In [25]:

    

include("../src/msd.jl")


    

    
Out[25]:





run_lorentz (generic function with 2 methods)

In [26]:

    

num_particles = 100000
num_collisions = 10000

@time stats_usual, stats_all = run_lorentz(num_particles, num_collisions, 10.0)


    

    




elapsed time: 3886.964435818 seconds (2034691974496 bytes allocated, 42.01% gc time)






    
Out[26]:





([(0.0,0.0,0.0,NaN,NaN,100000),(10.0,0.004842370044674483,6.486963373552059,-0.03748580106477242,2.068068819795122,100000),(20.0,0.009797134241836713,15.112662045509722,-0.03424206297997898,3.276570472611298,100000),(30.0,0.00788703507405834,24.406260237965384,-0.011231884876512662,4.380177707799779,100000),(40.0,0.014381403859915494,34.25630913483406,-0.030602340706122073,5.475669954416327,100000),(50.0,0.010780346974572497,44.576787643108005,-0.022616315359748312,6.431770772119384,100000),(60.0,-0.0011960678768010182,54.874850106497796,-0.010166302610563099,7.318341305852128,100000),(70.0,0.0008962022314963746,65.17290429044053,-0.007552916978548962,7.979849961127602,100000),(80.0,0.011031524773363147,75.73122943598699,0.0008173388361607941,8.744236245676078,100000),(90.0,0.007294865416705214,86.31874606622227,0.017551203833677472,9.579441504152038,100000)  …  (21500.0,13031.99537599018,NaN,NaN,NaN,1),(21510.0,13039.511090398435,NaN,NaN,NaN,1),(21520.0,13039.66002014777,NaN,NaN,NaN,1),(21530.0,13040.015115694592,NaN,NaN,NaN,1),(21540.0,13039.463463395428,NaN,NaN,NaN,1),(21550.0,13031.973383016435,NaN,NaN,NaN,1),(21560.0,13025.790463825948,NaN,NaN,NaN,1),(21570.0,13024.879697807515,NaN,NaN,NaN,1),(21580.0,13027.958255968157,NaN,NaN,NaN,1),(21590.0,13031.831818548515,NaN,NaN,NaN,1)],[(10.0,-3.3868479496986282e-6,6.545293675266838,0.0023534952211485636,2.114605203319618,17158540),(20.0,0.0003254971628674024,15.282965575911987,0.00446387289157865,3.3549290279414317,17138272),(30.0,-0.00021433103949885547,24.631950014590004,0.007129517369118432,4.395689518382686,17118501),(40.0,-0.0007052379225168648,34.366045273592036,0.009647948088844605,5.37154384310778,17098405),(50.0,-0.0020829739149326857,44.34759961864984,0.011641930263116424,6.302553508089547,17078622),(60.0,-0.002011335925923074,54.56829120448842,0.01625785950896143,7.183865173880676,17058540),(70.0,-0.001715688525806037,64.95074762850084,0.01961557171765193,8.040443404332095,17038272),(80.0,-0.0022292649469375756,75.4757263744712,0.022977500867979426,8.875333776670772,17018501),(90.0,-0.0027577198545159732,86.14448965706872,0.026092292014390284,9.687793320424797,16998405),(100.0,-0.004117096387705116,96.90715512396342,0.028645788007312264,10.490678330458225,16978622)  …  (21500.0,13037.26754334663,55.591497268837216,0.0,-2.0,2),(21510.0,13037.933940955514,4.97480073061158,0.0,-2.0,2),(21520.0,13037.553022820965,8.878875470326477,0.0,-2.0,2),(21530.0,13039.269849674696,1.1108428808205613,0.0,-2.0,2),(21540.0,13040.930804815294,4.30618168490867,0.0,-2.0,2),(21550.0,13031.973383016435,NaN,NaN,NaN,1),(21560.0,13025.790463825948,NaN,NaN,NaN,1),(21570.0,13024.879697807515,NaN,NaN,NaN,1),(21580.0,13027.958255968157,NaN,NaN,NaN,1),(21590.0,13031.831818548515,NaN,NaN,NaN,1)])

In [33]:

    

stats_usual1, stats_all1 = stats_usual, stats_all


    

    
Out[33]:





