1.1146792 + 384000 0.99439496 1.0461009 -0.095485509 1.1101174 + 386000 0.9964491 0.96726205 -0.096570092 1.1043801 + 388000 0.98660387 0.92002862 -0.050238768 1.1028544 + 390000 0.97619357 0.95568771 -0.0093958893 1.0994103 + 392000 0.97043698 1.1278757 0.078765507 1.1095933 + 394000 0.97478556 0.93908482 0.010033169 1.0896552 + 396000 0.98483138 0.88172231 -0.0092943479 1.0731932 + 398000 0.99224177 0.84195437 -0.0059744644 1.0682901 + 400000 1.0140238 0.88969569 -0.14294787 1.0626823 + 402000 0.98939257 0.91691411 0.0064466276 1.0892164 + 404000 0.9930004 0.91196344 -0.15724573 1.0852194 + 406000 0.98184881 0.93556127 -0.030604809 1.0779626 + 408000 1.0097979 0.97009028 -0.011737511 1.0779471 + 410000 0.9913927 0.9406984 0.00091540813 1.0902918 + 412000 0.95799086 1.1298786 -0.03512312 1.1138864 + 414000 1.0089501 0.84475916 0.13645298 1.1142398 + 416000 0.9897256 0.98316262 0.010485716 1.1164657 + 418000 1.0133333 0.86050241 0.055260598 1.1048567 + 420000 0.97407581 0.97216618 0.098782939 1.1125666 + 422000 1.0009494 0.88470049 0.038139624 1.1163397 + 424000 0.97321563 1.1466493 -0.086272829 1.1173945 + 426000 0.96442304 1.0810966 -0.061944411 1.1068751 + 428000 0.9982547 0.87602547 0.081196445 1.1070854 + 430000 0.97915448 1.1485682 -0.065531916 1.1259179 + 432000 0.96422041 1.1298461 -0.0082763069 1.1175144 + 434000 0.99510123 1.0224406 -0.11423626 1.1160931 + 436000 1.0240236 0.88695443 0.0075708194 1.1085978 + 438000 0.99001944 1.0244717 0.075879487 1.1212094 + 440000 1.0116423 0.89412767 -0.11768379 1.1190682 + 442000 0.98993631 0.92631483 0.067324168 1.111235 + 444000 0.95107091 1.1508927 0.0019160629 1.1098578 + 446000 0.98621381 0.91043895 -0.061521131 1.1148618 + 448000 0.97695569 1.177126 -0.05322695 1.1104409 + 450000 0.99066051 0.99745105 0.080431605 1.1058023 + 452000 1.0146071 0.95227428 0.007801217 1.1249178 + 454000 0.99162513 0.96925579 -0.036153968 1.1100001 + 456000 1.0215781 0.88427275 -0.050979723 1.1071667 + 458000 0.98021089 0.84902388 0.08620799 1.1003492 + 460000 0.98981752 1.0990911 0.047765387 1.1091971 + 462000 0.97418524 1.023144 -0.11243577 1.101482 + 464000 0.98172755 1.0676962 0.065603574 1.0966983 + 466000 0.99352242 0.88377489 0.11849997 1.0934089 + 468000 0.9916114 0.9404547 0.041191002 1.0843991 + 470000 0.9675487 1.0416201 0.038992075 1.0909162 + 472000 0.97960188 1.0249638 0.1102279 1.087763 + 474000 0.97114134 1.1160983 0.046857123 1.0919439 + 476000 0.99567674 0.93675154 -0.06832563 1.0879316 + 478000 0.9784867 1.0660872 0.0030176417 1.0834439 + 480000 0.99936399 0.97607692 0.096835801 1.0780983 + 482000 1.0274496 0.87081314 0.054818419 1.0724507 + 484000 0.97139265 1.0730706 -0.12345378 1.0754362 + 486000 0.97408298 0.99765268 -0.0064488819 1.0691212 + 488000 0.9873109 1.0488011 0.001679366 1.0680362 + 490000 1.0289514 0.77625996 -0.090952895 1.0799008 + 492000 0.98122494 0.97560083 0.068756789 1.0746541 + 494000 1.0009648 1.0046735 0.013556863 1.074882 + 496000 0.96262432 0.94043431 -0.1359217 1.078487 + 498000 1.00248 1.1101056 -0.065062628 1.0774483 + 500000 0.964375 1.1119972 0.062483884 1.0744491 +Loop time of 78.4755 on 1 procs for 500000 steps with 800 atoms + +Pair time (%) = 54.1325 (68.9801) +Neigh time (%) = 12.1352 (15.4637) +Comm time (%) = 1.85499 (2.36378) +Outpt time (%) = 0.00424814 (0.00541334) +Other time (%) = 10.3486 (13.1871) + +Nlocal: 800 ave 800 max 800 min +Histogram: 1 0 0 0 0 0 0 0 0 0 +Nghost: 267 ave 267 max 267 min +Histogram: 1 0 0 0 0 0 0 0 0 0 +Neighs: 5583 ave 5583 max 5583 min +Histogram: 1 0 0 0 0 0 0 0 0 0 + +Total # of neighbors = 5583 +Ave neighs/atom = 6.97875 +Neighbor list builds = 58699 +Dangerous builds = 0 + +variable eta equal v_v11 +print "running average viscosity: ${eta}" +running average viscosity: 1.0744491378557243788 diff --git a/examples/VISCOSITY/log.mp.2d.12Sep13 b/examples/VISCOSITY/log.mp.2d.12Sep13 new file mode 100644 index 0000000000..140c5dbae8 --- /dev/null +++ b/examples/VISCOSITY/log.mp.2d.12Sep13 @@ -0,0 +1,225 @@ +LAMMPS (10 Sep 2013) +# sample LAMMPS input script for viscosity of 2d LJ liquid +# Muller-Plathe via fix viscosity + +# settings + +variable x equal 20 +variable y equal 20 + +variable rho equal 0.6 +variable t equal 1.0 +variable rc equal 2.5 + +# problem setup + +units lj +dimension 2 +atom_style atomic +neigh_modify delay 0 every 1 + +lattice sq2 ${rho} +lattice sq2 0.5999999999999999778 +Lattice spacing in x,y,z = 1.82574 1.82574 1.82574 +region simbox block 0 $x 0 $y -0.1 0.1 +region simbox block 0 20 0 $y -0.1 0.1 +region simbox block 0 20 0 20 -0.1 0.1 +create_box 1 simbox +Created orthogonal box = (0 0 -0.182574) to (36.5148 36.5148 0.182574) + 1 by 1 by 1 MPI processor grid +create_atoms 1 box +Created 800 atoms + +pair_style lj/cut ${rc} +pair_style lj/cut 2.5 +pair_coeff * * 1 1 + +mass * 1.0 +velocity all create $t 97287 +velocity all create 1 97287 + +fix 1 all nve +fix 2 all langevin $t $t 0.1 498094 +fix 2 all langevin 1 $t 0.1 498094 +fix 2 all langevin 1 1 0.1 498094 +fix 3 all enforce2d + +# equilibration run + +thermo 1000 +run 5000 +Memory usage per processor = 2.07097 Mbytes +Step Temp E_pair E_mol TotEng Press + 0 1 -1.56492 0 -0.56617 -1.535262 + 1000 0.95906897 -1.571142 0 -0.61327189 0.82593948 + 2000 1.0164992 -1.6006146 0 -0.58538603 0.88642098 + 3000 1.0429232 -1.5801639 0 -0.53854441 1.157286 + 4000 1.0955206 -1.6156387 0 -0.52148756 0.94410568 + 5000 0.94117594 -1.6155055 0 -0.67550602 0.79354125 +Loop time of 0.944804 on 1 procs for 5000 steps with 800 atoms + +Pair time (%) = 0.529388 (56.0316) +Neigh time (%) = 0.111678 (11.8202) +Comm time (%) = 0.0178316 (1.88733) +Outpt time (%) = 5.48363e-05 (0.00580398) +Other time (%) = 0.285851 (30.2551) + +Nlocal: 800 ave 800 max 800 min +Histogram: 1 0 0 0 0 0 0 0 0 0 +Nghost: 256 ave 256 max 256 min +Histogram: 1 0 0 0 0 0 0 0 0 0 +Neighs: 5583 ave 5583 max 5583 min +Histogram: 1 0 0 0 0 0 0 0 0 0 + +Total # of neighbors = 5583 +Ave neighs/atom = 6.97875 +Neighbor list builds = 551 +Dangerous builds = 0 + +unfix 2 + +# turn on Muller-Plathe driving force and equilibrate some more + +velocity all scale $t +velocity all scale 1 + +fix 4 all viscosity 100 x y 20 +fix 5 all ave/spatial 20 50 1000 y center 0.05 vx units reduced file profile.mp.2d + +# equilibration run + +variable dVx equal f_5[10][3]-f_5[1][3] + +thermo 1000 +thermo_style custom step temp epair etotal press f_4 v_dVx +run 20000 +WARNING: Fix viscosity comes before fix ave/spatial (../fix_viscosity.cpp:129) +Memory usage per processor = 2.07189 Mbytes +Step Temp E_pair TotEng Press 4 dVx + 5000 1 -1.6155055 -0.61675549 0.82879157 0 0 + 6000 0.98975585 -1.6044976 -0.61597892 0.88929475 -39.757283 0.42593886 + 7000 1.0171117 -1.6325992 -0.61675882 0.77321875 -75.466189 0.65862967 + 8000 0.9983443 -1.6139399 -0.61684356 0.99800071 -108.9786 0.70669193 + 9000 1.0021377 -1.617938 -0.61705295 0.96356104 -140.71079 0.70647412 + 10000 0.98041956 -1.5963475 -0.61715341 0.91025147 -166.90846 0.97780186 + 11000 0.99600832 -1.6118627 -0.61709934 0.92678088 -196.07977 1.0297476 + 12000 1.0032773 -1.6185577 -0.61653447 0.83123611 -224.27343 1.2014002 + 13000 0.99446644 -1.6102636 -0.61704022 1.0408681 -249.65561 1.4461765 + 14000 0.99703794 -1.6124962 -0.6167046 0.88919618 -274.47539 1.4692527 + 15000 0.99889843 -1.6143324 -0.61668259 1.0041418 -301.54284 1.1538268 + 16000 1.0234202 -1.639108 -0.61696709 0.76317815 -330.0367 1.1365768 + 17000 0.98929215 -1.6045613 -0.61650577 1.0634542 -357.1234 1.2404845 + 18000 1.0287489 -1.6442118 -0.61674884 0.77339567 -380.94903 1.3784319 + 19000 1.0100899 -1.6257365 -0.6169092 0.87836452 -405.45675 1.4104175 + 20000 1.026862 -1.641991 -0.61641257 0.70998705 -432.85955 1.2180696 + 21000 1.0191092 -1.6350774 -0.61724212 0.95544428 -457.90745 1.2240015 + 22000 1.0494154 -1.6646933 -0.61658976 0.71132454 -483.85578 1.1606127 + 23000 0.99407102 -1.6095995 -0.61677106 0.87254846 -513.39632 1.2518235 + 24000 1.0074971 -1.6233079 -0.61707018 0.87490828 -537.79433 1.4449174 + 25000 0.98809909 -1.6039328 -0.61706881 1.0343859 -564.04288 1.4316162 +Loop time of 3.07336 on 1 procs for 20000 steps with 800 atoms + +Pair time (%) = 2.13088 (69.3338) +Neigh time (%) = 0.477607 (15.5402) +Comm time (%) = 0.0734417 (2.38962) +Outpt time (%) = 0.000259161 (0.00843249) +Other time (%) = 0.391175 (12.7279) + +Nlocal: 800 ave 800 max 800 min +Histogram: 1 0 0 0 0 0 0 0 0 0 +Nghost: 274 ave 274 max 274 min +Histogram: 1 0 0 0 0 0 0 0 0 0 +Neighs: 5645 ave 5645 max 5645 min +Histogram: 1 0 0 0 0 0 0 0 0 0 + +Total # of neighbors = 5645 +Ave neighs/atom = 7.05625 +Neighbor list builds = 2341 +Dangerous builds = 0 + +# data gathering run +# reset fix viscosity to zero flux accumulation + +unfix 4 +fix 4 all viscosity 100 x y 20 + +variable visc equal -(f_4/(2*(step*0.005-125)*lx+1.0e-10))/(v_dVx/(ly/2)) +fix vave all ave/time 1000 1 1000 v_visc ave running start 26000 + +thermo_style custom step temp f_4 v_dVx v_visc f_vave + +#dump 1 all custom 100 dump.mp.2d id type x y z vx + +run 50000 +Memory usage per processor = 2.11004 Mbytes +Step Temp 4 dVx visc vave + 25000 0.98809909 0 1.4316162 -0 0 + 26000 0.99537148 -23.157779 1.2733222 0.90934485 0.45467242 + 27000 0.98172329 -50.105785 1.1200918 1.1183411 0.6758953 + 28000 0.98101288 -76.343112 1.2514133 1.0167586 0.76111113 + 29000 0.99394022 -104.74751 1.2910989 1.0141314 0.81171518 + 30000 1.0325928 -133.8316 1.1423095 1.1715879 0.87169397 + 31000 0.99207021 -162.86199 1.1537115 