https://iridia.ulb.ac.be/w/index.php?title=Study_of_yield_predictions_of_a_self-assembling_system_-_extended&feed=atom&action=historyStudy of yield predictions of a self-assembling system - extended - Revision history2024-03-29T13:47:20ZRevision history for this page on the wikiMediaWiki 1.35.4https://iridia.ulb.ac.be/w/index.php?title=Study_of_yield_predictions_of_a_self-assembling_system_-_extended&diff=7212&oldid=prevDj: /* Todo */2016-04-20T14:40:21Z<p><span dir="auto"><span class="autocomment">Todo</span></span></p>
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</table>Djhttps://iridia.ulb.ac.be/w/index.php?title=Study_of_yield_predictions_of_a_self-assembling_system_-_extended&diff=7211&oldid=prevDj: /* Schedule */2016-04-20T14:39:59Z<p><span dir="auto"><span class="autocomment">Schedule</span></span></p>
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</table>Djhttps://iridia.ulb.ac.be/w/index.php?title=Study_of_yield_predictions_of_a_self-assembling_system_-_extended&diff=7177&oldid=prevDj: Created page with "== Schedule == * SWARM2015 paper: camera ready version submitted on 1st September, 2015. * Submit extended version by December 2015. == Todo == * Increase number of trials ..."2015-11-03T14:04:42Z<p>Created page with "== Schedule == * SWARM2015 paper: camera ready version submitted on 1st September, 2015. * Submit extended version by December 2015. == Todo == * Increase number of trials ..."</p>
<p><b>New page</b></p><div>== Schedule ==<br />
* SWARM2015 paper: camera ready version submitted on 1st September, 2015.<br />
* Submit extended version by December 2015.<br />
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== Todo ==<br />
* Increase number of trials to 40.<br />
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== 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 all substructures, and all target structures for increasing number of components<br />
* Physical experiments<br />
** Probability of the formation of all substructures, and all target structures for increasing number of components<br />
<br />
=== Particulars of simulation experiments (10000 trials each) ===<br />
* Probability of the formation of all target structures and substructures in experiments with increasing number of components from 8 - 40<br />
<br />
=== Particulars of physical experiments (40 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 all substructures and 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 />
== What to include in the extended version of the paper ==<br />
* More (40) trials<br />
* Details of the model<br />
* Geometry calculations<br />
* Master equation<br />
* More pictures<br />
* Video in multimedia section<br />
* Geometry of the parts<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>Dj