([(0.0,0.0,0.0,NaN,NaN,100000),(10.0,0.004842370044674483,6.486963373552059,-0.03748580106477242,2.068068819795122,100000),(20.0,0.009797134241836713,15.112662045509722,-0.03424206297997898,3.276570472611298,100000),(30.0,0.00788703507405834,24.406260237965384,-0.011231884876512662,4.380177707799779,100000),(40.0,0.014381403859915494,34.25630913483406,-0.030602340706122073,5.475669954416327,100000),(50.0,0.010780346974572497,44.576787643108005,-0.022616315359748312,6.431770772119384,100000),(60.0,-0.0011960678768010182,54.874850106497796,-0.010166302610563099,7.318341305852128,100000),(70.0,0.0008962022314963746,65.17290429044053,-0.007552916978548962,7.979849961127602,100000),(80.0,0.011031524773363147,75.73122943598699,0.0008173388361607941,8.744236245676078,100000),(90.0,0.007294865416705214,86.31874606622227,0.017551203833677472,9.579441504152038,100000)  …  (21500.0,13031.99537599018,NaN,NaN,NaN,1),(21510.0,13039.511090398435,NaN,NaN,NaN,1),(21520.0,13039.66002014777,NaN,NaN,NaN,1),(21530.0,13040.015115694592,NaN,NaN,NaN,1),(21540.0,13039.463463395428,NaN,NaN,NaN,1),(21550.0,13031.973383016435,NaN,NaN,NaN,1),(21560.0,13025.790463825948,NaN,NaN,NaN,1),(21570.0,13024.879697807515,NaN,NaN,NaN,1),(21580.0,13027.958255968157,NaN,NaN,NaN,1),(21590.0,13031.831818548515,NaN,NaN,NaN,1)],[(10.0,-3.3868479496986282e-6,6.545293675266838,0.0023534952211485636,2.114605203319618,17158540),(20.0,0.0003254971628674024,15.282965575911987,0.00446387289157865,3.3549290279414317,17138272),(30.0,-0.00021433103949885547,24.631950014590004,0.007129517369118432,4.395689518382686,17118501),(40.0,-0.0007052379225168648,34.366045273592036,0.009647948088844605,5.37154384310778,17098405),(50.0,-0.0020829739149326857,44.34759961864984,0.011641930263116424,6.302553508089547,17078622),(60.0,-0.002011335925923074,54.56829120448842,0.01625785950896143,7.183865173880676,17058540),(70.0,-0.001715688525806037,64.95074762850084,0.01961557171765193,8.040443404332095,17038272),(80.0,-0.0022292649469375756,75.4757263744712,0.022977500867979426,8.875333776670772,17018501),(90.0,-0.0027577198545159732,86.14448965706872,0.026092292014390284,9.687793320424797,16998405),(100.0,-0.004117096387705116,96.90715512396342,0.028645788007312264,10.490678330458225,16978622)  …  (21500.0,13037.26754334663,55.591497268837216,0.0,-2.0,2),(21510.0,13037.933940955514,4.97480073061158,0.0,-2.0,2),(21520.0,13037.553022820965,8.878875470326477,0.0,-2.0,2),(21530.0,13039.269849674696,1.1108428808205613,0.0,-2.0,2),(21540.0,13040.930804815294,4.30618168490867,0.0,-2.0,2),(21550.0,13031.973383016435,NaN,NaN,NaN,1),(21560.0,13025.790463825948,NaN,NaN,NaN,1),(21570.0,13024.879697807515,NaN,NaN,NaN,1),(21580.0,13027.958255968157,NaN,NaN,NaN,1),(21590.0,13031.831818548515,NaN,NaN,NaN,1)])

In [27]:

    

using PyPlot


    

In [28]:

    

stats2_usual = filter(x->x[6] > num_collisions/2, stats_usual)
stats2_all = filter(x->x[6] > 10000, stats_all)

times = [data[1] for data in stats2_usual];
means =[data[2] for data in stats2_usual]; 
msds = [data[3] for data in stats2_usual];


times2 = [data[1] for data in stats2_all];
means2 = [data[2] for data in stats2_all];
msds2 = [data[3] for data in stats2_all];


    

In [29]:

    

plot(times, msds, "o-", label="usual")
plot(times2, msds2, "o-", label="all origins")
# plot(times, means, "o-", label="usual")
# plot(times2, means2, "o-", label="all origins")

xlim(0, 800)
ylim(0, 1000)
#ylim(-1, 1)
legend()


    

    













    
Out[29]:





PyObject <matplotlib.legend.Legend object at 0x118162a90>

In [31]:

    

semilogx(times, msds ./ times, "o-")
semilogx(times2, msds2 ./ times2, "o-")
xlim(0, 1000)
#ylim(0, 2)
ylim(0.6, 1.3)


