Predictive Modeling and Simulation ofPredictive Modeling and Simulation of the Dynamic Response of Materials at
CaltechCaltech
Michael OrtizBeijing University of Aeronautics and Astronautics (BUAA)
School of Jet PropulsionSchool of Jet Propulsion Beijing, March 14, 2011
PSAAP: Predictive Science Academic Alliance Program
Michael OrtizBUAA 3/14/11 - 1
Caltech & Jet Propulsion Lab (JPL)
PSAAP: Predictive Science Academic Alliance Program
Michael OrtizBUAA 3/14/11 - 2
DoE - ASC/PSAAP Centers
PSAAP: Predictive Science Academic Alliance Program
Michael OrtizBUAA 3/14/11 - 3
Overarching objectives – QMU
• Aim: Quantify performance Margin & Uncertainty (QMU) in the behavior of complex physical/engineered systems
• Example: Short-term weather prediction,– Old: Prediction that tomorrow will rain in Beijing…
New: Guarantee same with 99% confidence– New: Guarantee same with 99% confidence…
• QMU is important for achieving confidence in high-consequence decisions, designs (e.g., aircraft safety)
• Paradigm shift in experimental science, modeling and simulation, scientific computing (predictive science):
Deterministic Non deterministic systems– Deterministic → Non-deterministic systems– Mean performance → Mean performance + uncertainties– Tight integration of experiments, theory and simulation
PSAAP: Predictive Science Academic Alliance Program
– Robust design: Design systems to minimize uncertainty– Resource allocation: Eliminate main uncertainty sources Michael Ortiz
BUAA 3/14/11- 4
Application: Hypervelocity impact
Challenge: Predict hypervelocity impact phenomena (10Km/s ) with quantified margins and uncertainties
NASA Ames Research Center E fl h f h l it t tEnergy flash from hypervelocity test
at 7.9 Km/s
PSAAP: Predictive Science Academic Alliance Program
Hypervelocity impact test bumper shield(Ernst-Mach Institut, Freiburg Germany)
Michael OrtizBUAA 3/14/11- 5
Annual UQ campaigns
April 15 2008
UQ campaign timelineTarget Ballistic (SBGG)April 15, 2008
Center startsPlate
Ballistic (SBGG)
•Aluminum plates•Steel impactor (50g)•Thickness: 0.125-0.5”
Target Plate
Ballistic (SPHIR)
•Steel/Ta plates
Target Plate
Hypervelocity (SPHIR)
•Aluminum plates
•Velocity: 0.4-1 Km/s
Target Plate
Ballistic (SPHIR)
•Aluminum plates•Steel/Ta plates•Steel impactor•Thick.: 50-105 mils•Obliquity: 0-30°
•Aluminum plates•Nylon impactor•Thick.: 10-105 mils•Obliquity: 0-80°
•Aluminum plates•Steel impactor•Thick.: 50-105 mils•Obliquity: 0-30°
Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q1Q1 Q2 Q3 Q4 Q1 Q2 QQ4
•Velocity: 2-3 Km/s •Velocity: 3-10 Km/s•Velocity: 2-3 Km/s
PSAAP: Predictive Science Academic Alliance Program
Michael OrtizBUAA 3/14/11 - 6
Hypervelocity impact as system
performance measures:
response function(black box)
system inputs: measures:(black box)inputs:
• Random • Observablesvariables
• Known or k df
• Observables• Subject to
performance unknown pdfs
• Controllable• Uncontrollable
specifications• Random (due to
randomness in• Uncontrollable• Unknown-
unknowns (Z)
randomness in inputs, system)
• Noisy (unknown Probability of
PSAAP: Predictive Science Academic Alliance Program
Michael OrtizBUAA 3/14/11- 7
unknowns)y
Failure?
