Difference between revisions of "Theory of incompatible substructure problem"

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== Schedule ==
  
== Schedule ==
  +
* SWARM2015 paper: camera ready version submitted on 1st September, 2015.
−
* 19th December, 2014 : Submit final draft of incompatible substructure paper to Marco
  
  +
* Submit extended version by December 2015.
−
* 30th November, 2014 : Finish results, create plots
  
   
 
== Todo ==
  
== Todo ==
  +
* Increase number of trials to 40.
   
 
== Parameters ==
  
== Parameters ==
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== Experiments ==
  
== Experiments ==
 
* Simulated experiments
  
* Simulated experiments
−
** Probability of the formation of 1, 2, 3, 4 and 5 targets for increasing number of components
 +
** Probability of the formation of all substructures, and all target structures for increasing number of components
 
* Physical experiments
  
* Physical experiments
−
** Probability of the formation of 1, 2, 3, 4 and 5 targets for increasing number of components
 +
** Probability of the formation of all substructures, and all target structures for increasing number of components
   
−
=== Particulars of physical experiments (10000 trials each) ===
 +
=== Particulars of simulation experiments (10000 trials each) ===
−
* Probability of the formation of 1 target structure in experiments with increasing number of components from 8 - 40
 +
* Probability of the formation of all target structures and substructures in experiments with increasing number of components from 8 - 40
−
* Probability of the formation of 2 target structure in experiments with increasing number of components from 16 - 40
  
−
* Probability of the formation of 3 target structure in experiments with increasing number of components from 24 - 40
  
−
* Probability of the formation of 4 target structure in experiments with increasing number of components from 32 - 40
  
−
* Probability of the formation of 5 target structure in experiments with 40 components
  
   
−
=== Particulars of physical experiments (10 trials each) ===
 +
=== Particulars of physical experiments (40 trials each) ===
 
* Photos of initial condition and final condition
  
* Photos of initial condition and final condition
 
* Assembly of one target structure
  
* Assembly of one target structure
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* Results to show
  
* Results to show
−
** The simulated probability of the formation of 1, 2, 3, 4 and 5 target structures in self-assembly experiments
 +
** 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
 
** 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
  +
  +
== 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 ==
  
== 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. '''How would this be reflected in the plots? '''
 +
* 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.

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.
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