    

    













    
Out[31]:





(0.6,1.3)

In [116]:

    

function run_particle(billiard_table, num_collisions)
    x, v = initial_condition(billiard_table, -.5, .5, -.5, .5)
    l = Vector2D(0, 0)
    p = ParticleOnLattice(x, v, l)
        
    xs, ls, free_paths = billiard_dynamics_on_lattice(p, billiard_table, num_collisions)
    positions, times = continuous_time(xs, ls, free_paths, delta_t)
end

function run_particles(billiard_table, num_particles, num_collisions)
    for i in 1:num_particles
        run_particle(billiard_table, num_collisions)
        #gc()
    end
end


    

    
Out[116]:





run_particles (generic function with 1 method)

In [114]:

    

gc()
@time run_particle(billiard_table, 1000000)


    

    




elapsed time: 3.674504946 seconds (1992654648 bytes allocated, 46.68% gc time)






    
Out[114]:





([Vector2D{Float64}(-0.385964099684619,-0.4339483397361421),Vector2D{Float64}(-1.3534749163722164,0.9223598719220781),Vector2D{Float64}(-2.6585034246282877,3.707211400970422),Vector2D{Float64}(-3.512326750455456,-1.0187893629672),Vector2D{Float64}(-4.372546762428787,-5.53659631503165),Vector2D{Float64}(-2.249596421449907,-4.446637200469559),Vector2D{Float64}(-2.7735205356063504,-3.5724369935788407),Vector2D{Float64}(-5.372964287368319,-4.425007096380261),Vector2D{Float64}(-10.333173851214074,-7.404398974273148),Vector2D{Float64}(-13.539744050958841,-8.217696758262218)  …  Vector2D{Float64}(-1680.4497803957017,-903.4676016108131),Vector2D{Float64}(-1683.356904776948,-904.0113374824958),Vector2D{Float64}(-1679.8419278514543,-904.4236647405563),Vector2D{Float64}(-1677.507344005385,-903.1599301741296),Vector2D{Float64}(-1679.4081531640593,-902.7141195393959),Vector2D{Float64}(-1670.985783717843,-901.4953059789648),Vector2D{Float64}(-1671.574245464399,-898.0888224299193),Vector2D{Float64}(-1670.5210319836021,-895.2538944104726),Vector2D{Float64}(-1671.570630072419,-895.6774385482373),Vector2D{Float64}(-1672.4683812593757,-894.8706467145633)],[0.0,10.0,20.0,30.0,40.0,50.0,60.0,70.0,80.0,90.0  …  856740.0,856750.0,856760.0,856770.0,856780.0,856790.0,856800.0,856810.0,856820.0,856830.0])

In [118]:

    

gc()
@time run_particles(billiard_table, 10000, 1000)


    

    




elapsed time: 40.862335964 seconds (19636428640 bytes allocated, 49.07% gc time)

In [32]:

    

num_particles = 100000
num_collisions = 100000

@time stats_usual_new, stats_all_new = run_lorentz(num_particles, num_collisions, 50.0)


    

    




elapsed time: 36591.352598857 seconds (19927628495560 bytes allocated, 44.47% gc time)






    
Out[32]:





