53,619 research outputs found
Self-Replicating Strands that Self-Assemble into User-Specified Meshes
It has been argued that a central objective of nanotechnology is to make
products inexpensively, and that self-replication is an effective approach to
very low-cost manufacturing. The research presented here is intended to be a
step towards this vision. In previous work (JohnnyVon 1.0), we simulated
machines that bonded together to form self-replicating strands. There were two
types of machines (called types 0 and 1), which enabled strands to encode
arbitrary bit strings. However, the information encoded in the strands had no
functional role in the simulation. The information was replicated without being
interpreted, which was a significant limitation for potential manufacturing
applications. In the current work (JohnnyVon 2.0), the information in a strand
is interpreted as instructions for assembling a polygonal mesh. There are now
four types of machines and the information encoded in a strand determines how
it folds. A strand may be in an unfolded state, in which the bonds are straight
(although they flex slightly due to virtual forces acting on the machines), or
in a folded state, in which the bond angles depend on the types of machines. By
choosing the sequence of machine types in a strand, the user can specify a
variety of polygonal shapes. A simulation typically begins with an initial
unfolded seed strand in a soup of unbonded machines. The seed strand replicates
by bonding with free machines in the soup. The child strands fold into the
encoded polygonal shape, and then the polygons drift together and bond to form
a mesh. We demonstrate that a variety of polygonal meshes can be manufactured
in the simulation, by simply changing the sequence of machine types in the
seed
Bouncing Cosmologies: Progress and Problems
We review the status of bouncing cosmologies as alternatives to cosmological
inflation for providing a description of the very early universe, and a source
for the cosmological perturbations which are observed today. We focus on the
motivation for considering bouncing cosmologies, the origin of fluctuations in
these models, and the challenges which various implementations face.Comment: 30 pages, 6 figures; references adde
A Falsification View of Success Typing
Dynamic languages are praised for their flexibility and expressiveness, but
static analysis often yields many false positives and verification is
cumbersome for lack of structure. Hence, unit testing is the prevalent
incomplete method for validating programs in such languages.
Falsification is an alternative approach that uncovers definite errors in
programs. A falsifier computes a set of inputs that definitely crash a program.
Success typing is a type-based approach to document programs in dynamic
languages. We demonstrate that success typing is, in fact, an instance of
falsification by mapping success (input) types into suitable logic formulae.
Output types are represented by recursive types. We prove the correctness of
our mapping (which establishes that success typing is falsification) and we
report some experiences with a prototype implementation.Comment: extended versio
The coarsening of folds in hanging drapes
We consider the elastic energy of a hanging drape -- a thin elastic sheet,
pulled down by the force of gravity, with fine-scale folding at the top that
achieves approximately uniform confinement. This example of energy-driven
pattern formation in a thin elastic sheet is of particular interest because the
length scale of folding varies with height. We focus on how the minimum elastic
energy depends on the physical parameters. As the sheet thickness vanishes, the
limiting energy is due to the gravitational force and is relatively easy to
understand. Our main accomplishment is to identify the "scaling law" of the
correction due to positive thickness. We do this by (i) proving an upper bound,
by considering the energies of several constructions and taking the best; (ii)
proving an ansatz-free lower bound, which agrees with the upper bound up to a
parameter-independent prefactor. The coarsening of folds in hanging drapes has
also been considered in the recent physics literature, using a self-similar
construction whose basic cell has been called a "wrinklon." Our results
complement and extend that work, by showing that self-similar coarsening
achieves the optimal scaling law in a certain parameter regime, and by showing
that other constructions (involving lateral spreading of the sheet) do better
in other regions of parameter space. Our analysis uses a geometrically linear
F\"{o}ppl-von K\'{a}rm\'{a}n model for the elastic energy, and is restricted to
the case when Poisson's ratio is zero.Comment: 34 page
Self-Replication and Self-Assembly for Manufacturing
It has been argued that a central objective of nanotechnology is to make
products inexpensively, and that self-replication is an effective approach
to very low-cost manufacturing. The research presented here is intended to
be a step towards this vision. We describe a computational simulation of
nanoscale machines floating in a virtual liquid. The machines can bond
together to form strands (chains) that self-replicate and self-assemble
into user-specified meshes. There are four types of machines and the
sequence of machine types in a strand determines the shape of the mesh
they will build. A strand may be in an unfolded state, in which the bonds
are straight, or in a folded state, in which the bond angles depend on the
types of machines. By choosing the sequence of machine types in a strand,
the user can specify a variety of polygonal shapes. A simulation typically
begins with an initial unfolded seed strand in a soup of unbonded machines.
The seed strand replicates by bonding with free machines in the soup. The
child strands fold into the encoded polygonal shape, and then the polygons
drift together and bond to form a mesh. We demonstrate that a variety of
polygonal meshes can be manufactured in the simulation, by simply changing
the sequence of machine types in the seed
Large deviations and ensembles of trajectories in stochastic models
We consider ensembles of trajectories associated with large deviations of
time-integrated quantities in stochastic models. Motivated by proposals that
these ensembles are relevant for physical processes such as shearing and glassy
relaxation, we show how they can be generated directly using auxiliary
stochastic processes. We illustrate our results using the Glauber-Ising chain,
for which biased ensembles of trajectories can exhibit ferromagnetic ordering.
We discuss the relation between such biased ensembles and quantum phase
transitions.Comment: 14 pages, 1 fi
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