1.1763628 0.91521808 + 32000 0.99574775 -195.02329 1.0309914 1.3511496 0.96970952 + 33000 1.006688 -224.4372 1.1635661 1.205546 0.99591357 + 34000 1.0133299 -249.93292 1.3493303 1.029041 0.99922631 + 35000 0.98760774 -276.64509 1.1427464 1.2104395 1.0184275 + 36000 1.007095 -305.71096 1.1144655 1.2468715 1.0374645 + 37000 0.99906577 -336.66963 1.2337889 1.1369774 1.0451194 + 38000 1.0084072 -363.13013 1.3542332 1.0313249 1.044134 + 39000 1.0121876 -388.77058 1.2526117 1.1084571 1.0484222 + 40000 1.0137703 -413.8783 1.1818774 1.1672905 1.0558515 + 41000 1.0269059 -441.65914 0.92138637 1.4979436 1.0818569 + 42000 1.0299181 -469.53275 1.3483691 1.0241844 1.0786529 + 43000 1.0114277 -496.95032 1.2993557 1.0623862 1.0777968 + 44000 1.0113759 -521.99588 1.3795162 0.99576461 1.0736951 + 45000 1.0141433 -548.17271 1.3207574 1.0376105 1.0719768 + 46000 0.99162488 -575.96021 1.3977095 0.98112936 1.0678474 + 47000 1.0220618 -603.83376 1.5462099 0.88755703 1.0600087 + 48000 1.0111765 -631.33375 1.341417 1.0231454 1.0584727 + 49000 0.97881848 -659.55746 1.3111744 1.0479751 1.0580528 + 50000 1.0216782 -685.35361 1.3794426 0.99366747 1.0555765 + 51000 1.028535 -710.54876 1.2310643 1.1099663 1.0575909 + 52000 1.0143597 -739.56707 1.2837456 1.0668536 1.0579217 + 53000 1.0108168 -764.66386 1.3060981 1.0454583 1.0574919 + 54000 1.0114331 -790.87474 1.240819 1.0989332 1.0588733 + 55000 1.0164027 -817.72537 1.2392495 1.0997589 1.0601922 + 56000 0.99176035 -844.83648 1.2950359 1.0522021 1.0599425 + 57000 1.0004064 -870.94837 1.3578173 1.0022385 1.0581939 + 58000 1.0117453 -900.0605 1.1632948 1.1722979 1.0615499 + 59000 0.99226606 -923.07079 1.2653911 1.0727569 1.0618701 + 60000 1.0031829 -952.55552 1.2676453 1.0734814 1.0621926 + 61000 1.0223094 -981.61993 1.286994 1.0593375 1.0621155 + 62000 1.0242885 -1012.8531 1.3191083 1.0376103 1.0614706 + 63000 0.99566343 -1041.4676 1.4601043 0.93853027 1.0583183 + 64000 0.9974131 -1067.1595 1.4441391 0.94738323 1.0555449 + 65000 1.0126848 -1095.0891 1.2932156 1.0584944 1.0556168 + 66000 1.0008861 -1120.8615 1.0981903 1.2446879 1.0601185 + 67000 1.0029467 -1146.778 1.0225731 1.3350752 1.0665129 + 68000 1.0000345 -1173.301 1.0810257 1.2620454 1.0709568 + 69000 1.0173152 -1205.3517 1.2663892 1.0815931 1.0711932 + 70000 0.98187515 -1231.6872 1.1488964 1.1911791 1.0738015 + 71000 1.0102662 -1257.5675 1.365684 1.0009059 1.0722506 + 72000 1.0069313 -1286.4021 1.134593 1.2061707 1.0750406 + 73000 0.98551805 -1315.8466 0.9631242 1.4231534 1.0821449 + 74000 1.0249532 -1342.624 1.1303208 1.212067 1.0847434 + 75000 0.9987759 -1370.2176 1.1940813 1.1475077 1.085974 +Loop time of 7.68848 on 1 procs for 50000 steps with 800 atoms + +Pair time (%) = 5.3275 (69.2921) +Neigh time (%) = 1.19674 (15.5654) +Comm time (%) = 0.184742 (2.40284) +Outpt time (%) = 0.000782728 (0.0101805) +Other time (%) = 0.978711 (12.7296) + +Nlocal: 800 ave 800 max 800 min +Histogram: 1 0 0 0 0 0 0 0 0 0 +Nghost: 261 ave 261 max 261 min +Histogram: 1 0 0 0 0 0 0 0 0 0 +Neighs: 5581 ave 5581 max 5581 min +Histogram: 1 0 0 0 0 0 0 0 0 0 + +Total # of neighbors = 5581 +Ave neighs/atom = 6.97625 +Neighbor list builds = 5860 +Dangerous builds = 0 diff --git a/examples/VISCOSITY/log.nemd.2d.12Sep13 b/examples/VISCOSITY/log.nemd.2d.12Sep13 new file mode 100644 index 0000000000..421a80017f --- /dev/null +++ b/examples/VISCOSITY/log.nemd.2d.12Sep13 @@ -0,0 +1,264 @@ +LAMMPS (10 Sep 2013) +# sample LAMMPS input script for viscosity of 2d LJ liquid +# NEMD via fix deform and fix nvt/sllod + +# settings + +variable x equal 20 +variable y equal 20 + +variable rho equal 0.6 +variable t equal 1.0 +variable rc equal 2.5 + +variable srate equal 2.7 + +# problem setup + +units lj +dimension 2 +atom_style atomic +neigh_modify delay 0 every 1 + +# problem setup + +lattice sq2 ${rho} +lattice sq2 0.5999999999999999778 +Lattice spacing in x,y,z = 1.82574 1.82574 1.82574 +region simbox prism 0 $y 0 $y -0.1 0.1 0.0 0.0 0.0 +region simbox prism 0 20 0 $y -0.1 0.1 0.0 0.0 0.0 +region simbox prism 0 20 0 20 -0.1 0.1 0.0 0.0 0.0 +create_box 1 simbox +Created triclinic box = (0 0 -0.182574) to (36.5148 36.5148 0.182574) with tilt (0 0 0) + 1 by 1 by 1 MPI processor grid +create_atoms 1 box +Created 800 atoms + +pair_style lj/cut ${rc} +pair_style lj/cut 2.5 +pair_coeff * * 1 1 + +mass * 1.0 +velocity all create $t 97287 +velocity all create 1 97287 + +fix 1 all nve +fix 2 all langevin $t $t 0.1 498094 +fix 2 all langevin 1 $t 0.1 498094 +fix 2 all langevin 1 1 0.1 498094 +fix 3 all enforce2d + +# equilibration run + +thermo 1000 +run 5000 +Memory usage per processor = 2.07097 Mbytes +Step Temp E_pair E_mol TotEng Press + 0 1 -1.56492 0 -0.56617 -1.535262 + 1000 0.9455393 -1.573329 0 -0.62897162 0.91884199 + 2000 1.0359047 -1.6229551 0 -0.58834528 0.96136682 + 3000 1.0171488 -1.5468681 0 -0.53099077 1.1078235 + 4000 1.0040221 -1.5977142 0 -0.59494717 0.92428924 + 5000 0.95883045 -1.6087309 0 -0.65109902 0.92015626 +Loop time of 0.995848 on 1 procs for 5000 steps with 800 atoms + +Pair time (%) = 0.530232 (53.2443) +Neigh time (%) = 0.155753 (15.6403) +Comm time (%) = 0.0214312 (2.15206) +Outpt time (%) = 5.38826e-05 (0.00541073) +Other time (%) = 0.288377 (28.958) + +Nlocal: 800 ave 800 max 800 min +Histogram: 1 0 0 0 0 0 0 0 0 0 +Nghost: 266 ave 266 max 266 min +Histogram: 1 0 0 0 0 0 0 0 0 0 +Neighs: 5604 ave 5604 max 5604 min +Histogram: 1 0 0 0 0 0 0 0 0 0 + +Total # of neighbors = 5604 +Ave neighs/atom = 7.005 +Neighbor list builds = 548 +Dangerous builds = 0 + +unfix 1 +unfix 2 + +# turn on NEMD shear and equilibrate some more + +velocity all scale $t +velocity all scale 1 + +variable xyrate equal ${srate}/lx +variable xyrate equal 2.7000000000000001776/lx + +fix 1 all nvt/sllod temp $t $t 0.1 +fix 1 all nvt/sllod temp 1 $t 0.1 +fix 1 all nvt/sllod temp 1 1 0.1 +fix 2 all deform 1 xy erate ${xyrate} remap v +fix 2 all deform 1 xy erate 0.07394254526319743448 remap v +fix 4 all ave/spatial 20 250 5000 y center 0.05 vx units reduced file profile.nemd.2d + +compute usual all temp +compute tilt all temp/deform + +thermo 1000 +thermo_style custom step temp c_usual epair etotal press pxy +thermo_modify temp tilt +run 50000 +Memory usage per processor = 2.07189 Mbytes +Step Temp usual E_pair TotEng Press Pxy + 5000 2.2074694 1 -1.6087309 0.59597912 1.6684031 -0.13173607 + 6000 0.91633679 1.0719617 -1.6395918 -0.72440047 0.75849191 -0.095097981 + 7000 1.0124825 1.1977616 -1.6934341 -0.68221723 0.70703149 -0.15913906 + 8000 1.0360742 1.244051 -1.6664702 -0.63169111 0.87208594 -0.17196758 + 9000 0.97397154 1.2397496 -1.6727765 -0.7000224 0.80220669 -0.11127356 + 10000 0.95658497 1.2726404 -1.6735904 -0.71820119 0.67518534 0.021843949 + 11000 0.99924023 1.3580428 -1.67571 -0.67771886 0.70353983 -0.095458782 + 12000 1.0433584 1.3936154 -1.6710176 -0.6289634 0.78515023 -0.10560886 + 13000 1.0405816 1.4490361 -1.6830775 -0.64379669 0.61832448 -0.11781994 + 14000 1.0497802 1.4357015 -1.6534549 -0.60498685 0.76907329 0.017545708 + 15000 0.96121525 1.3821511 -1.6498177 -0.68980398 0.95020534 -0.080877133 + 16000 1.0267815 1.4361052 -1.6538729 -0.62837492 0.68232896 -0.070333365 + 17000 0.93630695 1.3935392 -1.6232359 -0.68809929 0.76153713 0.0065771149 + 18000 1.0096924 1.5362618 -1.6690032 -0.66057292 0.74673844 -0.0020401284 + 19000 0.98814671 1.4707103 -1.6447486 -0.65783707 0.72488074 -0.13287245 + 20000 0.99667627 1.5457608 -1.6408152 -0.64538473 0.60598401 -0.0076374847 + 21000 0.98153893 1.5408205 -1.6148102 -0.63449823 0.80827079 -0.13251983 + 22000 1.0074242 1.6101043 -1.6422641 -0.63609914 0.90042046 -0.24385712 + 23000 0.95365942 1.5736051 -1.6412154 -0.68874806 0.8559935 -0.2467715 + 24000 0.98446077 1.5616505 -1.6395606 -0.65633045 0.73483641 -0.08920475 + 25000 1.0485516 1.6856359 -1.6399653 -0.5927244 0.84977844 -0.075926647 + 26000 0.96582655 1.5721629 -1.5882566 -0.62363728 0.81869074 0.090152592 + 27000 0.97557823 1.6668575 -1.6191458 -0.64478708 0.91081614 -0.19376266 + 28000 1.0303654 1.6964024 -1.6092391 -0.5801616 0.86334845 -0.17578668 + 29000 1.0622338 1.7710626 -1.6229948 -0.5620888 0.99336949 -0.14536132 + 30000 0.96943779 1.6600645 -1.6139092 -0.6456832 0.9989094 -0.02138527 + 31000 0.93832908 1.6925042 -1.6176446 -0.68048846 0.95346065 -0.17742851 + 32000 0.9875824 1.725668 -1.6119922 -0.62564431 0.96558919 -0.043195696 + 33000 0.99760198 1.7058006 -1.6052067 -0.60885172 0.98003863 -0.1333913 + 34000 1.0279367 1.7569574 -1.599245 -0.5725932 0.92585533 -0.16404413 + 35000 0.93404083 1.7440669 -1.6103769 -0.67750362 0.85837384 -0.23365559 + 36000 1.050384 1.8439426 -1.6563916 -0.60732054 0.67392288 -0.10063943 + 37000 0.94243088 1.7640322 -1.6138567 -0.6726039 0.96591044 -0.027194268 + 38000 0.98755975 1.8113344 -1.6079596 -0.62163426 1.0223699 -0.201769 + 39000 1.0420603 1.8627119 -1.5973478 -0.55659 1.0381788 0.12071081 + 40000 1.0335545 1.8837126 -1.5851743 -0.5529117 0.94822902 -0.10987028 + 41000 0.94213103 1.8188004 -1.6049587 -0.66400536 0.97923033 0.01154085 + 42000 1.0356435 1.8901318 -1.6212526 -0.58690373 0.95585859 -0.19557187 + 43000 0.99015606 1.8799525 -1.6090628 -0.62014448 0.9274227 -0.2300794 + 44000 1.0161294 1.9551452 -1.6180455 -0.60318623 1.0355228 -0.12706459 + 45000 0.98674382 1.8916077 -1.6468656 -0.66135521 0.78299308 -0.15774308 + 46000 1.0113469 1.9533202 -1.5957721 -0.58568941 0.78737351 0.13820702 + 47000 1.0571363 1.9631114 -1.5772356 -0.52142074 0.95792606 0.029844288 + 48000 0.94855706 1.8697175 -1.6015863 -0.65421497 0.90993104 -0.34180657 + 49000 1.0607674 1.9704564 -1.5868247 -0.52738329 1.0716947 -0.034892185 + 50000 0.97263672 1.9338729 -1.6082924 -0.63687146 1.0235045 -0.16412663 + 51000 1.0378868 1.9671463 -1.5809392 -0.54434973 1.1981016 0.057155145 + 52000 1.005245 1.9432386 -1.6053723 -0.60138379 0.96669621 -0.04065554 + 53000 1.0051888 1.9494803 -1.592364 -0.58843173 0.94235557 -0.082756851 + 54000 0.98792555 1.9333497 -1.5977723 -0.6110817 1.0539616 -0.052439197 + 55000 1.0215148 1.9761517 -1.6026169 -0.58237902 0.98461466 -0.014054852 +Loop time of 13.2512 on 1 procs for 50000 steps with 800 atoms + +Pair time (%) = 5.62991 (42.486) +Neigh time (%) = 3.31133 (24.9889) +Comm time (%) = 0.333608 (2.51757) +Outpt time (%) = 0.00183129 (0.0138198) +Other time (%) = 3.97453 (29.9937) + +Nlocal: 800 ave 800 max 800 min +Histogram: 1 0 0 0 0 0 0 0 0 0 +Nghost: 276 ave 276 max 276 min +Histogram: 1 0 0 0 0 0 0 0 0 0 +Neighs: 5608 ave 5608 max 5608 min +Histogram: 1 0 0 0 0 0 0 0 0 0 + +Total # of neighbors = 5608 +Ave neighs/atom = 7.01 +Neighbor list builds = 11158 +Dangerous builds = 0 + +# data gathering run + +variable visc equal -pxy/(v_srate/ly) +fix vave all ave/time 10 100 1000 v_visc ave running start 56000 + +thermo_style custom step temp press pxy v_visc f_vave +WARNING: New thermo_style command, previous thermo_modify settings will be lost (../output.cpp:664) +thermo_modify temp tilt + +#dump 1 all custom 10 dump.nemd.2d id type x y z vx + +run 50000 +Memory usage per processor = 2.11211 Mbytes +Step Temp Press Pxy visc vave + 55000 1.0215148 0.98406243 -0.015573121 0.2106111 0 + 56000 0.97676391 0.7935725 -0.097217766 1.3147744 0.94442622 + 57000 0.98121663 0.97189374 -0.09906427 1.3397466 1.0348472 + 58000 0.99072249 1.0185041 -0.1107535 1.4978319 1.1148823 + 59000 1.0339566 1.1930503 -0.11512608 1.5569667 1.136778 + 60000 0.96659848 0.92099027 -0.040929962 0.55353737 1.1425378 + 61000 0.91281753 0.94424526 0.0057649576 -0.077965366 1.1569145 + 62000 0.94858877 1.0998838 -0.017149668 0.23193235 1.1483313 + 63000 0.95337651 0.89712297 -0.11187696 1.5130256 1.2009105 + 64000 1.0210948 0.9602771 -0.054478663 0.73677019 1.2148796 + 65000 1.0504997 0.94778551 -0.15854746 2.1441981 1.2093498 + 66000 0.98082278 1.0669108 -0.079622124 1.0768107 1.2394021 + 67000 1.004502 1.0176002 0.0064462478 -0.087179144 1.2171347 + 68000 0.92374901 0.71524627 -0.16232949 2.1953463 1.2280608 + 69000 1.0515117 1.1458523 0.10895185 -1.4734664 1.2214747 + 70000 1.0555502 1.076672 -0.042203866 0.57076567 1.19651 + 71000 0.9770682 1.180182 -0.13504139 1.8263016 1.1565664 + 72000 1.0086134 1.022067 -0.037398667 0.50578009 1.1850636 + 73000 1.0162758 1.120033 -0.059765955 0.8082756 1.1911215 + 74000 0.99405946 0.89203552 -0.24842296 3.3596755 1.1878296 + 75000 0.98750361 0.94382542 -0.22651557 3.0633996 1.185964 + 76000 1.0464263 1.2902475 -0.054604453 0.73847137 1.1830982 + 77000 0.97443033 0.9748021 -0.0188378 0.25476266 1.1807479 + 78000 1.0458063 1.0029976 -0.073834161 0.99853421 1.1713126 + 79000 1.0144775 1.218542 0.062883654 -0.8504394 1.1810856 + 80000 1.0114425 0.86457858 0.0071905047 -0.097244484 1.1826166 + 81000 0.94134141 0.77988469 -0.12039379 1.6282073 1.1949499 + 82000 1.0043004 1.1044886 -0.071274637 0.96391918 1.1858594 + 83000 1.0183148 0.97315487 -0.17878927 2.4179486 1.1847614 + 84000 1.0089223 0.94988998 -0.14706747 1.9889425 1.186726 + 85000 0.99683237 1.1387674 -0.093287095 1.261616 1.1950365 + 86000 0.98703013 0.90123949 -0.071666603 0.96922013 1.1994887 + 87000 0.98715174 1.0031198 0.073329807 -0.99171332 1.2030095 + 88000 0.98802533 0.780636 -0.18839651 2.547877 1.206866 + 89000 0.98607737 1.0366379 -0.16016943 2.1661336 1.2122118 + 90000 1.0210319 1.0157699 -0.036734636 0.49679972 1.2136124 + 91000 1.0383205 1.0432409 -0.2294371 3.1029105 1.2119958 + 92000 1.0552856 1.2186718 -0.013410875 0.18136886 1.2082849 + 93000 1.0114907 1.075338 0.0035134444 -0.04751587 1.2094306 + 94000 0.94044675 1.054018 0.085446493 -1.1555795 1.203052 + 95000 1.0158089 0.97472916 -0.11967767 1.6185225 1.2030168 + 96000 1.020383 0.89405366 -0.14288077 1.9323215 1.2030977 + 97000 0.96955936 1.0480423 -0.11860582 1.6040268 1.2056096 + 98000 1.0091452 0.84288535 -0.1289184 1.7434942 1.1994042 + 99000 0.99665723 1.0303263 -0.02254625 0.3049158 1.194661 + 100000 0.94019285 0.98342349 -0.069073187 0.93414673 1.1935304 + 101000 1.0351616 1.0994068 -0.089112502 1.2051587 1.1778161 + 102000 0.94550389 1.0840839 -0.093572091 1.2654702 1.1855211 + 103000 1.0384124 1.0513178 -0.053925313 0.72928668 1.1787243 + 104000 1.0561611 0.87476291 -0.13807613 1.8673434 1.1807725 + 105000 1.0046808 0.95999328 0.015725114 -0.21266665 1.1820494 +Loop time of 13.826 on 1 procs for 50000 steps with 800 atoms + +Pair time (%) = 5.72616 (41.4159) +Neigh time (%) = 3.64084 (26.3333) +Comm time (%) = 0.359706 (2.60167) +Outpt time (%) = 0.0011127 (0.00804788) +Other time (%) = 4.09817 (29.6411) + +Nlocal: 800 ave 800 max 800 min +Histogram: 1 0 0 0 0 0 0 0 0 0 +Nghost: 264 ave 264 max 264 min +Histogram: 1 0 0 0 0 0 0 0 0 0 +Neighs: 5616 ave 5616 max 5616 min +Histogram: 1 0 0 0 0 0 0 0 0 0 + +Total # of neighbors = 5616 +Ave neighs/atom = 7.02 +Neighbor list builds = 12198 +Dangerous builds = 0 diff --git a/examples/VISCOSITY/log.wall.2d.12Sep13 b/examples/VISCOSITY/log.wall.2d.12Sep13 new file mode 100644 index 0000000000..2ddbd0d5f1 --- /dev/null +++ b/examples/VISCOSITY/log.wall.2d.12Sep13 @@ -0,0 +1,216 @@ +LAMMPS (10 Sep 2013) +# sample LAMMPS input script for viscosity of 2d LJ liquid +# use shearing wall, thermostat via fix langevin + +# settings + +variable x equal 20 +variable y equal 20 +variable ylo equal -2.5 +variable yhi equal 23 + +variable rho equal 0.6 +variable t equal 1.0 +variable rc equal 2.5 + +variable srate equal 2.7 + +# problem setup + +units lj +dimension 2 +atom_style atomic +neigh_modify delay 0 every 1 + +lattice sq2 ${rho} +lattice sq2 0.5999999999999999778 +Lattice spacing in x,y,z = 1.82574 1.82574 1.82574 +region simbox block 0 $x ${ylo} ${yhi} -0.1 0.1 +region simbox block 0 20 ${ylo} ${yhi} -0.1 0.1 +region simbox block 0 20 -2.5 ${yhi} -0.1 0.1 +region simbox block 0 20 -2.5 23 -0.1 0.1 +create_box 3 simbox +Created orthogonal box = (0 -4.56435 -0.182574) to (36.5148 41.9921 0.182574) + 1 by 1 by 1 MPI processor grid +create_atoms 1 box +Created 1020 atoms + +mass * 1.0 + +pair_style lj/cut ${rc} +pair_style lj/cut 2.5 +pair_coeff * * 1 1 + +region lower block INF INF INF 0.0 INF INF +region upper block INF INF $y INF INF INF +region upper block INF INF 20 INF INF INF +group lower region lower +120 atoms in group lower +group upper region upper +120 atoms in group upper +set group lower type 2 + 120 settings made for type +set group upper type 3 + 120 settings made for type +group wall union lower upper +240 atoms in group wall +group flow subtract all wall +780 atoms in group flow + +velocity flow create $t 97287 +velocity flow create 1 97287 +velocity upper set ${srate} 0.0 0.0 units box +velocity upper set 2.7000000000000001776 0.0 0.0 units box + +compute thermal flow temp/partial 0 1 0 +compute flow flow temp + +fix 1 all nve +fix 2 flow langevin $t $t 0.1 498094 +fix 2 flow langevin 1 $t 0.1 498094 +fix 2 flow langevin 1 1 0.1 498094 +fix_modify 2 temp thermal + +fix 3 wall setforce 0.0 0.0 0.0 +fix 4 flow ave/spatial 20 500 10000 y center 0.05 vx units reduced file profile.wall.2d +fix 5 all enforce2d + +# equilibration run + +variable ybox equal $y*ylat +variable ybox equal 20*ylat +compute tilt flow temp/ramp vx 0 ${srate} y 0 ${ybox} units box +compute tilt flow temp/ramp vx 0 2.7000000000000001776 y 0 ${ybox} units box +compute tilt flow temp/ramp vx 0 2.7000000000000001776 y 0 36.514837167011073404 units box + +thermo 1000 +thermo_style custom step temp c_tilt epair etotal press pxy + +run 20000 +Memory usage per processor = 2.07358 Mbytes +Step Temp tilt E_pair TotEng Press Pxy + 0 1.1937193 2.1893943 -1.4419854 -0.24943634 -0.78936698 0.014349737 + 1000 1.3454512 1.9300306 -1.5968842 -0.25275207 0.66766599 -0.14162185 + 2000 1.4039236 1.7347077 -1.5342253 -0.13167808 1.0083521 0.018815371 + 3000 1.3819158 1.5842676 -1.524631 -0.14406998 0.97986119 -0.20808108 + 4000 1.4881542 1.5610517 -1.5931464 -0.10645124 0.62306586 -0.033136726 + 5000 1.5698331 1.5343155 -1.4364232 0.13187076 1.5429086 0.04099089 + 6000 1.5016907 1.3826377 -1.5745056 -0.074287159 0.89913208 -0.17399314 + 7000 1.5675532 1.3910161 -1.5675986 -0.0015822389 0.88703243 -0.024467694 + 8000 1.5310724 1.2722437 -1.5156796 0.01389173 1.1371195 -0.16555072 + 9000 1.6032459 1.2470143 -1.5962343 0.0054397805 0.77091045 -0.086815594 + 10000 1.6039245 1.2027956 -1.4895158 0.11283619 1.3679611 0.11825916 + 11000 1.6678981 1.2385666 -1.5499806 0.11628229 1.0490591 0.0051108128 + 12000 1.6356227 1.1497443 -1.5538343 0.080184906 1.0649052 0.040263125 + 13000 1.7271885 1.2038792 -1.4858355 0.23965967 1.4062221 -0.26024536 + 14000 1.7125742 1.1453219 -1.5872938 0.12360137 0.88981816 -0.09475299 + 15000 1.697457 1.1240109 -1.4765483 0.21924452 1.3295682 0.071859191 + 16000 1.7020133 1.0993042 -1.5531753 0.14716935 1.0382104 -0.036836887 + 17000 1.776422 1.1390987 -1.5823549 0.19232551 1.0805974 0.10662874 + 18000 1.7459818 1.0439137 -1.5078975 0.23637253 1.313287 -0.082282891 + 19000 1.838868 1.1156637 -1.5844104 0.25265482 1.0841384 -0.10556118 + 20000 1.7992553 1.0250579 -1.5002936 0.29719771 1.3325389 0.16740981 +Loop time of 5.02844 on 1 procs for 20000 steps with 1020 atoms + +Pair time (%) = 2.58723 (51.4519) +Neigh time (%) = 0.77584 (15.429) +Comm time (%) = 0.099901 (1.98672) +Outpt time (%) = 0.000553131 (0.011) +Other time (%) = 1.56492 (31.1213) + +Nlocal: 1020 ave 1020 max 1020 min +Histogram: 1 0 0 0 0 0 0 0 0 0 +Nghost: 323 ave 323 max 323 min +Histogram: 1 0 0 0 0 0 0 0 0 0 +Neighs: 7032 ave 7032 max 7032 min +Histogram: 1 0 0 0 0 0 0 0 0 0 + +Total # of neighbors = 7032 +Ave neighs/atom = 6.89412 +Neighbor list builds = 3072 +Dangerous builds = 0 + +# data gathering run + +variable visc equal -pxy/(v_srate/ly) +fix vave all ave/time 1000 1 1000 v_visc ave running + +thermo_style custom step temp pxy v_visc f_vave +thermo_modify temp tilt +WARNING: Temperature for thermo pressure is not for group all (../thermo.cpp:438) + +#dump 1 all custom 1000 dump.wall.2d id type x y z + +run 50000 +Memory usage per processor = 2.11173 Mbytes +Step Temp Pxy visc vave + 20000 1.0250579 0.18425325 -3.1771004 -3.1771004 + 21000 1.032232 -0.011301665 0.19487594 -1.4911123 + 22000 1.0813633 -0.11758517 2.0275349 -0.31822987 + 23000 1.0220607 -0.25775248 4.4444563 0.87244166 + 24000 1.0210253 -0.068163349 1.1753486 0.93302306 + 25000 1.0177923 -0.021423703 0.36941143 0.83908779 + 26000 1.0382206 -0.21638355 3.731127 1.2522363 + 27000 1.0385115 -0.12852776 2.2162193 1.3727341 + 28000 1.0003333 -0.15923771 2.7457545 1.5252919 + 29000 1.0135986 0.022866973 -0.3942979 1.333333 + 30000 1.0194233 0.063159972 -1.0890748 1.1131141 + 31000 1.0514567 -0.2541318 4.3820244 1.3855233 + 32000 1.0285306 -0.054192652 0.93445026 1.3508253 + 33000 1.0071874 0.01731204 -0.29851354 1.2330154 + 34000 1.0322195 -0.0049804328 0.085878187 1.1565396 + 35000 1.0173715 0.14221616 -2.45225 0.93099026 + 36000 1.0409851 -0.23434525 4.0408426 1.1139228 + 37000 1.0664089 -0.027817311 0.47965716 1.0786858 + 38000 0.99623633 0.11484829 -1.9803425 0.91768428 + 39000 1.0449413 -0.023397198 0.40344064 0.8919721 + 40000 0.9563429 0.0041168584 -0.070987474 0.84611688 + 41000 1.0382254 -0.33271224 5.7369962 1.0684296 + 42000 1.0321466 0.031491943 -0.54301928 0.99836659 + 43000 1.0350994 -0.10776809 1.8582579 1.0341954 + 44000 1.0488543 -0.12171179 2.0986907 1.0767752 + 45000 0.96826694 0.061744254 -1.0646634 0.99441218 + 46000 1.0756992 -0.16891801 2.912673 1.0654589 + 47000 1.029474 -0.029124844 0.50220311 1.0453426 + 48000 1.0457638 0.23801238 -4.1040754 0.86777646 + 49000 1.016492 -0.058257033 1.0045329 0.87233501 + 50000 1.0220214 -0.11109438 1.9156134 0.90598915 + 51000 1.0346746 -0.19761354 3.4074736 0.98416054 + 52000 1.0209176 -0.017517632 0.30205859 0.96349078 + 53000 0.93831183 0.069226265 -1.1936766 0.90004468 + 54000 0.97965871 -0.090969867 1.5686041 0.91914638 + 55000 1.0079917 0.035017794 -0.60381594 0.87684187 + 56000 1.0115963 -0.22451618 3.8713589 0.95777476 + 57000 1.017181 -0.10151542 1.7504423 0.97863444 + 58000 0.99997602 0.095913805 -1.653853 0.91113476 + 59000 1.0264522 -0.14591873 2.5160939 0.95125874 + 60000 0.96275934 -0.031236122 0.53860812 0.94119409 + 61000 1.0350612 -0.16189857 2.7916362 0.98525223 + 62000 1.0187115 -0.072384719 1.2481382 0.99136586 + 63000 1.0180989 0.16057484 -2.7688109 0.9059073 + 64000 0.94578895 -0.12881896 2.2212405 0.93513692 + 65000 1.0563618 -0.011446086 0.19736621 0.91909843 + 66000 1.0213837 -0.20130056 3.4710492 0.97339525 + 67000 1.0426376 -0.053212874 0.91755585 0.97223193 + 68000 0.96934378 0.1068193 -1.8418977 0.91480072 + 69000 1.0618645 -0.10864818 1.8734334 0.93397337 + 70000 0.97359099 -0.090976899 1.5687254 0.94641949 +Loop time of 12.7119 on 1 procs for 50000 steps with 1020 atoms + +Pair time (%) = 6.47588 (50.9434) +Neigh time (%) = 2.05525 (16.1679) +Comm time (%) = 0.257193 (2.02324) +Outpt time (%) = 0.000914574 (0.00719461) +Other time (%) = 3.92268 (30.8583) + +Nlocal: 1020 ave 1020 max 1020 min +Histogram: 1 0 0 0 0 0 0 0 0 0 +Nghost: 320 ave 320 max 320 min +Histogram: 1 0 0 0 0 0 0 0 0 0 +Neighs: 7007 ave 7007 max 7007 min +Histogram: 1 0 0 0 0 0 0 0 0 0 + +Total # of neighbors = 7007 +Ave neighs/atom = 6.86961 +Neighbor list builds = 8152 +Dangerous builds = 0 diff --git a/examples/VISCOSITY/profile.gk.2d.12Sep13 b/examples/VISCOSITY/profile.gk.2d.12Sep13 new file mode 100644 index 0000000000..5c4effb643 --- /dev/null +++ b/examples/VISCOSITY/profile.gk.2d.12Sep13 @@ -0,0 +1,100654 @@ +# Time-correlated data for fix SS +# Timestep Number-of-time-windows +# Index TimeDelta Ncount v_pxy*v_pxy +0 400 +1 0 1 0.0111675 +2 5 0 0.0 +3 10 0 0.0 +4 15 0 0.0 +5 20 0 0.0 +6 25 0 0.0 +7 30 0 0.0 +8 35 0 0.0 +9 40 0 0.0 +10 45 0 0.0 +11 50 0 0.0 +12 55 0 0.0 +13 60 0 0.0 +14 65 0 0.0 +15 70 0 0.0 +16 75 0 0.0 +17 80 0 0.0 +18 85 0 0.0 +19 90 0 0.0 +20 95 0 0.0 +21 100 0 0.0 +22 105 0 0.0 +23 110 0 0.0 +24 115 0 0.0 +25 120 0 0.0 +26 125 0 0.0 +27 130 0 0.0 +28 135 0 0.0 +29 140 0 0.0 +30 145 0 0.0 +31 150 0 0.0 +32 155 0 0.0 +33 160 0 0.0 +34 165 0 0.0 +35 170 0 0.0 +36 175 0 0.0 +37 180 0 0.0 +38 185 0 0.0 +39 190 0 0.0 +40 195 0 0.0 +41 200 0 0.0 +42 205 0 0.0 +43 210 0 0.0 +44 215 0 0.0 +45 220 0 0.0 +46 225 0 0.0 +47 230 0 0.0 +48 235 0 0.0 +49 240 0 0.0 +50 245 0 0.0 +51 250 0 0.0 +52 255 0 0.0 +53 260 0 0.0 +54 265 0 0.0 +55 270 0 0.0 +56 275 0 0.0 +57 280 0 0.0 +58 285 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1905 0 0.0 +383 1910 0 0.0 +384 1915 0 0.0 +385 1920 0 0.0 +386 1925 0 0.0 +387 1930 0 0.0 +388 1935 0 0.0 +389 1940 0 0.0 +390 1945 0 0.0 +391 1950 0 0.0 +392 1955 0 0.0 +393 1960 0 0.0 +394 1965 0 0.0 +395 1970 0 0.0 +396 1975 0 0.0 +397 1980 0 0.0 +398 1985 0 0.0 +399 1990 0 0.0 +400 1995 0 0.0 +2000 400 +1 0 401 0.00780999 +2 5 400 0.00675924 +3 10 399 0.00478685 +4 15 398 0.00321645 +5 20 397 0.00228417 +6 25 396 0.00178282 +7 30 395 0.00138486 +8 35 394 0.000912684 +9 40 393 0.000374759 +10 45 392 -0.000164163 +11 50 391 -0.000589718 +12 55 390 -0.00084365 +13 60 389 -0.000930282 +14 65 388 -0.000858088 +15 70 387 -0.00071976 +16 75 386 -0.000663726 +17 80 385 -0.000712406 +18 85 384 -0.000777529 +19 90 383 -0.000739826 +20 95 382 -0.000575946 +21 100 381 -0.000342473 +22 105 380 -0.000144525 +23 110 379 -0.000147725 +24 115 378 -0.000308334 +25 120 377 -0.000458769 +26 125 376 -0.00071773 +27 130 375 -0.00110153 +28 135 374 -0.00132177 +29 140 373 -0.00124284 +30 145 372 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331 0.000489142 +72 355 330 0.000612759 +73 360 329 0.000634617 +74 365 328 0.000514397 +75 370 327 0.000370118 +76 375 326 0.000194329 +77 380 325 -0.000101034 +78 385 324 -0.000435326 +79 390 323 -0.000705204 +80 395 322 -0.000921196 +81 400 321 -0.00110681 +82 405 320 -0.00118584 +83 410 319 -0.00113336 +84 415 318 -0.00111632 +85 420 317 -0.00116059 +86 425 316 -0.00110123 +87 430 315 -0.00101388 +88 435 314 -0.00101828 +89 440 313 -0.000977086 +90 445 312 -0.000740246 +91 450 311 -0.000334118 +92 455 310 5.28145e-05 +93 460 309 0.00018239 +94 465 308 0.000170725 +95 470 307 0.000310255 +96 475 306 0.000554661 +97 480 305 0.000674987 +98 485 304 0.000531525 +99 490 303 0.000252777 +100 495 302 6.14324e-05 +101 500 301 7.45564e-05 +102 505 300 0.000211101 +103 510 299 0.000358512 +104 515 298 0.000464895 +105 520 297 0.00041211 +106 525 296 0.000192525 +107 530 295 9.52133e-05 +108 535 294 0.000240856 +109 540 293 0.000409012 +110 545 292 0.00054322 +111 550 291 0.000706062 +112 555 290 0.000902134 +113 560 289 0.000984842 +114 565 288 0.000829133 +115 570 287 0.000559888 +116 575 286 0.000404388 +117 580 285 0.000397544 +118 585 284 0.000420978 +119 590 283 0.000318899 +120 595 282 8.13422e-05 +121 600 281 -0.000223857 +122 605 280 -0.000500311 +123 610 279 -0.000603696 +124 615 278 -0.000548599 +125 620 277 -0.000488179 +126 625 276 -0.000511511 +127 630 275 -0.000552123 +128 635 274 -0.000635473 +129 640 273 -0.000824469 +130 645 272 -0.00102082 +131 650 271 -0.00104376 +132 655 270 -0.000756354 +133 660 269 -0.000249336 +134 665 268 0.000184784 +135 670 267 0.000335244 +136 675 266 0.000303633 +137 680 265 0.000243351 +138 685 264 0.000133069 +139 690 263 6.45789e-05 +140 695 262 0.000113541 +141 700 261 0.000256409 +142 705 260 0.000404249 +143 710 259 0.000379719 +144 715 258 0.000212401 +145 720 257 0.000163835 +146 725 256 0.000190199 +147 730 255 9.12258e-05 +148 735 254 -7.54937e-05 +149 740 253 -0.000213304 +150 745 252 -0.000375014 +151 750 251 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0.144425 + 2 0.075 9.8 0.209658 + 3 0.125 9.884 0.368581 + 4 0.175 9.856 0.497307 + 5 0.225 9.672 0.656497 + 6 0.275 9.596 0.76955 + 7 0.325 9.26 0.905718 + 8 0.375 9.24 0.994601 + 9 0.425 10.112 1.09254 + 10 0.475 10.08 1.30981 + 11 0.525 10.248 1.50662 + 12 0.575 9.984 1.65788 + 13 0.625 10.196 1.65357 + 14 0.675 10.38 1.8222 + 15 0.725 10.54 1.94923 + 16 0.775 10.128 2.03795 + 17 0.825 9.964 2.06985 + 18 0.875 10.344 2.24552 + 19 0.925 10.324 2.47268 + 20 0.975 9.988 2.65924 diff --git a/examples/VISCOSITY/profile.wall.2d.12Sep13 b/examples/VISCOSITY/profile.wall.2d.12Sep13 new file mode 100644 index 0000000000..b6c5bf01e2 --- /dev/null +++ b/examples/VISCOSITY/profile.wall.2d.12Sep13 @@ -0,0 +1,66 @@ +# Spatial-averaged data for fix 4 and group flow +# Timestep Number-of-bins +# Bin Coord Ncount vx +10000 20 + 1 0.025 0 0 + 2 0.075 0 0 + 3 0.125 44.736 0.0137168 + 4 0.175 52.768 0.000823768 + 5 0.225 52.386 -0.0464089 + 6 0.275 50.08 -0.0171689 + 7 0.325 50.766 0.0646337 + 8 0.375 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