([(0.0,0.0,0.0,NaN,NaN,100000),(50.0,0.017305010917974605,44.65507863931822,0.022799980430700424,6.115959405906301,100000),(100.0,0.048111397060719714,97.42713875013999,0.05447394577392689,10.184302705995218,100000),(150.0,0.046430096848310884,152.5581251653949,0.012134228707699838,13.836820075918876,100000),(200.0,0.03355186997650198,208.1941979506868,-0.056354977504601216,16.457370457112575,100000),(250.0,0.05066875174855612,263.58326607424425,-0.07292320478919148,19.431831235889433,100000),(300.0,0.056705107115976865,321.2084924372402,-0.09182774753796995,22.513104699816527,100000),(350.0,0.05230307405468847,380.72508637258346,-0.10169050107948359,26.39749819989671,100000),(400.0,0.06144658581294162,440.72160561210666,-0.1310106276454254,30.24651891340254,100000),(450.0,0.06881316188689357,500.5585631576715,-0.1632386497953707,34.069184270583506,100000)  …  (478500.0,516.2313965663321,NaN,NaN,NaN,1),(478550.0,510.5854451418633,NaN,NaN,NaN,1),(478600.0,506.7417424999431,NaN,NaN,NaN,1),(478650.0,516.1487836223027,NaN,NaN,NaN,1),(478700.0,509.9619189249421,NaN,NaN,NaN,1),(478750.0,520.2949755306167,NaN,NaN,NaN,1),(478800.0,506.0370662087873,NaN,NaN,NaN,1),(478850.0,511.87472001378836,NaN,NaN,NaN,1),(478900.0,508.9573858527127,NaN,NaN,NaN,1),(478950.0,517.8003444107999,NaN,NaN,NaN,1)],[(50.0,0.00013791421918360017,44.36004881560537,-0.003025254003753477,6.3014391171687265,34287241),(100.0,0.0007734965469196507,96.89445521624849,-0.0012672892198786337,10.500293162504718,34267271),(150.0,0.001516633176202603,151.98630958327152,0.001505580730133381,14.262962262623777,34247193),(200.0,0.0019437565695509882,208.73967876647262,0.009678452467242577,17.82317393769913,34227208),(250.0,0.0010335128155721256,266.8439751361774,0.018600449057861748,21.251102509576516,34207265),(300.0,0.001170106757760268,325.9818333786798,0.025343105598705656,24.58561273159152,34187241),(350.0,0.0017521783007769553,385.8757937738715,0.03061867689364674,27.855169578050717,34167271),(400.0,0.0024477276443325186,446.36098439307085,0.03781778358280069,31.026741548639585,34147193),(450.0,0.0028205557405570386,507.4972413533574,0.04960040111154175,34.184420071124705,34127208),(500.0,0.0017784503795190694,569.2358185734843,0.06092159894992022,37.27282287207687,34107265)  …  (478500.0,518.2632622131014,8.256956013042373,0.0,-2.0,2),(478550.0,508.31133183995223,10.343182619857627,0.0,-2.0,2),(478600.0,509.3083074214927,13.174510993057797,0.0,-2.0,2),(478650.0,512.5531609021347,25.857005491577404,0.0,-2.0,2),(478700.0,513.8812078324979,30.721651081781143,0.0,-2.0,2),(478750.0,520.2949755306167,NaN,NaN,NaN,1),(478800.0,506.0370662087873,NaN,NaN,NaN,1),(478850.0,511.87472001378836,NaN,NaN,NaN,1),(478900.0,508.9573858527127,NaN,NaN,NaN,1),(478950.0,517.8003444107999,NaN,NaN,NaN,1)])

In [34]:

    

stats_usual, stats_all = stats_usual_new, stats_all_new


    

    
Out[34]:





([(0.0,0.0,0.0,NaN,NaN,100000),(50.0,0.017305010917974605,44.65507863931822,0.022799980430700424,6.115959405906301,100000),(100.0,0.048111397060719714,97.42713875013999,0.05447394577392689,10.184302705995218,100000),(150.0,0.046430096848310884,152.5581251653949,0.012134228707699838,13.836820075918876,100000),(200.0,0.03355186997650198,208.1941979506868,-0.056354977504601216,16.457370457112575,100000),(250.0,0.05066875174855612,263.58326607424425,-0.07292320478919148,19.431831235889433,100000),(300.0,0.056705107115976865,321.2084924372402,-0.09182774753796995,22.513104699816527,100000),(350.0,0.05230307405468847,380.72508637258346,-0.10169050107948359,26.39749819989671,100000),(400.0,0.06144658581294162,440.72160561210666,-0.1310106276454254,30.24651891340254,100000),(450.0,0.06881316188689357,500.5585631576715,-0.1632386497953707,34.069184270583506,100000)  …  (478500.0,516.2313965663321,NaN,NaN,NaN,1),(478550.0,510.5854451418633,NaN,NaN,NaN,1),(478600.0,506.7417424999431,NaN,NaN,NaN,1),(478650.0,516.1487836223027,NaN,NaN,NaN,1),(478700.0,509.9619189249421,NaN,NaN,NaN,1),(478750.0,520.2949755306167,NaN,NaN,NaN,1),(478800.0,506.0370662087873,NaN,NaN,NaN,1),(478850.0,511.87472001378836,NaN,NaN,NaN,1),(478900.0,508.9573858527127,NaN,NaN,NaN,1),(478950.0,517.8003444107999,NaN,NaN,NaN,1)],[(50.0,0.00013791421918360017,44.36004881560537,-0.003025254003753477,6.3014391171687265,34287241),(100.0,0.0007734965469196507,96.89445521624849,-0.0012672892198786337,10.500293162504718,34267271),(150.0,0.001516633176202603,151.98630958327152,0.001505580730133381,14.262962262623777,34247193),(200.0,0.0019437565695509882,208.73967876647262,0.009678452467242577,17.82317393769913,34227208),(250.0,0.0010335128155721256,266.8439751361774,0.018600449057861748,21.251102509576516,34207265),(300.0,0.001170106757760268,325.9818333786798,0.025343105598705656,24.58561273159152,34187241),(350.0,0.0017521783007769553,385.8757937738715,0.03061867689364674,27.855169578050717,34167271),(400.0,0.0024477276443325186,446.36098439307085,0.03781778358280069,31.026741548639585,34147193),(450.0,0.0028205557405570386,507.4972413533574,0.04960040111154175,34.184420071124705,34127208),(500.0,0.0017784503795190694,569.2358185734843,0.06092159894992022,37.27282287207687,34107265)  …  (478500.0,518.2632622131014,8.256956013042373,0.0,-2.0,2),(478550.0,508.31133183995223,10.343182619857627,0.0,-2.0,2),(478600.0,509.3083074214927,13.174510993057797,0.0,-2.0,2),(478650.0,512.5531609021347,25.857005491577404,0.0,-2.0,2),(478700.0,513.8812078324979,30.721651081781143,0.0,-2.0,2),(478750.0,520.2949755306167,NaN,NaN,NaN,1),(478800.0,506.0370662087873,NaN,NaN,NaN,1),(478850.0,511.87472001378836,NaN,NaN,NaN,1),(478900.0,508.9573858527127,NaN,NaN,NaN,1),(478950.0,517.8003444107999,NaN,NaN,NaN,1)])

In [35]:

    

stats2_usual = filter(x->x[6] > num_collisions/2, stats_usual)
stats2_all = filter(x->x[6] > 10000, stats_all)

times = [data[1] for data in stats2_usual];
means =[data[2] for data in stats2_usual]; 
msds = [data[3] for data in stats2_usual];


times2 = [data[1] for data in stats2_all];
means2 = [data[2] for data in stats2_all];
msds2 = [data[3] for data in stats2_all];


    

In [36]:

    

plot(times, msds, "o-", label="usual")
plot(times2, msds2, "o-", label="all origins")
# plot(times, means, "o-", label="usual")
# plot(times2, means2, "o-", label="all origins")

xlim(0, 800)
ylim(0, 1000)
#ylim(-1, 1)
legend()


    

    













    
Out[36]:





PyObject <matplotlib.legend.Legend object at 0x10b762690>

In [39]:

    

semilogx(times, msds ./ times, "o-")
semilogx(times2, msds2 ./ times2, "o-")
xlim(0, 10000)
#ylim(0, 2)
ylim(0.6, 2)


    

    













    
Out[39]:





(0.6,2)

In [40]:

    

stats_all_new


    

    
Out[40]:





9579-element Array{(Float64,Float64,Float64,Float64,Float64,Int64),1}:
 (50.0,0.00013791421918360017,44.36004881560537,-0.003025254003753477,6.3014391171687265,34287241) 
 (100.0,0.0007734965469196507,96.89445521624849,-0.0012672892198786337,10.500293162504718,34267271)
 (150.0,0.001516633176202603,151.98630958327152,0.001505580730133381,14.262962262623777,34247193)  
 (200.0,0.0019437565695509882,208.73967876647262,0.009678452467242577,17.82317393769913,34227208)  
 (250.0,0.0010335128155721256,266.8439751361774,0.018600449057861748,21.251102509576516,34207265)  
 (300.0,0.001170106757760268,325.9818333786798,0.025343105598705656,24.58561273159152,34187241)    
 (350.0,0.0017521783007769553,385.8757937738715,0.03061867689364674,27.855169578050717,34167271)   
 (400.0,0.0024477276443325186,446.36098439307085,0.03781778358280069,31.026741548639585,34147193)  
 (450.0,0.0028205557405570386,507.4972413533574,0.04960040111154175,34.184420071124705,34127208)   
 (500.0,0.0017784503795190694,569.2358185734843,0.06092159894992022,37.27282287207687,34107265)    
 (550.0,0.0019117977948443496,631.5013315633257,0.07255301283898664,40.33770073753005,34087241)    
 (600.0,0.0026010106639973705,694.1850381533852,0.08310505183574068,43.37680846266,34067271)       
 (650.0,0.003328340006958328,757.161884209161,0.09594700533646834,46.3483069456003,34047193)       
 ⋮                                                                                                 
 (478400.0,511.36788431079395,17.144227923135634,0.707034986057333,-1.5,3)                         
 (478450.0,516.278159883176,32.59477225474702,-0.45507097399705015,-1.5000000000000002,3)          
 (478500.0,518.2632622131014,8.256956013042373,0.0,-2.0,2)                                         
 (478550.0,508.31133183995223,10.343182619857627,0.0,-2.0,2)                                       
 (478600.0,509.3083074214927,13.174510993057797,0.0,-2.0,2)                                        
 (478650.0,512.5531609021347,25.857005491577404,0.0,-2.0,2)                                        
 (478700.0,513.8812078324979,30.721651081781143,0.0,-2.0,2)                                        
 (478750.0,520.2949755306167,NaN,NaN,NaN,1)                                                        
 (478800.0,506.0370662087873,NaN,NaN,NaN,1)                                                        
 (478850.0,511.87472001378836,NaN,NaN,NaN,1)                                                       
 (478900.0,508.9573858527127,NaN,NaN,NaN,1)                                                        
 (478950.0,517.8003444107999,NaN,NaN,NaN,1)                                                        

