Difference between revisions of "Assembly"
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==Definition== | ==Definition== | ||
An assembly in $n$-dimensional space (most commonly taken to be $n=2$ or $n=3$) is a partial function ${\alpha}:{\mathbb{Z}^n} \dashrightarrow {T}$. | An assembly in $n$-dimensional space (most commonly taken to be $n=2$ or $n=3$) is a partial function ${\alpha}:{\mathbb{Z}^n} \dashrightarrow {T}$. | ||
| − | == | + | ==Tau-stable Assembly== |
An assembly is $\tau$-stable if it cannot be broken up into smaller assemblies without breaking bonds of total strength at least $\tau$ for some $\tau \in \mathbb{N}$. For example, in models such as the [[Abstract Tile Assembly Model (aTAM)]] and the [[Two-Handed Assembly Model (2HAM)]] all assemblies are $\tau$ stable where $\tau$ is the [[Temperature]] of the system, but in models such as the [[Kinetic Tile Assembly Model (kTAM)]] there can exist an assembly that is not $\tau$-stable. | An assembly is $\tau$-stable if it cannot be broken up into smaller assemblies without breaking bonds of total strength at least $\tau$ for some $\tau \in \mathbb{N}$. For example, in models such as the [[Abstract Tile Assembly Model (aTAM)]] and the [[Two-Handed Assembly Model (2HAM)]] all assemblies are $\tau$ stable where $\tau$ is the [[Temperature]] of the system, but in models such as the [[Kinetic Tile Assembly Model (kTAM)]] there can exist an assembly that is not $\tau$-stable. | ||
[[Category: Terminology]] | [[Category: Terminology]] | ||
Revision as of 15:13, 21 May 2013
Informal Description
An assembly generally refers to the structure created from tiles binding together.
Definition
An assembly in \(n\)-dimensional space (most commonly taken to be \(n=2\) or \(n=3\)) is a partial function \({\alpha}:{\mathbb{Z}^n} \dashrightarrow {T}\).
Tau-stable Assembly
An assembly is \(\tau\)-stable if it cannot be broken up into smaller assemblies without breaking bonds of total strength at least \(\tau\) for some \(\tau \in \mathbb{N}\). For example, in models such as the Abstract Tile Assembly Model (aTAM) and the Two-Handed Assembly Model (2HAM) all assemblies are \(\tau\) stable where \(\tau\) is the Temperature of the system, but in models such as the Kinetic Tile Assembly Model (kTAM) there can exist an assembly that is not \(\tau\)-stable.
