Difference between revisions of "Multiple Temperature Model"
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| − | The multiple temperature model is a natural generalization of the aTAM, where the temperature of a tile system is dynamically adjusted by the experimenter as self-assembly proceeds. This allows sections of assemblies that are bound with less strength to break off of the assembly whenever the temperature is raised. Aggarwal, Cheng, Goldwasser, Kao, and Schweller proved that the number of tile types required to assemble “thin” $k \times N$ rectangles can be reduced from $\Omega (\frac{N^{1/k}}{k})$ (in the aTAM) to $\Omega (\frac{log N}{log log N})$ if the temperature is allowed to change but once. Subsequently, Kao and Schweller discovered a clever “bit-flipping” scheme capable of assembling any $N \times N$ square using $O(1)$ tile types and $\Theta(log N)$ temperature changes. Note that the multiple temperature model has a similar flavor to that of the staged self-assembly model in the sense that the input to a tile system in both models can be encoded into a sequence of laboratory operations.<ref name="RTCwTemp"/> | + | The multiple temperature model is a natural generalization of the aTAM, where the temperature of a tile system is dynamically adjusted by the experimenter as self-assembly proceeds. This allows sections of assemblies that are bound with less strength to break off of the assembly whenever the temperature is raised. Aggarwal, Cheng, Goldwasser, Kao, and Schweller proved that the number of tile types required to assemble “thin” $k \times N$ rectangles can be reduced from $\Omega (\frac{N^{1/k}}{k})$ (in the aTAM) to $\Omega (\frac{log N}{log log N})$ if the temperature is allowed to change but once. Subsequently, Kao and Schweller discovered a clever “bit-flipping” scheme capable of assembling any $N \times N$ square using $O(1)$ tile types and $\Theta(log N)$ temperature changes. Note that the multiple temperature model has a similar flavor to that of the staged self-assembly model in the sense that the input to a tile system in both models can be encoded into a sequence of laboratory operations.<ref name="RTCwTemp"/> |
==References== | ==References== | ||
Revision as of 10:17, 20 July 2016
The multiple temperature model is a natural generalization of the aTAM, where the temperature of a tile system is dynamically adjusted by the experimenter as self-assembly proceeds. This allows sections of assemblies that are bound with less strength to break off of the assembly whenever the temperature is raised. Aggarwal, Cheng, Goldwasser, Kao, and Schweller proved that the number of tile types required to assemble “thin” \(k \times N\) rectangles can be reduced from \(\Omega (\frac{N^{1/k}}{k})\) (in the aTAM) to \(\Omega (\frac{log N}{log log N})\) if the temperature is allowed to change but once. Subsequently, Kao and Schweller discovered a clever “bit-flipping” scheme capable of assembling any \(N \times N\) square using \(O(1)\) tile types and \(\Theta(log N)\) temperature changes. Note that the multiple temperature model has a similar flavor to that of the staged self-assembly model in the sense that the input to a tile system in both models can be encoded into a sequence of laboratory operations.[1]
References
- ↑
Scott M. Summers - Reducing Tile Complexity for the Self-Assembly of Scaled Shapes Through Temperature Programming
