How long can left and How long can left and right handed life forms right handed life forms coexist? coexist? Axel Brandenburg, Anja Axel Brandenburg, Anja Andersen, Susanne H Andersen, Susanne H öfner öfner , , Martin Nilsson, Martin Nilsson, Tuomas Multam Tuomas Multam äki äki ( ( Nordita Nordita ) ) rig. Life Evol. Biosph. (in press), q-bio.BM/0401 rig. Life Evol. Biosph. (in press), q-bio.BM/04010 nt. J. Astrobio. 3, 209 (2004), also q-bio.BM/0407 nt. J. Astrobio. 3, 209 (2004), also q-bio.BM/04070
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How long can left and right handed life forms coexist?
How long can left and right handed life forms coexist?. Axel Brandenburg, Anja Andersen, Susanne H öfner , Martin Nilsson, Tuomas Multam äki ( Nordita ). Orig. Life Evol. Biosph. (in press), q-bio.BM/0401036 Int. J. Astrobio. 3, 209 (2004), also q-bio.BM/0407008. - PowerPoint PPT Presentation
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How long can left and right How long can left and right handed life forms coexist?handed life forms coexist?
Axel Brandenburg, Anja Andersen, Axel Brandenburg, Anja Andersen, Susanne HSusanne Höfneröfner, Martin Nilsson,, Martin Nilsson,
Tuomas MultamTuomas Multamäkiäki
((NorditaNordita))
Orig. Life Evol. Biosph. (in press), q-bio.BM/0401036Orig. Life Evol. Biosph. (in press), q-bio.BM/0401036Int. J. Astrobio. 3, 209 (2004), also q-bio.BM/0407008Int. J. Astrobio. 3, 209 (2004), also q-bio.BM/0407008
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Aminoacids in proteins: left-handedAminoacids in proteins: left-handedSugars in DNA and RNA: right-handedSugars in DNA and RNA: right-handed
Louis PasteurLouis Pasteur(1822-1895)(1822-1895)
animoanimogroupgroup
carboxylcarboxylgroupgroup
chlorophyllchlorophyll
Is chirality:Is chirality:(i) prerequisite(i) prerequisite
(ii) consequence(ii) consequenceof life?of life?
3
Contergan: was sold as racemic mixtureContergan: was sold as racemic mixture
Proto type: Fisher’s equationProto type: Fisher’s equation
'')1( XXXX
)( ctxfX 2c
wave speedwave speed
wwith Tuomas Multamith Tuomas Multamääki, Int. J. Astrobio. 3, 209 (2004)ki, Int. J. Astrobio. 3, 209 (2004)
Spread of the black Spread of the black deathdeath
LLRLLR
L
dt
dL
RRRLLR
R
dt
dR
222
2
222
2
)(
)(
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1D model (reaction-diffusion equation)1D model (reaction-diffusion equation)
Propagation into racemic environmentPropagation into racemic environment
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Polymerization polymerization in 1DPolymerization polymerization in 1D
chain growth, Rn and Ln in different placeschain growth, Rn and Ln in different places
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2D model (reaction-diffusion equation)2D model (reaction-diffusion equation)
short runshort runRR LL
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2D model (reaction-diffusion equation)2D model (reaction-diffusion equation)
Time scale longer than for simple frontsTime scale longer than for simple fronts
SAA
A
t
Ad
1
1
d
d
2
2
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Piecewise linear increasePiecewise linear increase
SAA
A
t
Ad
1
1
d
d
2
2
SSS 221
ASAAS
ASA 2
22
222
add/subtract:add/subtract:
LRLLR
L
dt
dL
RRLLR
R
dt
dR
)(
)(
22
2
22
2
Reduced equationsReduced equations
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Effects of turbulenceEffects of turbulence
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The Pencil CodeThe Pencil Code• History: as many versions as there are people??
