https://iridia.ulb.ac.be/w/api.php?action=feedcontributions&user=Awinslow&feedformat=atomIridiaWiki - User contributions [en]2024-03-29T10:00:40ZUser contributionsMediaWiki 1.35.4https://iridia.ulb.ac.be/w/index.php?title=Theory_of_incompatible_substructure_problem&diff=7029Theory of incompatible substructure problem2014-11-27T22:31:07Z<p>Awinslow: Added some open problems.</p>
<hr />
<div>== Schedule ==<br />
* 19th December, 2014 : Submit final draft of incompatible substructure paper to Marco<br />
* 30th November, 2014 : Finish results, create plots<br />
<br />
== Todo ==<br />
<br />
== Parameters ==<br />
* Components<br />
** Radius of each component: 25 mm<br />
** Thickness of each component: '''8 mm'''<br />
** Radius of magnet: 1.5 mm<br />
** Strength of magnet: N48<br />
** Polyamide<br />
<br />
* Container<br />
** Radius of container: 125 mm<br />
** Depth of container: 9 mm<br />
** Material: Acrylic<br />
<br />
* Shaker<br />
** Mode: Orbital shaking<br />
** Speed: 300 rpm<br />
** Duration for shaking: until stable structures are formed<br />
<br />
== Variable(s) ==<br />
* Number of components used in each experiment<br />
<br />
== Experiments ==<br />
* Simulated experiments<br />
** Probability of the formation of 1, 2, 3, 4 and 5 targets for increasing number of components<br />
* Physical experiments<br />
** Probability of the formation of 1, 2, 3, 4 and 5 targets for increasing number of components<br />
<br />
=== Particulars of simulation experiments (10000 trials each) ===<br />
* Probability of the formation of 1 target structure in experiments with increasing number of components from 8 - 40<br />
* Probability of the formation of 2 target structure in experiments with increasing number of components from 16 - 40<br />
* Probability of the formation of 3 target structure in experiments with increasing number of components from 24 - 40<br />
* Probability of the formation of 4 target structure in experiments with increasing number of components from 32 - 40<br />
* Probability of the formation of 5 target structure in experiments with 40 components<br />
<br />
=== Particulars of physical experiments (10 trials each) ===<br />
* Photos of initial condition and final condition<br />
* Assembly of one target structure<br />
** Data to be collected: number of targets and number of incompatible substructures, time for steady state<br />
* Assembly of two target structures<br />
** Data to be collected: number of targets and number of incompatible substructures, time for steady state<br />
* Assembly of three target structures<br />
** Data to be collected: number of targets and number of incompatible substructures, time for steady state<br />
* Assembly of four target structures <br />
** Data to be collected: number of targets and number of incompatible substructures, time for steady state<br />
* Assembly of five target structures <br />
** Data to be collected: number of targets and number of incompatible substructures, time for steady state<br />
<br />
* Results to show<br />
** The simulated probability of the formation of 1, 2, 3, 4 and 5 target structures in self-assembly experiments<br />
** Comparison of simulated probability vs. probability achieved in physical experiments<br />
** Reasons for similarities and/or differences between simulated probability vs. probability of physical experiments<br />
<br />
== Open problems ==<br />
<br />
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.<br />
<br />
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.<br />
<br />
* Probabilities of yields. <br />
** f(n, k, 1) + f(n, k, 2) + ...: What is the probability that at least one target structure forms?<br />
** f(n, k, floor(n/k)): What is the probability that the maximum number of target substructures form?<br />
** f(n, k, 1) * 1 + f(n, k, 2) * 2 + ...: What is the average number of target substructures that form?<br />
** General closed form for f(n, k, i): what is the probability that i substructures form for some fixed i?<br />
<br />
* Unexpected behavior.<br />
** Prove that f(n, k, m) is non-increasing as a function of n.<br />
<br />
== Meeting points ==<br />
* 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. <br />
** Doesn't this skew the probability graph? Also, how would this be reflected in the analysis?<br />
** Obviously, this applies to the cases of 2, 4, 5 target structures (16, 32, 40 components) as well.</div>Awinslowhttps://iridia.ulb.ac.be/w/index.php?title=Theory_of_incompatible_substrucutre_problem&diff=7028Theory of incompatible substrucutre problem2014-11-27T22:01:58Z<p>Awinslow: Awinslow moved page Theory of incompatible substrucutre problem to Theory of incompatible substructure problem: Typo in title.</p>
<hr />
<div>#REDIRECT [[Theory of incompatible substructure problem]]</div>Awinslowhttps://iridia.ulb.ac.be/w/index.php?title=Theory_of_incompatible_substructure_problem&diff=7027Theory of incompatible substructure problem2014-11-27T22:01:58Z<p>Awinslow: Awinslow moved page Theory of incompatible substrucutre problem to Theory of incompatible substructure problem: Typo in title.</p>
<hr />
<div>== Schedule ==<br />
* 19th December, 2014 : Submit final draft of incompatible substructure paper to Marco<br />
* 30th November, 2014 : Finish results, create plots<br />
<br />
== Todo ==<br />
<br />
== Parameters ==<br />
* Components<br />
** Radius of each component: 25 mm<br />
** Thickness of each component: '''8 mm'''<br />
** Radius of magnet: 1.5 mm<br />
** Strength of magnet: N48<br />
** Polyamide<br />
<br />
* Container<br />
** Radius of container: 125 mm<br />
** Depth of container: 9 mm<br />
** Material: Acrylic<br />
<br />
* Shaker<br />
** Mode: Orbital shaking<br />
** Speed: 300 rpm<br />
** Duration for shaking: until stable structures are formed<br />
<br />
== Variable(s) ==<br />
* Number of components used in each experiment<br />
<br />
== Experiments ==<br />
* Simulated experiments<br />
** Probability of the formation of 1, 2, 3, 4 and 5 targets for increasing number of components<br />
* Physical experiments<br />
** Probability of the formation of 1, 2, 3, 4 and 5 targets for increasing number of components<br />
<br />
=== Particulars of simulation experiments (10000 trials each) ===<br />
* Probability of the formation of 1 target structure in experiments with increasing number of components from 8 - 40<br />
* Probability of the formation of 2 target structure in experiments with increasing number of components from 16 - 40<br />
* Probability of the formation of 3 target structure in experiments with increasing number of components from 24 - 40<br />
* Probability of the formation of 4 target structure in experiments with increasing number of components from 32 - 40<br />
* Probability of the formation of 5 target structure in experiments with 40 components<br />
<br />
=== Particulars of physical experiments (10 trials each) ===<br />
* Photos of initial condition and final condition<br />
* Assembly of one target structure<br />
** Data to be collected: number of targets and number of incompatible substructures, time for steady state<br />
* Assembly of two target structures<br />
** Data to be collected: number of targets and number of incompatible substructures, time for steady state<br />
* Assembly of three target structures<br />
** Data to be collected: number of targets and number of incompatible substructures, time for steady state<br />
* Assembly of four target structures <br />
** Data to be collected: number of targets and number of incompatible substructures, time for steady state<br />
* Assembly of five target structures <br />
** Data to be collected: number of targets and number of incompatible substructures, time for steady state<br />
<br />
* Results to show<br />
** The simulated probability of the formation of 1, 2, 3, 4 and 5 target structures in self-assembly experiments<br />
** Comparison of simulated probability vs. probability achieved in physical experiments<br />
** Reasons for similarities and/or differences between simulated probability vs. probability of physical experiments<br />
<br />
== Meeting points ==<br />
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 experiemnt 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 and 5 target structures as well.</div>Awinslow