Transcript Packing - University of Kansas

Development and Analysis of a
Gravity-Simulated Particle-Packing
Algorithm for Modeling Optimized
Rocket Propellants
Mark Stockmyer
October 5, 2007
Approved for public release; distribution is unlimited.
Acknowledgments
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Dr. Hossein Saiedian
Dr. Arvin Agah
Dr. Xue-Wen Chen
Dr. Travis Laker
Kristina Stockmyer
ONR – Office of Naval Research
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Outline
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Problem
Significance
Methodology/Solution
Results/Evaluation
Conclusion
Further Research
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Outline
 Problem
• Significance
• Methodology/Solution
• Results/Evaluation
• Conclusion
• Further Research
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China Lake – Naval Air Warfare Center:
Weapons Division*
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RDT&E: Research, Develop, Test, and Evaluate
*http://www.nawcwpns.navy.mil
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Energetics Development
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Energetics
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Explosives
Rocket propellant
Fuzes
Igniters
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Rocket Propellant
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Properties (Miller 1982)
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Thrust
Smoke
Exhaust signature
Heat
Burn rate
Various rocket applications
• How to optimize these properties?
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Rocket Propellant
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Currently
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(continued)
Research chemist
Think up new formulations
Test out best candidates
Problems
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Very expensive
Research community is limited
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Combinatorial Chemistry
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Computer simulation
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Input millions of random combinations
See what the results are
Used in drug synthesis (Furka 1995)
• Very difficult
• Not currently feasible for energetic materials
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More complex than drugs
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Steps to Combinatorial Chemistry
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PEP (Propellant Equilibrium Program)
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Determine internal structure of propellant
(Knott, Jackson, & Buckmaster 2001)
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Optimizing version written last year at C/L
Done, but slow
Simulate burning of the propellant
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Still in progress; very slow
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Outline
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Problem
 Significance
• Methodology/Solution
• Results/Evaluation
• Conclusion
• Further Research
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Packing: State of the Art
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Physical simulation is difficult (Agarwal 2002)
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Requires “plausible” motion
Momentum
Parallelization
In a word: Slow
CSAR (Center for Simulation of Advanced Rockets)
(Knott et al. 2001)
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Kinematic model
100,000 particles
• 64 processors
• 100 hours
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Kinematic Modeling Is Too Slow
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Assembly algorithms are faster
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Get close to modeling reality
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Place particles in best location
Final location is fixed (sticky)
Without all the slowness
Problem: Can be algorithm specific
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Too specific to be of use
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What Is a Good Simulation?*
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DOD method/modeling and simulation
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Subject matter experts
Hierarchy of indicators
Weighting of indicators
Rule-based knowledge base
*(Balci 2001)
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How Do You Measure Quality of Packing?
Speed
• Packing fraction
• Randomness
• Scalability
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Speed
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How long does it take?
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100 hours is too long
Faster the better
Target: 100,000 particles in a minute
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86,000 runs/processor/day
1 Million runs in 12 days
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Packing Fraction
How “dense” is the pack?
• Relationship between
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Volume of the particles
Volume of the empty container
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High Density Packing Example
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Medium Density Packing Example
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Low Density Packing Example
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How Dense Is Dense?
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Ball bearing experiments (McGeary 1961)
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Kilgore and Scott (1969)
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Drop a few ball bearings in graduated cylinders
Shake and vibrate
Repeat until the cylinder is full
Final packing fraction: 0.625
0.6366
Our target: 0.63
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Randomness
Difficult to measure
• Looking for patterns
• How far are particles from one specific
particle?
• RDF (Radial Distribution Function)
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Statistical tool
Can be used to measure particle relationships
Direct RDF example later
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High Density – Patterns Evident
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Scalability
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How do the properties change as the number of
particles change?
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Speed
Packing fraction
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Relation to Computer Science
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Modeling
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Abstraction of reality
Data structures
• Algorithm development
• Algorithm analysis
• Complexity analysis
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Solving a real complex problem
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Outline
Problem
• Significance
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 Methodology/Solution
• Results/Evaluation
• Conclusion
• Further Research
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How Do You Make a Rocket Motor?
(Simplified)
Get a rocket case
• Pour in propellant
• Attach exhaust
nozzle
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Image from http://www.aerospaceweb.org/
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What Does Propellant Look Like?
Molecules of
propellant
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spheres
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Image from http://www.aerospaceweb.org/
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How Do Things Fall?
Gravity
• Falling
• Collision
• How does a falling particle know where to go?
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Simple to the human eye
How do I create an algorithm to do the same thing?