Center’s assets
Experimental Science Simulation codes
SPHIRPhysics models UQ tools
VTF EurekaHSRTPhysics models UQ tools
PSAAP: Predictive Science Academic Alliance Program
Michael OrtizBUAA 3/14/11 - 8
Plasma/EoS Probability/CoM UQ pipelineStrength
Center’s assets
Experimental Science Simulation codes
SPHIRPhysics models UQ tools
VTF EurekaHSRTPhysics models UQ tools
PSAAP: Predictive Science Academic Alliance Program
Michael OrtizBUAA 3/14/11 - 9
Plasma/EoS Probability/CoM UQ pipelineStrength
Hypervelocity impact at Caltech
PSAAP: Predictive Science Academic Alliance Program
Michael OrtizBUAA 3/14/11- 10
Caltech’s Small Particle Hypervelocity Impact Range facility(Prof. A.J. Rosakis, Director)
Hypervelocity impact at Caltech
BREECH PUMP TUBE
LAUNCH TUBE
FLIGHT TUBE
TARGET TANK
Front Spall Cloud
Debris Cloud
Witness Plate
STAGE 1 STAGE 2
Impactor
TargetWitness Plate
aluminum witness plates replaced by capture media
Target Materials•SteelAluminum Ø 71 mil (1x10-3 in)
by capture media
• Impact Speeds: 2 to 10 km/sI t Obli iti 0 t 80 d
•Aluminum•Tantalum
Impactor Materials•Steel
Ø 71 mil (1x10 3 in) launch tube bore
PSAAP: Predictive Science Academic Alliance Program 11
• Impact Obliquities: 0 to 80 degrees• Impactor Mass: 1 to 50 mg
Steel•Nylon
Michael OrtizBUAA 3/14/11- 11
SPHIR – A reconfigurable facility
A il 15 2008
SPHIR configuration timeline
April 15, 2008
Center starts
Target Ballistic impactTarget Plate
Hypervel. impact
•Al/Steel multi platesPlatea s c pac
•Steel/Al plates•Steel/nylon impactor
•Al/Steel multi-plates•nylon impactor
Target Hypervel. impactTarget Plate
Ballistic impact
•Steel plates•Steel impactor
Target Plate
Ballistic/Hypervel.
•Al plates•Steel/nylon impactor
Plateype e pact
•Al/Steel/Ta bi-plates•nylon impactor•Soft-gel capture
Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q1Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q1Q4 Q1 Q2 Q3 Q4Q4
PSAAP: Predictive Science Academic Alliance Program
Michael OrtizBUAA 3/14/11 - 12
Hypervelocity impact at Caltech
April 15 2008
Diagnostic deployment timeline
VelocimetryApril 15, 2008
Center starts
Perforation areaProfilometry
Optimet
Velocimetry
Valyn Multi-Beam VISAR
Real-time CGSFull-field
surface slopesPerforation area
Olympus SZ61 Microscope
OptimetMiniConoscan
3000
surface slopes
Backlighting
Real time
Spectrometry
Real-time
Z
YX
Real-time shadowgraph
imagingspectra
Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q1Q1 Q2 Q3 Q4 Q1 Q2 QQ4
Y
PSAAP: Predictive Science Academic Alliance Program
Michael OrtizBUAA 3/14/11- 13
SPHIR – Inputs and Metrics
System Outputs (Y)System inputs (X)
Diagnostics
Conoscope
MetricsProfilometry
Perforation area Slope
Projectile velocity
Projectile mass Conoscope
Backlighting shadowgraph
Perforation area, Slope Contour Area
Real-time back-surface bulge and ejecta/debris
cloud formation
Projectile mass
Number of target plates shadowgraph
VISAR
cloud formation
Real-time, back-surface velocimetry
R l ti f ll fi ld
plates
Plate thicknesses
CGS
Spectro-
Real-time, full-field back-surface deformation
Impact flash, debris and spall clouds spectra
Plate obliquities
Projectile/plate
PSAAP: Predictive Science Academic Alliance Program
Michael Ortiz
pphotometer spall clouds, spectra
over IR to UV range
j pmaterials
BUAA 3/14/11- 14
SPHIR - Sample data
• Added challenges:– Experimental
!10
11
12
Plot assumes average of obliquities (a) for all targets tested of a given thickness (h)
Vbl = Ho*( h/Dp)^n / (cos a)^sA = if V<Vbl, 0, K*Dp^2 * {(h/Dp)^p} * {[cos(a)]^u} * {tanh[(V/Vbl)-1]}^m
A = perforation area (mm^2)) scatter!– Impact velocity
uncontrollable!7
8
9
ea (m
m)
A = perforation area (mm 2)h = target thickness (mm)a = imapct obliquity (rad)V = impact speed (km/s)Dp = imactor diameter (mm)Ho, K, n, s, p, u, m are curve fit parametersre
a (m
m2 )
Distribution of Speeds Obtained
0 8
0.9
1
peed
Fit Errors: Uniform = 0.32 Gaussian = 0.08
GaussianMean = 2.49StDev = 0.25
Measured speed distribution
bilit
y
4
5
6
Perfo
ratio
n A
re
1.9mm Data
2.3mm Data
2 6mm Datarfora
tion
a
0.4
0.5
0.6
0.7
0.8
roba
bilit
y of
Low
er S
pat
ive
prob
ab
1
2
32.6mm Data
1.9mm Model
2.3mm Model
2.6mm Model
Impactor area
Per
0
0.1
0.2
0.3
0.4
Cum
ulat
ive
PrC
umul
a
01.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3
Impact Speed (km/s)Impact speed (km/s)Experimental ballistic curves (SPHIR)
PSAAP: Predictive Science Academic Alliance Program
Michael OrtizBUAA 3/14/11- 15
1.6 1.8 2 2.2 2.4 2.6 2.8 3
Impact Speed (km/sImpact speed (km/s)Experimental ballistic curves (SPHIR)
440 C Steel spherical projectiles304 Stainless Steel plate targets
Ballistic impact – GALCIT Small Bore Gas Gun (SBGG) facility( ) y
Barrel Pressure Gun
Light detectorsdetectors(velocity )
Data recorder LeCroy
PSAAP: Predictive Science Academic Alliance Program
Michael OrtizBUAA 3/14/11- 16
Caltech’s Small Bore Gas Gun (SBGG) facility(Prof. G. Ravichandran, Director)
Ballistic impact – SBGG
System inputs (X) System Outputs (Y)
Projectile velocity
Plate thickness
Diagnostics
Conoscope
MetricsProfilometry Plate thickness
Projectile/plate materials
Conoscope yPerforation area
materials
PSAAP: Predictive Science Academic Alliance Program
Michael OrtizBUAA 3/14/11- 17
Ballistic impact - Sample data
350
400
m/s)
50
60
2)
200
250
300
not perforated
perforated
Velocity
(m
30
40
d area
(mm
2
32 milli‐inch
40 milli‐inchOptimet
MiniConoscan
100
150
200
Projectile
0
10
20
Perforated 50 milli‐inch
63 milli‐inch
MiniConoscan3000
30 40 50 60 70Plate thickness (milli‐inch)
0 100 200 300 400
Impact Velocity (m/s)
Perforation area vs impact velocity Perforation/non perforationPerforation area vs. impact velocity(note small data scatter!)
Perforation/non-perforationboundary
Experimental ballistic curves (SBGG)
PSAAP: Predictive Science Academic Alliance Program
Michael Ortiz
p ( )S2 Steel spherical projectiles
Al 6061 plate targetsBUAA 3/14/11- 18
High Strain-Rate Testing (HSRT)
1 2(1 )peq eq
Pk kDt
d
Stress:
3peq
dkh
Strain:
S li H ki
Shear Compression Specimen (SCS)
Split Hokinson (Kolsky) pressure bar
Strength Dissipation
Measure )t(and)t(),t(
p
Full field imaging
PSAAP: Predictive Science Academic Alliance Program
Michael Ortiz
Full-field imaging,Sub-grain resolution
BUAA 3/14/11- 19
Caltech’s High Strain-Rate Testing (HSRT) facility(Prof. G. Ravichandran, Director)
Conventional validation - Examples
Shear compression specimen Power-law work hardening
Pa)
Pa)
Power-law strain-rate sensitivity
Stre
ss (M
P
Stre
ss (M
P
ent S
hear
S
ent S
hear
S
Equ
ival
e
Equ
ival
e
M. Vural, D. Rittel and G. Ravichandran, “Large strain mechanical behavior of 1018 cold rolled steel over a wide range of strain rates ”
Equivalent Shear Strain Equivalent Shear Strain
PSAAP: Predictive Science Academic Alliance Program
behavior of 1018 cold-rolled steel over a wide range of strain rates, Metallurgical and Materials Transactions A, Vol. 34A (2003) p. 2873.
Michael OrtizBUAA 3/14/11 - 20
Conventional validation - Examples
Power-law strain-rate sensitivity
)re
ss (M
Pa Experimental
Model
She
ar S
trE
quiv
alen
t E
Equivalent Shear Strain Rate (1/s)
PSAAP: Predictive Science Academic Alliance Program
M. Vural, D. Rittel and G. Ravichandran, “Large strain mechanical behavior of 1018 cold-rolled steel over a wide range of strain rates,” Metallurgical and Materials Transactions A, Vol. 34A (2003) p. 2873. Michael Ortiz
BUAA 3/14/11 - 21
High Strain-Rate Testing (HSRT)
250Incident Shock
Ideal Mach State
Al Impactor at 1 km/s
Al Impactor at 2 km/s
Tantalum Hugoniot
Us2 > Us1
Reflected Shocksteel
200
Simulated Mach StateTa Impactor at 1 km/s
Ta Impactor at 2 km/sUs1
Mach
Mach Disk
150
P (G
Pa) 3.1x
(4.7 km/s)
Mach Stem
Impactorp (G
Pa) steel
50
100
P
3.6x(2.9 km/s)
4x(5 5 k / )
Al Impactor at 1 km/s
Al Impactor at 2 km/s
Mach-Lens Test
p
0
50
4.5x(3.4 km/s)
(2.9 km/s)(5.5 km/s)
Ta Impactor at 1 km/s
Ta Impactor at 2 km/s
Al Impactor at 2 km/s
PSAAP: Predictive Science Academic Alliance Program
Michael Ortiz
0 0.5 1 1.5 2 2.5
Up (km/s)Up (km/s)BUAA 3/14/11- 22
Experimental data at Caltech
• The Caltech center has its own in-house experimental facilities:– Small Particle Hypervelocity Impact Range– Small Bore Gas Gun Facility (ballistics)– High-Strain Rate Facility (constitutive characterization)High Strain Rate Facility (constitutive characterization)
• Experimental facilities are reconfigurable and may be regarded as black boxes mapping inputs to outputs
• Experimental facilities supply specific instances of systems to be modeled, tested and certified
• Experimental facilities supply data in for purposes of• Experimental facilities supply data in for purposes of Uncertainty Quantification– Integral ‘data on demand’ at fixed inputs
PSAAP: Predictive Science Academic Alliance Program
Michael OrtizBUAA 3/14/11- 23
– Integral legacy data (by accumulation)– Component data (e.g., constitutive data)
Center’s assets
Experimental Science Simulation codes
SPHIRPhysics models UQ tools
VTF EurekaHSRTPhysics models UQ tools
PSAAP: Predictive Science Academic Alliance Program
Michael OrtizBUAA 3/14/11 - 24
Plasma/EoS Probability/CoM UQ pipelineStrength
Focus simulation - Roadmap
Simulation roadmapTargetE k OTMTargetL i VTF TargetE l i VTFA il 15 2008
TargetABAQUS Explicit
Target Plate
Eureka OTM
•Update-Lagrange•Optimal transport•Meshfree/MPM
Target Plate
Lagrangian VTF
•Lagrangian FEM•Explicit dynamics•Proxy ball contact
Target Plate
Eulerian VTF
•Eulerian AMR•FD/WENO•EoS/strength
April 15, 2008
Center starts
Target Plate
ABAQUS Explicit
•Lagrangian FEM•Explicit dynamics•Explicit contact
•Meshfree/MPM•Variational dyns•Seizing contact•Erosion/fracture
•Proxy-ball contact•Element erosion•Engr. Models/EoS•Massively parallel
•EoS/strength•Multiphase/BC•Ghost fluid•Massive parallelExplicit contact
•Element erosion•Engr. Models•Serial
•Multiscale models
Serial Parallel
Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q1Q1 Q2 Q3 Q4 Q1 Q2 QQ4
PSAAP: Predictive Science Academic Alliance Program
Michael OrtizBUAA 3/14/11 - 25
Center’s assets
Experimental Science Simulation codes
SPHIRPhysics models UQ tools
VTF EurekaHSRTPhysics models UQ tools
PSAAP: Predictive Science Academic Alliance Program
Michael OrtizBUAA 3/14/11 - 28
Plasma/EoS Probability/CoM UQ pipelineStrength
Multiscale models - Strength
Full-scalecalculations
ms
calculationsDirect numerical simulation of polycrystals, effective models
µs
Subgrain structures:Hall-Petch scaling,martensite…
Dislocation dynamics: Forest hardening, cross slip…
ns
MD: Core energies, kink mobilities…
QM: Multiphase EoS, transport, plasma…
PSAAP: Predictive Science Academic Alliance Program
Michael OrtizBUAA 3/14/11 - 29
mmnm µm
n QM: Multiphase EoS, transport, plasma…
Multiscale Modeling - Strength
Ballistic impact
Polycrystalplasticity
Void-growth
Single-crystal
plasticity
Equilibrium properties Dissipation
EoS Elastic moduli Viscosity Hardening
PSAAP: Predictive Science Academic Alliance Program
Michael Ortiz
Heat capacity
Rate sensitivity
BUAA 3/14/11 - 30
Multiscale Modeling - EoS
Ballistic impact
Polycrystalplasticity
Void-growth
Single-crystal
plasticity
Equilibrium properties Dissipation
EoS Elastic moduli Viscosity Hardening
PSAAP: Predictive Science Academic Alliance Program
Michael Ortiz
Heat capacity
Rate sensitivity
BUAA 3/14/11 - 31
Multiscale Modeling – Computed EoS
bcc
a
bcc Fe hcp
GP
a
Pressure (GPa)
100
12050 500
A)
20
40
60
80
100
0K 250K500K
10
20
30
40
P(G
Pa)
2000 K200
300
400
P(G
Pa)
bcc Fe
hcp Fe bcc V
ssur
e (G
PA
0.7 0.8 0.9 1.0 1.1 1.2-40
-20
0
20
V/V0
500K 1000K 1500K 2000K 2500K 3000K
0.90 0.95 1.00 1.05 1.10 1.15 1.20
-20
-10
0
0 K
V/V0
2000 K
40 45 50 55 60 65 70 75 80
0
100
0 K
V (bohr3)
3000 KPre
s
Volume Volume Volume
PSAAP: Predictive Science Academic Alliance Program
Michael Ortiz
0( )Volume Volume VolumeFirst-principles EoS, heat capacity, elastic moduli
(Wasserman, Stixrude and Cohen, PRB 53, 8296, 1996)BUAA 3/14/11 - 32
Multiscale Modeling - Viscosity
Ballistic impact
Polycrystalplasticity
Void-growth
Single-crystal
plasticity
Equilibrium properties Dissipation
EoS Elastic moduli Viscosity Hardening
Viscosity vs (p,T) for liquid Ta,
PSAAP: Predictive Science Academic Alliance Program
Michael Ortiz
Heat capacity
Rate sensitivity
y (p ) qFe, from shear stress autocorr. function (Axel van de Walle)
BUAA 3/14/11 - 33
Multiscale Modeling - Transport
Ballistic impact
Polycrystalplasticity
Void-growth
Single-crystal
plasticity
Equilibrium properties Dissipation
EoS Elastic moduli Viscosity Hardening
PSAAP: Predictive Science Academic Alliance Program
Michael Ortiz
Heat capacity
Rate sensitivity
BUAA 3/14/11 - 34
Multiscale Modeling – Rate sensitivity
1/2<111> screw dislocation1/2<111> screw dislocationSingle Kinks (<112> kink)Kink
Negative core (n)Positive core (p)Positive core (p)
• From kink dynamics (MD): – Formation energies– Migration energy barriers
• From thermal activation theory:
PSAAP: Predictive Science Academic Alliance Program
Michael Ortiz
– Dislocation mobility– Rate sensitivity
BUAA 3/14/11 - 35
Multiscale Modeling - Hardening
Ballistic impact
Polycrystalplasticity
Void-growth
Single-crystal
plasticity
Equilibrium properties Dissipation
EoS Elastic moduli Viscosity Hardening
PSAAP: Predictive Science Academic Alliance Program
Michael Ortiz
Heat capacity
Rate sensitivity
BUAA 3/14/11 - 36
Multiscale Modeling – Hardening
Ta
• From dislocation dynamics:From dislocation dynamics: – Anisotropic line tension– Secondary dislocations– Dislocation multiplication
PSAAP: Predictive Science Academic Alliance Program
Michael Ortiz
• Percolation analysis (Kocks):– Hardening relations (analytical)
BUAA 3/14/11 - 37
Multiscale models – Ductile fracture
Material point erosion:Fracture & fragmentation
ms
Space-filling hollow spheres:Void growth & coalescence
Fracture & fragmentation
µs Q i ti
Void growth & coalescence
Quasicontinuum: Nanovoid cavitation
ns
QM: Vacancies, binding & migration energies
KMC: Nanovoid nucleation rates
PSAAP: Predictive Science Academic Alliance Program
Michael OrtizBUAA 3/14/11 - 38
38mmnm µm
g g g
Multiscale Modeling – Fracture (FE2)
Ballistic impact
Polycrystalplasticity
Void-growth
Single-crystal
Void nucleation(not implemented)
plasticity
Equilibrium properties Dissipation
EoS Elastic moduli Viscosity Hardening
PSAAP: Predictive Science Academic Alliance Program
Michael Ortiz
Heat capacity
Rate sensitivity
BUAA 3/14/11 - 39
Multiscale Modeling - Polycrystal
Ballistic impact
Polycrystalplasticity
Void-growth
Single-crystal
plasticity
Equilibrium properties Dissipation
EoS Elastic moduli Viscosity Hardening
PSAAP: Predictive Science Academic Alliance Program
Michael Ortiz
Heat capacity
Rate sensitivity
BUAA 3/14/11 - 40
Multiscale Modeling - Polycrystal
• Multiscale models integrated into full-scale simulations!
