188,669 research outputs found
Intrinsic universality and the computational power of self-assembly
This short survey of recent work in tile self-assembly discusses the use of
simulation to classify and separate the computational and expressive power of
self-assembly models. The journey begins with the result that there is a single
universal tile set that, with proper initialization and scaling, simulates any
tile assembly system. This universal tile set exhibits something stronger than
Turing universality: it captures the geometry and dynamics of any simulated
system. From there we find that there is no such tile set in the
noncooperative, or temperature 1, model, proving it weaker than the full tile
assembly model. In the two-handed or hierarchal model, where large assemblies
can bind together on one step, we encounter an infinite set, of infinite
hierarchies, each with strictly increasing simulation power. Towards the end of
our trip, we find one tile to rule them all: a single rotatable flipable
polygonal tile that can simulate any tile assembly system. It seems this could
be the beginning of a much longer journey, so directions for future work are
suggested.Comment: In Proceedings MCU 2013, arXiv:1309.104
Coarse-grained simulation of amphiphilic self-assembly
We present a computer simulation study of amphiphilic self assembly performed using a computationally efficient single-site model based on Gay-Berne and Lennard-Jones particles. Molecular dynamics simulations of these systems show that free self-assembly of micellar, bilayer and inverse micelle arrangements can be readily achieved for a single model parameterisation. This self-assembly is predominantly driven by the anisotropy of the amphiphile-solvent interaction, amphiphile-amphiphile interactions being found to be of secondary importance. While amphiphile concentration is the main determinant of phase stability, molecular parameters such as headgroup size and interaction strength also have measurable affects on system properties. </p
Entropy stabilizes floppy crystals of mobile DNA-coated colloids
Grafting linkers with open ends of complementary single-stranded DNA makes a
flexible tool to tune interactions between colloids,which facilitates the
design of complex self-assembly structures. Recently, it has been proposed to
coat colloids with mobile DNA linkers, which alleviates kinetic barriers
without high-density grafting, and also allows the design of valency without
patches.However, the self-assembly mechanism of this novel system is poorly
understood.Using a combination of theory and simulation, we obtain phase
diagrams forthe system in both two and three dimensional spaces, and find
stable floppy squareand CsCl crystals when the binding strength is strong, even
in the infinite bindingstrength limit. We demonstrate that these floppy phases
are stabilized by vibrational entropy, and "floppy" modes play an important
role in stabilizing the floppy phases for the infinite binding strength limit.
This special entropic effect in the self-assembly of mobile DNA-coated colloids
is very different from conventional molecular self-assembly, and it offers new
axis to help design novel functional materials using mobile DNA-coated
colloids.Comment: Accepted in Physical Review Letter
Temperature 1 Self-Assembly: Deterministic Assembly in 3D and Probabilistic Assembly in 2D
We investigate the power of the Wang tile self-assembly model at temperature
1, a threshold value that permits attachment between any two tiles that share
even a single bond. When restricted to deterministic assembly in the plane, no
temperature 1 assembly system has been shown to build a shape with a tile
complexity smaller than the diameter of the shape. In contrast, we show that
temperature 1 self-assembly in 3 dimensions, even when growth is restricted to
at most 1 step into the third dimension, is capable of simulating a large class
of temperature 2 systems, in turn permitting the simulation of arbitrary Turing
machines and the assembly of squares in near optimal
tile complexity. Further, we consider temperature 1 probabilistic assembly in
2D, and show that with a logarithmic scale up of tile complexity and shape
scale, the same general class of temperature systems can be simulated
with high probability, yielding Turing machine simulation and
assembly of squares with high probability. Our results show a sharp
contrast in achievable tile complexity at temperature 1 if either growth into
the third dimension or a small probability of error are permitted. Motivated by
applications in nanotechnology and molecular computing, and the plausibility of
implementing 3 dimensional self-assembly systems, our techniques may provide
the needed power of temperature 2 systems, while at the same time avoiding the
experimental challenges faced by those systems
Intrinsic Universality in Self-Assembly
We show that the Tile Assembly Model exhibits a strong notion of universality
where the goal is to give a single tile assembly system that simulates the
behavior of any other tile assembly system. We give a tile assembly system that
is capable of simulating a very wide class of tile systems, including itself.
Specifically, we give a tile set that simulates the assembly of any tile
assembly system in a class of systems that we call \emph{locally consistent}:
each tile binds with exactly the strength needed to stay attached, and that
there are no glue mismatches between tiles in any produced assembly.