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SGMP: Spin Gap Move Protocol
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Move a particle downward until there’s a
collision
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Spin - Move the particle in a circle
Gap - Find out where there’s no collision
Move - Move the particle in the direction of noncollision
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SGMP – Visualization
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Custom tool
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Particle/Primitive system (Ebert 1996)
Demonstration
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SGMP – Collision Calculations
Calculated many, many times
• Computationally expensive
• Use neighbor lists to reduce number of checks
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SGMP– Neighbor Lists*
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Find a small number of particles
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List will always contain fixed (or less) number
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The neighbors
Near the object particle
Around 10-20
A computationally expensive process
*(Torquato 2002)
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SGMP – Complexity
Specify all possible computations (Hartmanis
and Hopcroft 1971)
• Repeated steps
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Generate neighbor list
Downward drop
Circular sweep
Find largest gap
Move particle into gap
 Sweep,
Gap, and Move can be grouped
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Generate Neighbor List
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One-time complexity
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O(n)
Compare one to all the rest
Total complexity (entire pack)
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O(n2)
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Downward Drop
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One-time complexity
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O(1)
Constant drop distance
Total complexity (entire pack)
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O(n)
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Spin, Gap, and Move
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One-time complexity
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O(1)
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Remember, fixed # of particles in the neighbor list
Total complexity (entire pack)
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O(n log(n))
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n – all particles
log(n) – cross section of pack
Example
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Why log(n)?
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Outline
Problem
• Significance
• Methodology/Solution
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 Results
• Evaluation
• Conclusion
• Further Research
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SGMP Starting Arrangements
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Single Column
Small Dense
Large Dense
Loose Random
Number of particles tested
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150, 300, 750, 1002, 2001, 3000, 6000, 9000
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SGMP – Single Column
Single column of particles above control volume
• Demonstration
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Results – Single Column
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Packing fraction
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300 particles - 0.62
9000 particles - 0.60
Speed
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9000 particles
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41424 seconds (~12 hours)
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Results – Single Column
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Results – Single Column
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SGMP – Small Dense
Densely packed starting grid
• Only within the control volume
• Demonstration
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Small Dense – Results
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Packing fraction
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750 particles - 0.61
9000 particles - 0.60
Speed
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9000 particles
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56337 seconds (~15 hours)
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Small Dense -- Results
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SGMP – Large Dense
Densely packed starting grid
• Within the expanded volume
• Demonstration
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Large Dense – Results
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Packing fraction
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9000 particles - 0.59
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Other packs were very similar
Speed
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9000 particles
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19699 seconds (~5.4 hours)
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Large Dense -- Results
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SGMP – Loose Random
Loosely packed random starting grid
• Only within the control volume
• Demonstration
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Loose Random – Results
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Packing fraction
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9000 Particles - 0.59
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Other packs were very similar
Speed
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9000 particles
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456715 seconds (~5.2 days)
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Loose Random – Results
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Outline
Problem
• Significance
• Methodology/Solution
• Results
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 Evaluation
• Conclusion
• Further Research
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Evaluation – Packing Fraction
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Packing fractions
were similar
Model
Packing
Fraction
Single Column
0.62
Small Dense
0.61
Large Dense
0.59
Loose Random
0.59
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Evaluation - Speed
Wildly different completion times for the
various models. Why?
• Most steps “basically” the same
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Number of Spin, Gap, and Move cycles
Falling height very different from model to
model
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Falling Height
Model
Highest distance
Time (seconds)
Large Dense
2.1
19699
Small Dense
3.4
56337
Loose Random
21.6
456715 (5 days!)
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Demonstration
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Outline
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Problem
Significance
Methodology/Solution
Results
Evaluation
 Conclusion
• Further Research
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Packing Fraction – All
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Speed – All
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Conclusions – The Bad
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Packing fraction
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Target -- 0.63
Result -- < 0.59
Speed
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Target -- 100,00 particles in 1 minute
Result – 9,000 particles in 5 hours
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Conclusions – The Good
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Randomness
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All RDF graphs looked normal
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Outline
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Problem
Significance
Methodology/Solution
Results
Evaluation
Conclusion
 Further
Research
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Future Work
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Improve speed
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Improve packing fraction
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Better downward fall algorithm
Variable spin granularity
Higher spin granularity
Contact model (non-zero coordination number)
Algorithm additions
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Multi-modal pack (various sphere sizes)
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Requires random ‘fall’ vectors
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Presentation References
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Balci, O. (2001), ‘A methodology for certification of modeling and
simulation applications’, ACM Trans. Model. Comput. Simul. 11(4),
352–377.
Ebert, D. S. (1996), ‘Advanced modeling techniques for computer
graphics’, ACM Comput. Surv. 28(1), 153–156.
Furka, A. (1995), ‘History of combinatorial chemistry’, Drug
Development Research 36(1), 1–12.
Hartmanis, J. & Hopcroft, J. E. (1971), ‘An overview of the theory
of computational complexity’, J. ACM 18(3), 444–475.
Knott, G. M., Jackson, T. L. & Buckmaster, J. (2001), ‘The random
packing of heterogeneous propellants’, AIAA Journal 39(4), 678–
686.
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Presentation References
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(continued)
McGeary, R. K. (1961), ‘Mechanical packing of spherical particles’,
Journal of the American Ceramic Society 44(10), 513–522.
Miller, R. B. (1982), Effects of particle size on reduced smoke
propellant ballistics, in ‘AIAA/SAE/ASME 18th Joint Propulsion
Conference and Exhibit’, number AIAA-82-1096.
Torquato, S. (2002), Random heterogeneous materials:
Microstructure and macroscopic properties, 1st edn, SpringerVerlag, New York.
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End of Presentation
Thank you
• Questions are welcome
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