OTM i l ti h h t i l i t C li d t iki
PSAAP: Predictive Science Academic Alliance Program
OTM simulation where each material point represents a randomly oriented crystal
Copper cylinder striking frictionless rigid wall at 227m/s
Michael OrtizBUAA 3/14/11 - 41
Center’s assets
Experimental Science Simulation codes
SPHIRPhysics models UQ tools
VTF EurekaHSRTPhysics models UQ tools
PSAAP: Predictive Science Academic Alliance Program
Michael OrtizBUAA 3/14/11 - 42
Plasma/EoS Probability/CoM UQ pipelineStrength
Development of UQ methodology
April 15 2008
UQ methodology timelineApril 15, 2008
Center starts
Data on Demand Data on Demand Legacy DataData-on-DemandProtocol (I)
McDiarmidInequality
Data-on-DemandProtocol (II)
McDiarmidinequality
Legacy-DataProtocol
McDiarmidinequalityInequality
Noiseless dataControllable
inputs
inequalityNoisy data
Uncontrollable inputs
inequalityLipschitzconstantsNoisy data
Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q1Q1 Q2 Q3 Q4 Q1 Q2 QQ4
PSAAP: Predictive Science Academic Alliance Program
Michael OrtizBUAA 3/14/11 - 43
The data-on-Demand UQ protocol
ModelinggError
SystemUncertainty
PSAAP: Predictive Science Academic Alliance Program
The Annual Assessment CycleMichael Ortiz
BUAA 3/14/11 - 44
The data-on-Demand UQ Protocol
UQ
Modeling d
ExperimentalS i
PSAAP: Predictive Science Academic Alliance Program
Michael OrtizBUAA 3/14/11- 45
andSimulation
Science
Tightly-integrated simulations and experiments!
Caltech’s UQ pipeline - CSE OTMEffort led by Caltech’s
Center for AdvancedComputing Research
Challenge: Develop Computational Scienceand Engineering (CSE) i f t t f t i t
Mystic optimizer SPHIR
infrastructure for uncertainty quantification (UQ) analysis.
Mystic optimizer SPHIR
PSAAP: Predictive Science Academic Alliance Program
Michael OrtizLANL’s coyoteBUAA 3/14/11 - 46
UQ orchestrates all activities
Computational Fluid
D iDynamics
Computational Science and E i i
Probability and Statistics Engineeringand Statistics
UQExperimental
ScienceMaterials
Models and
UQScience
Computational Solid
Properties
PSAAP: Predictive Science Academic Alliance Program
Michael Ortiz
Dynamics
BUAA 3/14/11 - 47
Our vision for Predictive Science…
A Walk through PS Evolution must lid t
mustcertifyA Walk through PS Evolution
must computefast, big…
must havephysics…
validate… certify…
g p y
circa 1995 circa 1998 circa 2002
• QMU is the next logical step in the evolution of PS• Articulating QMU in precise, rigorous and quantitative
terms is a grand challenge of our time!
PSAAP: Predictive Science Academic Alliance Program
terms is a grand challenge of our time!Michael Ortiz
BUAA 3/14/11 - 48