In [41]:

    

include("../src/StatisticsAccumulator.jl")


    

    
Out[41]:





get_statistics (generic function with 1 method)

In [42]:

    

Array(StatisticsObject, 3)


    

    
Out[42]:





3-element Array{StatisticsObject,1}:
 #undef
 #undef
 #undef

In [43]:

    

StatisticsObject[]


    

    
Out[43]:





0-element Array{StatisticsObject,1}

In [44]:

    

billiard_table = Sinai_billiard(0.354, true, true)  # periodic in x and y


    

    
Out[44]:





BilliardTable{Float64}(Obstacle{Float64}[Disc{Float64}(Vector2D{Float64}(0.0,0.0),0.354),CellBoundary{Float64}(Vector2D{Float64}(0.5,-0.5),Vector2D{Float64}(-1.0,0.0),Vector2D{Int64}(1,0),CellBoundary{Float64}(Vector2D{Float64}(-0.5,0.5),Vector2D{Float64}(1.0,0.0),Vector2D{Int64}(-1,0),CellBoundary{Float64}(#= circular reference =#))),CellBoundary{Float64}(Vector2D{Float64}(-0.5,0.5),Vector2D{Float64}(1.0,0.0),Vector2D{Int64}(-1,0),CellBoundary{Float64}(Vector2D{Float64}(0.5,-0.5),Vector2D{Float64}(-1.0,0.0),Vector2D{Int64}(1,0),CellBoundary{Float64}(#= circular reference =#))),CellBoundary{Float64}(Vector2D{Float64}(0.5,0.5),Vector2D{Float64}(0.0,-1.0),Vector2D{Int64}(0,1),CellBoundary{Float64}(Vector2D{Float64}(-0.5,-0.5),Vector2D{Float64}(0.0,1.0),Vector2D{Int64}(0,-1),CellBoundary{Float64}(#= circular reference =#))),CellBoundary{Float64}(Vector2D{Float64}(-0.5,-0.5),Vector2D{Float64}(0.0,1.0),Vector2D{Int64}(0,-1),CellBoundary{Float64}(Vector2D{Float64}(0.5,0.5),Vector2D{Float64}(0.0,-1.0),Vector2D{Int64}(0,1),CellBoundary{Float64}(#= circular reference =#)))])

In [45]:

    

x0, v0 = initial_condition(billiard_table, -.5, .5, -.5, .5)
        l = Vector2D(0, 0)
        p = ParticleOnLattice(x0, v0, l)


    

    
Out[45]:





ParticleOnLattice{Float64}(Vector2D{Float64}(-0.22404895495792077,-0.35342502848393953),Vector2D{Float64}(-0.9593715402632275,0.28214579162724107),Vector2D{Int64}(0,0))

In [48]:

    

xs, ls, free_paths = billiard_dynamics_on_lattice(p, billiard_table, num_collisions)
        positions, times = continuous_time(xs, ls, free_paths, delta_t)


    

    
Out[48]:





([Vector2D{Float64}(0.10488770797543749,-0.33810437547547256),Vector2D{Float64}(356.12614125394515,-38.58417321367659)],[0.0,5.0])

In [47]:

    

delta_t = 5
num_collisions = 10


    

    
Out[47]:





10

In [49]:

    

free_paths


    

    
Out[49]:





10-element Array{Float64,1}:
 0.820149
 0.342202
 0.304586
 1.55061 
 0.73345 
 0.381409
 0.771764
 0.339464
 0.337281
 0.760213

In [ ]: