6,996 research outputs found
Identification of the transition rule in a modified cellular automata model: the case of dendritic NH4Br crystal growth
A method of identifying the transition rule, encapsulated in a modified cellular automata (CA) model, is demonstrated using experimentally observed evolution of dendritic crystal growth patterns in NH4Br crystals. The influence of the factors, such as experimental set-up and image pre-processing, colour and size calibrations, on the method of identification are discussed in detail. A noise reduction parameter and the diffusion velocity of the crystal boundary are also considered. The results show that the proposed method can in principle provide a good representation of the dendritic growth anisotropy of any system
Lattice Gauge Tensor Networks
We present a unified framework to describe lattice gauge theories by means of
tensor networks: this framework is efficient as it exploits the high amount of
local symmetry content native of these systems describing only the gauge
invariant subspace. Compared to a standard tensor network description, the
gauge invariant one allows to speed-up real and imaginary time evolution of a
factor that is up to the square of the dimension of the link variable. The
gauge invariant tensor network description is based on the quantum link
formulation, a compact and intuitive formulation for gauge theories on the
lattice, and it is alternative to and can be combined with the global symmetric
tensor network description. We present some paradigmatic examples that show how
this architecture might be used to describe the physics of condensed matter and
high-energy physics systems. Finally, we present a cellular automata analysis
which estimates the gauge invariant Hilbert space dimension as a function of
the number of lattice sites and that might guide the search for effective
simplified models of complex theories.Comment: 28 pages, 9 figure
A Quantum Game of Life
This research describes a three dimensional quantum cellular automaton (QCA)
which can simulate all other 3D QCA. This intrinsically universal QCA belongs
to the simplest subclass of QCA: Partitioned QCA (PQCA). PQCA are QCA of a
particular form, where incoming information is scattered by a fixed unitary U
before being redistributed and rescattered. Our construction is minimal amongst
PQCA, having block size 2 x 2 x 2 and cell dimension 2. Signals, wires and
gates emerge in an elegant fashion.Comment: 13 pages, 10 figures. Final version, accepted by Journ\'ees Automates
Cellulaires (JAC 2010)
Upper Bound on the Products of Particle Interactions in Cellular Automata
Particle-like objects are observed to propagate and interact in many
spatially extended dynamical systems. For one of the simplest classes of such
systems, one-dimensional cellular automata, we establish a rigorous upper bound
on the number of distinct products that these interactions can generate. The
upper bound is controlled by the structural complexity of the interacting
particles---a quantity which is defined here and which measures the amount of
spatio-temporal information that a particle stores. Along the way we establish
a number of properties of domains and particles that follow from the
computational mechanics analysis of cellular automata; thereby elucidating why
that approach is of general utility. The upper bound is tested against several
relatively complex domain-particle cellular automata and found to be tight.Comment: 17 pages, 12 figures, 3 tables,
http://www.santafe.edu/projects/CompMech/papers/ub.html V2: References and
accompanying text modified, to comply with legal demands arising from
on-going intellectual property litigation among third parties. V3: Accepted
for publication in Physica D. References added and other small changes made
per referee suggestion
Entanglement Dynamics in 1D Quantum Cellular Automata
Several proposed schemes for the physical realization of a quantum computer
consist of qubits arranged in a cellular array. In the quantum circuit model of
quantum computation, an often complex series of two-qubit gate operations is
required between arbitrarily distant pairs of lattice qubits. An alternative
model of quantum computation based on quantum cellular automata (QCA) requires
only homogeneous local interactions that can be implemented in parallel. This
would be a huge simplification in an actual experiment. We find some minimal
physical requirements for the construction of unitary QCA in a 1 dimensional
Ising spin chain and demonstrate optimal pulse sequences for information
transport and entanglement distribution. We also introduce the theory of
non-unitary QCA and show by example that non-unitary rules can generate
environment assisted entanglement.Comment: 12 pages, 8 figures, submitted to Physical Review
Broadcasting Automata and Patterns on Z^2
The Broadcasting Automata model draws inspiration from a variety of sources
such as Ad-Hoc radio networks, cellular automata, neighbourhood se- quences and
nature, employing many of the same pattern forming methods that can be seen in
the superposition of waves and resonance. Algorithms for broad- casting
automata model are in the same vain as those encountered in distributed
algorithms using a simple notion of waves, messages passed from automata to au-
tomata throughout the topology, to construct computations. The waves generated
by activating processes in a digital environment can be used for designing a
vari- ety of wave algorithms. In this chapter we aim to study the geometrical
shapes of informational waves on integer grid generated in broadcasting
automata model as well as their potential use for metric approximation in a
discrete space. An explo- ration of the ability to vary the broadcasting radius
of each node leads to results of categorisations of digital discs, their form,
composition, encodings and gener- ation. Results pertaining to the nodal
patterns generated by arbitrary transmission radii on the plane are explored
with a connection to broadcasting sequences and ap- proximation of discrete
metrics of which results are given for the approximation of astroids, a
previously unachievable concave metric, through a novel application of the
aggregation of waves via a number of explored functions
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