– CVS maintained, 20+ people actively contributing
• High order (6th order in space, 3rd order in time)– Cache & memory efficient
• MPI, can also run PacxMPI (across countries!)– Online data processing/visualization– Ideal for linux clusters– Pencil formulation (advantages, avoiding headaches)– Automatic validation (over night or any time)– Max resolution so far 10243 , 256 procs
• Sphere embedded in box– Fully convective stars (W. Dobler), geodynamo (D. McMillan)
• Other applications and future plans– Homochirality (models of origins of life, with T. Multamäki)– Spherical coordinates
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Pencil formulationPencil formulation
• In CRAY days: worked with full chunks f(nx,ny,nz,nvar)
– Now, on SGI, nearly 100% cache misses
• Instead work with f(nx,nvar), i.e. one nx-pencil• No cache misses, negligible work space, just 2N
– Can keep all components of derivative tensors
• Communication before sub-timestep• Then evaluate all derivatives, e.g. call curl(f,iA,B)
– Vector potential A=f(:,:,:,iAx:iAz), B=B(nx,3)
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A few headachesA few headaches
• All operations must be combined– Curl(curl), max5(smooth(divu)) must be in one go– out-of-pencil exceptions possible
• rms and max values for monitoring– call max_name(b2,i_bmax,lsqrt=.true.)– call sum_name(b2,i_brms,lsqrt=.true.)
• Similar routines for toroidal average, etc• Online analysis (spectra, slices, vectors)
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CVS maintainedCVS maintained
• pserver (password protected, port 2301)– non-public (ci/co, 21 people)– public (check-out only, 127 registered users)
• Set of 15 test problems in the auto-test– Nightly auto-test (different machines, web)
• Before check-in: run auto-test yourself• Mpi and nompi dummy module for single
processor machine (or use lammpi on laptops)
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Switch modulesSwitch modules
• magnetic or nomagnetic (e.g. just hydro)• hydro or nohydro (e.g. kinematic dynamo)• density or nodensity (burgulence)• entropy or noentropy (e.g. isothermal)• radiation or noradiation (solar convection, discs)• dustvelocity or nodustvelocity (planetesimals)• Coagulation, reaction equations• Homochirality (reaction-diffusion-advection equations)
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Pencil Code check-insPencil Code check-ins
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(i) Higher order – less viscosity(i) Higher order – less viscosity
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(ii) High-order temporal schemes(ii) High-order temporal schemes
),( 111 iiiii utFtww
Main advantage: low amplitude errors
iiii wuu 1
3)1()(
0 , uuuu nn
2/1 ,1 ,3/1
1 ,3/2 ,0
321
321
1 ,2/1
2/1 ,0
21
21
1
0
1
1
3rd order
2nd order
1st order
2N-RK3 scheme (Williamson 1980)
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Bottleneck effect: Bottleneck effect: 1D vs 1D vs 3D3D spectra spectra
Compensated spectra
(1D vs 3D)
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Relation to ‘laboratory’ 1D spectraRelation to ‘laboratory’ 1D spectra2222
3 )(4)( kuku kdkE kD yxkyxkE zzD d d ),,(2)(
2
1 u
kkkkkkkzk
z d )(4d ),(42
0
2
uu
kk
E
zk
D d 3
0zk
222zkkk
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Hyperviscous, Smagorinsky, normalHyperviscous, Smagorinsky, normal
Inertial range unaffected by artificial diffusionHau
gen
& B
rand
enbu
rg (
PR
E, a
stro
-ph/
0402
301)
height of bottleneck increased
onset of bottleneck at same position
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256 processor run at 1024256 processor run at 102433
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Structure function exponentsStructure function exponents
agrees with She-Leveque third moment
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Wallclock time versus processor #
nearly linearScaling
100 Mb/s showslimitations
1 - 10 Gb/sno limitation
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Sensitivity to layout onSensitivity to layout onLinux clustersLinux clusters
yprox x zproc
4 x 32 1 (speed)
8 x 16 3 times slower
16 x 8 17 times slower
Gigabituplink 100 Mbit
link only
24 procsper hub
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Why this sensitivity to layout?
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5
6 7 8 9 0 1 2 3 4
All processors need to communicatewith processors outside to group of 24
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Use exactly 4 columns
0 1 2 3
4 5 6 7
8 9 10 11
12 13 14 15
16 17 18 19
20 21 22 23
0 1 2 3
4 5 6 7
8 9 10 11
12 13 14 15
Only 2 x 4 = 8 processors need to communicate outside the group of 24 optimal use of speed ratio between 100 Mb ethernet switch and 1 Gb uplink
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Pre-processed data for animationsPre-processed data for animations
– Based on measurable processes– Predicts wavelike chromatograms (HPLC)
• Reduction to accurate simplified model– Homochirality in space (earth, interstellar, etc)– Timescales 500 Myr; fossil evidence of spatially fragmented
homochirality?
• Pencil Code: just google for it– Detailed manual, …