Our construction is reminiscent of the studies of \emph{intrinsic
universality} of cellular automata by Ollinger and others, in the sense that
our simulation of a tile system by a tile system represents each tile
in an assembly produced by by a block of tiles in , where
is a constant depending on but not on the size of the assembly
produces (which may in fact be infinite). Also, our construction improves on
earlier simulations of tile assembly systems by other tile assembly systems (in
particular, those of Soloveichik and Winfree, and of Demaine et al.) in that we
simulate the actual process of self-assembly, not just the end result, as in
Soloveichik and Winfree's construction, and we do not discriminate against
infinite structures. Both previous results simulate only temperature 1 systems,
whereas our construction simulates tile assembly systems operating at
temperature 2
Self-Assembly of Nanocomponents into Composite Structures: Derivation and Simulation of Langevin Equations
The kinetics of the self-assembly of nanocomponents into a virus,
nanocapsule, or other composite structure is analyzed via a multiscale
approach. The objective is to achieve predictability and to preserve key
atomic-scale features that underlie the formation and stability of the
composite structures. We start with an all-atom description, the Liouville
equation, and the order parameters characterizing nanoscale features of the
system. An equation of Smoluchowski type for the stochastic dynamics of the
order parameters is derived from the Liouville equation via a multiscale
perturbation technique. The self-assembly of composite structures from
nanocomponents with internal atomic structure is analyzed and growth rates are
derived. Applications include the assembly of a viral capsid from capsomers, a
ribosome from its major subunits, and composite materials from fibers and
nanoparticles. Our approach overcomes errors in other coarse-graining methods
which neglect the influence of the nanoscale configuration on the atomistic
fluctuations. We account for the effect of order parameters on the statistics
of the atomistic fluctuations which contribute to the entropic and average
forces driving order parameter evolution. This approach enables an efficient
algorithm for computer simulation of self-assembly, whereas other methods
severely limit the timestep due to the separation of diffusional and complexing
characteristic times. Given that our approach does not require recalibration
with each new application, it provides a way to estimate assembly rates and
thereby facilitate the discovery of self-assembly pathways and kinetic dead-end
structures.Comment: 34 pages, 11 figure
Self-Assembled Chiral Photonic Crystals From Colloidal Helices Racemate
Chiral crystals consisting of micro-helices have many optical properties
while presently available fabrication processes limit their large-scale
applications in photonic devices. Here, by using a simplified simulation
method, we investigate a bottom-up self-assembly route to build up helical
crystals from the smectic monolayer of colloidal helices racemate. With
increasing the density, the system undergoes an entropy-driven
co-crystallization by forming crystals of various symmetries with different
helical shapes. In particular, we identify two crystals of helices arranged in
the binary honeycomb and square lattices, which are essentially composed by two
sets of opposite-handed chiral crystal. Photonic calculations show that these
chiral structures can have large complete photonic bandgaps. In addition, in
the self-assembled chiral square crystal, we also find dual polarization
bandgaps that selectively forbid the propagation of circularly polarized lights
of a specific handedness along the helical axis direction. The self-assembly
process in our proposed system is robust, suggesting possibilities of using
chiral colloids to assemble photonic metamaterials.Comment: Accepted in ACS Nan
Elements of a Theory of Simulation
Unlike computation or the numerical analysis of differential equations,
simulation does not have a well established conceptual and mathematical
foundation. Simulation is an arguable unique union of modeling and computation.
However, simulation also qualifies as a separate species of system
representation with its own motivations, characteristics, and implications.
This work outlines how simulation can be rooted in mathematics and shows which
properties some of the elements of such a mathematical framework has. The
properties of simulation are described and analyzed in terms of properties of
dynamical systems. It is shown how and why a simulation produces emergent
behavior and why the analysis of the dynamics of the system being simulated
always is an analysis of emergent phenomena. A notion of a universal simulator
and the definition of simulatability is proposed. This allows a description of
conditions under which simulations can distribute update functions over system
components, thereby determining simulatability. The connection between the
notion of simulatability and the notion of computability is defined and the
concepts are distinguished. The basis of practical detection methods for
determining effectively non-simulatable systems in practice is presented. The
conceptual framework is illustrated through examples from molecular
self-assembly end engineering.Comment: Also available via http://studguppy.tsasa.lanl.gov/research_team/
Keywords: simulatability, computability, dynamics, emergence, system
representation, universal simulato
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