Difference between revisions of "Theory of incompatible substructure problem"
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== Schedule == |
== Schedule == |
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| + | * SWARM2015 paper: camera ready version submitted on 1st September, 2015. |
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| − | * 19th December, 2014 : Submit final draft of incompatible substructure paper to Marco |
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| + | * Submit extended version by December 2015. |
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| − | * 30th November, 2014 : Finish results, create plots |
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== Todo == |
== Todo == |
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| + | * Increase number of trials to 40. |
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== Parameters == |
== Parameters == |
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| Line 22: | Line 23: | ||
** Speed: 300 rpm |
** Speed: 300 rpm |
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** Duration for shaking: until stable structures are formed |
** Duration for shaking: until stable structures are formed |
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| + | |||
| + | == Variable(s) == |
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| + | * Number of components used in each experiment |
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== Experiments == |
== Experiments == |
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| + | * Simulated experiments |
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| − | * Assembly of 1 target structure |
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| − | * |
+ | ** Probability of the formation of all substructures, and all target structures for increasing number of components |
| + | * Physical experiments |
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| − | * Assembly of 3 target structures |
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| − | * |
+ | ** Probability of the formation of all substructures, and all target structures for increasing number of components |
| + | |||
| − | * Assembly of 5 target structures |
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| + | === Particulars of simulation experiments (10000 trials each) === |
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| + | * Probability of the formation of all target structures and substructures in experiments with increasing number of components from 8 - 40 |
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| − | === Particulars of experiments ( |
+ | === Particulars of physical experiments (40 trials each) === |
* Photos of initial condition and final condition |
* Photos of initial condition and final condition |
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* Assembly of one target structure |
* Assembly of one target structure |
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| Line 44: | Line 50: | ||
* Results to show |
* Results to show |
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| − | ** The simulated probability of the formation of |
+ | ** The simulated probability of the formation of all substructures and target structures in self-assembly experiments |
** Comparison of simulated probability vs. probability achieved in physical experiments |
** Comparison of simulated probability vs. probability achieved in physical experiments |
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** Reasons for similarities and/or differences between simulated probability vs. probability of physical experiments |
** Reasons for similarities and/or differences between simulated probability vs. probability of physical experiments |
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| − | == |
+ | == Open problems == |
| + | |||
| + | Using the model of Hosokawa 1995. The system starts as a set of n components. Then the following step is repeated until no longer possible: pick a random pair of structures with total size at most the size of a target structure. Combine them. The process stops when no such pair exists, i.e. when the two smallest structures have total size more than the size of a target structure. |
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| + | |||
| + | Consider a system of n components that form target structures of size k. Let f(n, k, i) be the probability that i target substructures form. |
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| + | |||
| + | * Probabilities of yields. |
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| + | ** f(n, k, 1) + f(n, k, 2) + ...: What is the probability that at least one target structure forms? |
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| + | ** f(n, k, floor(n/k)): What is the probability that the maximum number of target substructures form? |
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| + | ** f(n, k, 1) * 1 + f(n, k, 2) * 2 + ...: What is the average number of target substructures that form? |
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| + | ** General closed form for f(n, k, i): what is the probability that i substructures form for some fixed i? |
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| + | |||
| + | * Unexpected behavior. |
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| + | ** Prove that f(n, k, m) is non-increasing as a function of n. |
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| + | |||
| + | == What to include in the extended version of the paper == |
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| + | * More (40) trials |
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| + | * Details of the model |
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| + | * Geometry calculations |
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| + | * Master equation |
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| + | * More pictures |
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| + | * Video in multimedia section |
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| + | * Geometry of the parts |
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| + | |||
| + | == Meeting points == |
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| + | * In the case of the experiment where 24 components are used, if 2 target structures are formed (16 components consumed), then the third target structure will always form. This means that if the experiment is continued till the system reaches a steady state, then in the experiment with 24 components, there will never be a case where 2 target structures are formed. |
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| + | ** Doesn't this skew the probability graph? Also, how would this be reflected in the analysis? |
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| + | ** Obviously, this applies to the cases of 2, 4, 5 target structures (16, 32, 40 components) as well. |
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Latest revision as of 13:03, 7 September 2015
Schedule
- SWARM2015 paper: camera ready version submitted on 1st September, 2015.
- Submit extended version by December 2015.
Todo
- Increase number of trials to 40.
Parameters
- Components
- Radius of each component: 25 mm
- Thickness of each component: 8 mm
- Radius of magnet: 1.5 mm
- Strength of magnet: N48
- Polyamide
- Container
- Radius of container: 125 mm
- Depth of container: 9 mm
- Material: Acrylic
- Shaker
- Mode: Orbital shaking
- Speed: 300 rpm
- Duration for shaking: until stable structures are formed
Variable(s)
- Number of components used in each experiment
Experiments
- Simulated experiments
- Probability of the formation of all substructures, and all target structures for increasing number of components
- Physical experiments
- Probability of the formation of all substructures, and all target structures for increasing number of components
Particulars of simulation experiments (10000 trials each)
- Probability of the formation of all target structures and substructures in experiments with increasing number of components from 8 - 40
Particulars of physical experiments (40 trials each)
- Photos of initial condition and final condition
- Assembly of one target structure
- Data to be collected: number of targets and number of incompatible substructures, time for steady state
- Assembly of two target structures
- Data to be collected: number of targets and number of incompatible substructures, time for steady state
- Assembly of three target structures
- Data to be collected: number of targets and number of incompatible substructures, time for steady state
- Assembly of four target structures
- Data to be collected: number of targets and number of incompatible substructures, time for steady state
- Assembly of five target structures
- Data to be collected: number of targets and number of incompatible substructures, time for steady state
- Results to show
- The simulated probability of the formation of all substructures and target structures in self-assembly experiments
- Comparison of simulated probability vs. probability achieved in physical experiments
- Reasons for similarities and/or differences between simulated probability vs. probability of physical experiments
Open problems
Using the model of Hosokawa 1995. The system starts as a set of n components. Then the following step is repeated until no longer possible: pick a random pair of structures with total size at most the size of a target structure. Combine them. The process stops when no such pair exists, i.e. when the two smallest structures have total size more than the size of a target structure.
Consider a system of n components that form target structures of size k. Let f(n, k, i) be the probability that i target substructures form.
- Probabilities of yields.
- f(n, k, 1) + f(n, k, 2) + ...: What is the probability that at least one target structure forms?
- f(n, k, floor(n/k)): What is the probability that the maximum number of target substructures form?
- f(n, k, 1) * 1 + f(n, k, 2) * 2 + ...: What is the average number of target substructures that form?
- General closed form for f(n, k, i): what is the probability that i substructures form for some fixed i?
- Unexpected behavior.
- Prove that f(n, k, m) is non-increasing as a function of n.
What to include in the extended version of the paper
- More (40) trials
- Details of the model
- Geometry calculations
- Master equation
- More pictures
- Video in multimedia section
- Geometry of the parts
Meeting points
- In the case of the experiment where 24 components are used, if 2 target structures are formed (16 components consumed), then the third target structure will always form. This means that if the experiment is continued till the system reaches a steady state, then in the experiment with 24 components, there will never be a case where 2 target structures are formed.
- Doesn't this skew the probability graph? Also, how would this be reflected in the analysis?
- Obviously, this applies to the cases of 2, 4, 5 target structures (16, 32, 40 components) as well.
