102,670 research outputs found
Emergent gauge dynamics of highly frustrated magnets
Condensed matter exhibits a wide variety of exotic emergent phenomena such as
the fractional quantum Hall effect and the low temperature cooperative behavior
of highly frustrated magnets. I consider the classical Hamiltonian dynamics of
spins of the latter phenomena using a method introduced by Dirac in the 1950s
by assuming they are constrained to their lowest energy configurations as a
simplifying measure. Focusing on the kagome antiferromagnet as an example, I
find it is a gauge system with topological dynamics and non-locally connected
edge states for certain open boundary conditions similar to doubled
Chern-Simons electrodynamics expected of a spin liquid. These dynamics
are also similar to electrons in the fractional quantum Hall effect. The
classical theory presented here is a first step towards a controlled
semi-classical description of the spin liquid phases of many pyrochlore and
kagome antiferromagnets and towards a description of the low energy classical
dynamics of the corresponding unconstrained Heisenberg models.Comment: Updated with some appendices moved to the main body of the paper and
some additional improvements. 21 pages, 5 figure
Coarse-graining of cellular automata, emergence, and the predictability of complex systems
We study the predictability of emergent phenomena in complex systems. Using
nearest neighbor, one-dimensional Cellular Automata (CA) as an example, we show
how to construct local coarse-grained descriptions of CA in all classes of
Wolfram's classification. The resulting coarse-grained CA that we construct are
capable of emulating the large-scale behavior of the original systems without
accounting for small-scale details. Several CA that can be coarse-grained by
this construction are known to be universal Turing machines; they can emulate
any CA or other computing devices and are therefore undecidable. We thus show
that because in practice one only seeks coarse-grained information, complex
physical systems can be predictable and even decidable at some level of
description. The renormalization group flows that we construct induce a
hierarchy of CA rules. This hierarchy agrees well with apparent rule complexity
and is therefore a good candidate for a complexity measure and a classification
method. Finally we argue that the large scale dynamics of CA can be very
simple, at least when measured by the Kolmogorov complexity of the large scale
update rule, and moreover exhibits a novel scaling law. We show that because of
this large-scale simplicity, the probability of finding a coarse-grained
description of CA approaches unity as one goes to increasingly coarser scales.
We interpret this large scale simplicity as a pattern formation mechanism in
which large scale patterns are forced upon the system by the simplicity of the
rules that govern the large scale dynamics.Comment: 18 pages, 9 figure
Dynamical strategies for obstacle avoidance during Dictyostelium discoideum aggregation: a Multi-agent system model
Chemotaxis, the movement of an organism in response to chemical stimuli, is a
typical feature of many microbiological systems. In particular, the social
amoeba \textit{Disctyostelium discoideum} is widely used as a model organism,
but it is not still clear how it behaves in heterogeneous environments. A few
models focusing on mechanical features have already addressed the question;
however, we suggest that phenomenological models focusing on the population
dynamics may provide new meaningful data. Consequently, by means of a specific
Multi-agent system model, we study the dynamical features emerging from complex
social interactions among individuals belonging to amoeba colonies.\\ After
defining an appropriate metric to quantitatively estimate the gathering
process, we find that: a) obstacles play the role of local topological
perturbation, as they alter the flux of chemical signals; b) physical obstacles
(blocking the cellular motion and the chemical flux) and purely chemical
obstacles (only interfering with chemical flux) elicit similar dynamical
behaviors; c) a minimal program for robustly gathering simulated cells does not
involve mechanisms for obstacle sensing and avoidance; d) fluctuations of the
dynamics concur in preventing multiple stable clusters. Comparing those
findings with previous results, we speculate about the fact that chemotactic
cells can avoid obstacles by simply following the altered chemical gradient.
Social interactions are sufficient to guarantee the aggregation of the whole
colony past numerous obstacles
- …