876 research outputs found
Scalar Field Dark Matter: non-spherical collapse and late time behavior
We show the evolution of non-spherically symmetric balls of a
self-gravitating scalar field in the Newtonian regime or equivalently an ideal
self-gravitating condensed Bose gas. In order to do so, we use a finite
differencing approximation of the Shcr\"odinger-Poisson (SP) system of
equations with axial symmetry in cylindrical coordinates. Our results indicate:
1) that spherically symmetric ground state equilibrium configurations are
stable against non-spherical perturbations and 2) that such configurations of
the SP system are late-time attractors for non-spherically symmetric initial
profiles of the scalar field, which is a generalization of such behavior for
spherically symmetric initial profiles. Our system and the boundary conditions
used, work as a model of scalar field dark matter collapse after the turnaround
point. In such case, we have found that the scalar field overdensities tolerate
non-spherical contributions to the profile of the initial fluctuation.Comment: 8 revtex pages, 10 eps figures. Accepted for publication in PR
Novel continuum modeling of crystal surface evolution
We propose a novel approach to continuum modeling of the dynamics of crystal
surfaces. Our model follows the evolution of an ensemble of step
configurations, which are consistent with the macroscopic surface profile.
Contrary to the usual approach where the continuum limit is achieved when
typical surface features consist of many steps, our continuum limit is
approached when the number of step configurations of the ensemble is very
large. The model can handle singular surface structures such as corners and
facets. It has a clear computational advantage over discrete models.Comment: 4 pages, 3 postscript figure
Decay of one dimensional surface modulations
The relaxation process of one dimensional surface modulations is re-examined.
Surface evolution is described in terms of a standard step flow model.
Numerical evidence that the surface slope, D(x,t), obeys the scaling ansatz
D(x,t)=alpha(t)F(x) is provided. We use the scaling ansatz to transform the
discrete step model into a continuum model for surface dynamics. The model
consists of differential equations for the functions alpha(t) and F(x). The
solutions of these equations agree with simulation results of the discrete step
model. We identify two types of possible scaling solutions. