wolfgang(bauer( · 2013. 10. 28. · credit:bauer&wesall2013. october28,2013 7...

Wolfgang  Bauer  Department  of  Physics  and  Astronomy  &  Ins6tute  for  Cyber-­‐Enabled  Research  

•  Irina  Sagert,  MSU  PHY  (Lynen  Fellow)  •  Dirk  Colbry,  MSU  iCER  

•  Terrance  Strother,  LANL  (former  MSU  Ph.D.)  

•  Tobias  Bollenbach,  MSU  M.S.  (Studiens6Nung)  

•  Rodney  Picket,  MSU  CSE  undergraduate  

•  James  Howell,  MSU  CSE  undergraduate  

•  Alec  Staber,  MSU  AST  undergraduate  

October  28,  2013   2  

•  …  according  to  fluid  dynamics  experts  

October  28,  2013   3  

•  Conserva6on  Laws  – Linear  momentum  (Newton’s  2nd  Law)  – Energy  (including  Mass)  

•  Navier-­‐Stokes  Equa6on  

October  28,  2013   4  

ρ ∂v∂t

+ (vi∇)v⎛

⎝⎜⎞⎠⎟ = −

∇p +

∇T +

F

v = flow velocityp = pressureρ = fluid density

T = stress tensorF = external force Credit:  Thierry  Dugnolle  (Wikipedia)  

•  =  ra6o  of  iner6al  forces  to  viscous  (fric6on)  forces    

•                 

•  Rule  of  thumb:    Re  >  5,000  turbulent  flow                          Re  <  2,000  laminar  flow  

October  28,  2013   5  

Credit:  Horns  Rev  1  owned  by  Vaeenfall.  Photographer  Chris6an  Steiness;  

Re = ρvLη

ρ = fluid densityv = typical flow speedL = characteristic length scaleη = dynamic viscosity

Re = ρvLη

ρ = fluid densityv = typical flow speedL = characteristic length scaleη = dynamic viscosity

•  =  ra6o  of  mean  free  path  to  characteris6c  length  scale  

•  Needed  for  hydro  to  be  valid    •  Example  ideal  gas:    

– N2  molecules  at  STP:  Kn  ~  30  

October  28,  2013   6  

Kn = λL

Knideal gas =kBT

2(4πr2 )pL

Kn→ 0

Credit:  Bauer  &  Wesjall  2013  

October  28,  2013   7  

arXiv.org  >  cond-­‐mat  >  arXiv:1105.6256  

October  28,  2013   8  

Tfit  =  419  MeV                                Tfit  =  239  MeV  

Rela6vis6c  Heavy  Ion  Collider  (RHIC).    Data:  STAR  Collabora6on  

100  AGev  Au  +  Au  100  AGev    

October  28,  2013   9  

Credit:  McLerran  2013  

Cartoon  of  the  6me  evolu6on  of  an  ultra-­‐rela6vis6c  heavy  ion  collision  

•  Rela6vis6c  heavy  ion  collisions  

•  Scale  10-­‐15  m  

•  Shock  wave  (?)  •  Successful  @RHIC  

– v2    ✓

– η/s  small  ✓

October  28,  2013   10  

H. Stöcker, J.A. Maruhn, and W. Greiner, PRL 44, 725 (1980)"

October  28,  2013   11  

coordinate space

anisotropy

momentum space

anisotropy

( )( )⎟⎠⎞⎜

⎝⎛ Ψ−+

=

∑∞

=1

2

3

3

cos),(21

ddd

21

pdd

nrTn

TT

nypv

yppNNE

φ

π

Ø   Azimuthal  correlaBon  with          the  reacBon  plane.    

Ø   Built  up  in  the  early  stage,          therefore  supplies  the          early  informaBon  of  maHer          generated  in  the  collision.    

Credit:  Na  Li,  25th  WWND,  2009  

( )( )rn nv Ψ−= φcos

October  28,  2013   12  

PRL 98, 162301

Strong  indica6on  for  hydrodynamic  flow!  

•  Type  II  core  collapse  supernovae  

•  Scale  107  m  

•  Neutrino-­‐driven  dynamics  

•  Stalled  shock  wave  

October  28,  2013   13  

Fryer  &  Warren,  ApJ  574,  L65  (2002  )  

•  Na6onal  Igni6on  Facility  •  Most  powerful  laser  in  the  world:  0.5  PW    (1.8  MJ/4  ns)  

October  28,  2013   14  

•  ICF  capsule  •  Scale  10-­‐5  m  

•  Livermore  hydro  codes  fail  –  Igni6on  predicted,    but  not  achieved  

October  28,  2013   15  

•  Start  from  many-­‐body  Hamiltonian  

•  Construct  density  matrix  for  many  par6cle  wave  func6on    

•  BBGKY  (Bogoliubov–Born–Green–Kirkwood–Yvon)  Hierarchy  

•  Truncate  at  some  level  n:  – Here:  truncate  at  3-­‐body  level;  3-­‐body  ma6x  =  product  of  2-­‐body  density  matrices  

October  28,  2013   16  

i∂t ΨN = H ΨN

ρN = ΨN ΨN ⇒ i∂tρN = [H,ρN ]

∂t ρn = F(ρn ,ρn+1)

ρn+1 =G(ρn )

•  Introduce  Wigner  transform:  

•  Final  result:  6me  evolu6on  equa6on  for  1-­‐body  Wigner-­‐transform,  which  contains  two-­‐body  correla6ons  

October  28,  2013   17  

f (x, p,t) ≡ 1

πψ (x + y)∫ ψ (x − y) e2ipy/dy

•  Approximate  f  by  a  sum  of  delta  func6ons  in  phase  space:  

•  Insert  this  into  integral  transport  equa6on  to  obtain  equa6ons  of  mo6on  for  6  coordinates  of  each  test  par6cle  

October  28,  2013   18  Nuclear  EOS  

Coulomb  

2-­‐body  scaeering  

•  Energy  func6onal  as  a  func6on  of  density  temperature,  momentum,  isospin,  …  

•  Not  easy!  

October  28,  2013   19  

•  Two-­‐body  cross  sec6ons  from  experiment  •  Most  accurate  method:  Distance  of  closest  approach  

–  CPU  6me  O(N2)  –  Arbitrarily  precise  shock  wave  localiza6on  [J.  Cugnon  et  al.  NPA352,  505  (1981)]  

•  Fastest  method:  Direct  SimulaBon  Monte  Carlo  –  Scaeering  grid  –  CPU  6me  O(N  log  N)  –  Causality  viola6ons  and  shock  wave  diffusion  unavoidable  [F.J.  Alexander,  A.L.  Garcia,  B.J.  Alder,  PRL  74,  5212  (1995),    G.  Kortemeyer,  F.  Daffin,WB,  PLB  374,  25  (1996)]  

•  Best  of  both  Worlds?  [I.  Sagert  et  al,  sub.  Physics  of  Fluids  (2012)]  October  28,  2013   20  

•  Point  1:  Kine6c  theory  without  collisions  (=  Vlasov)  reproduces  mean  field  theory  (=  TDHF)  

October  28,  2013   21  

JOSEPH  J.  MOLITORIS,  DETLEV  HAHN,  HORST  STÖCKER,    Prog.  Nuc.  Part.  Phys.  15,  239  (1985)  

•  Point  2:  Kine6c  theory  with  collisions  (=  VUU,  BUU,  …)  reproduces  hydro!  

October  28,  2013   22  

JOSEPH  J.  MOLITORIS,  DETLEV  HAHN,  HORST  STÖCKER,    Prog.  Nuc.  Part.  Phys.  15,  239  (1985)  

October  28,  2013   23  

JOSEPH  J.  MOLITORIS,  DETLEV  HAHN,  HORST  STÖCKER,    Prog.  Nuc.  Part.  Phys.  15,  239  (1985)  

October  28,  2013   25  

Perform scattering

Update particles'

positions and velocities

Generate particle distriubtion

Loop over all bins

Collision partner search in

neighborhood bins

Collision partner search in

neighborhood binsCollision partner search in

neighborhood bins

Populate bins

[000]

[010]

[020]

[030]

[040]

[100] [200] [300] [400]

1 1 1 2 2 2 5 5 5

1 1 1 2 2 2 5 5 5

1 1 1 2 2 2 5 5 5

3 3 3 4 4 4 6 6 6

3 3 3 4 4 4 6 6 6

Parallel neighborhood search by six CPUs

(1)

(2)

(a) (b) (c)

0

0.02

0.04

0.06

0.08

0 0.02 0.04 0.06 0.08

y

x

Collision test 1Collision test 2Collision test 3

Particle of interest

October  28,  2013   26  

0

5

10

15

20

25

30

35

0 5 10 15 20 25 30 35

Sp

eed

-up

S=

T#C

PU

/T1

Number of CPUs

(d) SimulationIdeal speed-up

•  Observables  – Bulk  velocity        

– Pressure  (=  average  of  diagonal  elements  of  stress  tensor  per  volume)        

– Density  

October  28,  2013   27  

October  28,  2013   28  

Ini6al  condi6ons:  

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Ini6al  condi6ons:  

October  28,  2013   30  

October  28,  2013   31  

Homogeneous  gas  with  uniform  radial  inward  speed  vin

(                                        dof)    

October  28,  2013   32  

1

1.5

2

2.5

3

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Den

sity

n/n

in

x

Nbin=100Nbin=150Nbin=711Analytic

2.8

2.9

3

3.1

0 0.2 0.4 0.6 0.8

October  28,  2013   33  

•  No  wall  hea6ng  •  No  causality  viola6ons  

•  No  shock  wave  diffusion  •  No  “running  ahead”  of  shock  front  

October  28,  2013   34  

Turbulent  flow  

•  Code  passes  all  standard  hydrodynamic  tests  •  (Slow)  convergence  to  analy6c  results  with  increasing  test  par6cle  number  – Typical  number  of  test  par6cles  used  in  3d  tests:    10  million  –  100  million  

•  No  physical  limit  to  precision  of  shock  wave  localiza6on  

October  28,  2013   35  

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•  Large  mean  free  path,  large  Knudsen  number  •  Sod  shock  test:  

October  28,  2013   37  

λ    =  mean  free  path  dx    =  box  size  Fs    =  “free  streaming”,  λ  infinite  

•  Large  mean  free  path,  large  Knudsen  number  •  2d  Noh  shock  test:  

October  28,  2013   38  

λ    =  mean  free  path  dx    =  box  size  Fs    =  “free  streaming”,  λ  infinite  

•  Supernova  explosion  driven  by  neutrino  shock  (?)  •  Neutrinos  cannot  be  modeled  by  hydro  

– Extremely  small  cross  sec6ons  – Very  large  Knudsen  number  

•  Kine6c  theory:  no  problem  – Can  be  calculated  in  the  same  framework  

October  28,  2013   39  

40  

•  2-­‐body  collision  terms  structurally iden6cal  to  BUU  source  term  –  Couples  transport  equa6ons  of  baryons  and  neutrinos  –  Essen6al  input:  neutrino-­‐nucleus  cross  sec6ons  (Nakamura  et  al,  ApJ  1999;  K.  Sumiyoshi  et  al,  NPA  2001,  Fröhlich  et  al,  PRL  2006,  B.A.  Brown,  …)  

October  28,  2013  

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3  free  neutrons  

•  Explicitly  represent  all  nuclei  – Many  hundreds  of  isotopes  – Lots  of  work:  reac6on  network,  weak  interac6on  cross  sec6ons  

– All  Z,A  between  drip  lines  – Ensemble  propaga6on  

– “Coupled  channels”  in  reac6on  network  

– Free  baryons  

October  28,  2013  

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•  Start  with  Woosley  &  Weaver’s  15  M¤  progenitor  

Use  for  the  first  107  years  Concentrate  on  last  0.3  seconds  

October  28,  2013  

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•  Mcore  =  1.33  M¤  •  Spherically  symmetric  

•  Radius  ≈  1000  km  

October  28,  2013  

44  

•  Single  processor  (spherical  symmetry)  •  1  million  maeer  test  par6cles  

–  385  nuclei  +  free  baryons  •  Cold  soN  BKD  nuclear  EOS  •  Weak  interac6on  network  

–  Electron  capture  (reduced  FFN  rates)  –  Neutrino-­‐maeer  interac6ons  

–  Neutrino  oscilla6ons  a  la  “MSW”  

•  No  fusion  or  photo-­‐disintegra6on  channels  included  

October  28,  2013  

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Interplay  of  macro-­‐  and  micro-­‐scales  forces  very  large  number  of  compara6vely  small  6me  steps    (c  ~  1  N/ns)    Δt  =  10-­‐5  s    =>  Mostly  boring  ini6al  6me  evolu6on  (take  1000  steps  between  frames)  

October  28,  2013  

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3%  c  

Boring  first  9000  6me  steps  are  done  Now:  Movie  

October  28,  2013  

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~0.002ρ0  

~0.2ρ0  

58  km  

October  28,  2013  

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Remnant  •  M=0.25  M¤  •  R=7.3  km  •   ρcentral  =  1.7ρ0  •   ηcentral  =  0.27  

October  28,  2013  

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•  Electron  frac6on  spike  “cuts”  the  core  in  two  –  Proto-­‐remnant  “gently”  assumes  ideal  configura6on  

–  Role  of  nuclear  EOS  totally  different  •  How  does  the  spike  form?  

–   ρ(rexp)  ~  0.002ρ0  –  Study  neutrino-­‐maeer  interac6on  probabili6es  

•  Nuclear  structure  •  Rela6vis6c  electron  gas  sta6s6cal  mechanics  

•  Essen6al  input:  neutrino  cross  sec6ons  &  nuclear  structure  (weak  neutral  current  ~  A2)  

October  28,  2013  

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t  =  0.01000  s  

Average  neutrino  interac6on  probability  

Isotope  composi6on  

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t  =  0.03000  s  

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t  =  0.05000  s  

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t  =  0.07000  s  

October  28,  2013  

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nuclear  structure  

t  =  0.09000  s  

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Free  neutrons  

t  =  0.10000  s  

October  28,  2013  

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electron  gas  degeneracy  

t  =  0.11265  s  

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t  =  0.12000  s  

October  28,  2013  

October  28,  2013   67  

P.  Sorensen  (this  mee6ng)  

•  Angular  momentum  conserva6on  

•  Baryons  fall  in  on  equator;  neutrinos  escape  along  poles  

•  Macroscopic  parity  viola6on  

•  Finite  recoil  of  neutron  start  

October  28,  2013   68  

69  

•  New  solu6on  method  for  supernova  dynamics  –  Test  par6cle  method  

–  Link  between  nuclear  dynamics  and  astrophysics  –  Passes  all  standard  hydrodynamic  verifica6on  tests  

•  New  explosion  mechanism  –  Shockwave  originates  ~  50  km  above  neutron  star  surface  

–  Due  to  neutrino  hea6ng  /  opacity  change  –  VERY  dependent  on  nuclear  structure  and  neutrino  cross  sec6ons  

October  28,  2013  

October  28,  2013   70  

Mike  Lisa:  

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NOT  YET!  

October  28,  2013   77  

RANP  4  Advisory  Board,  August  1995  

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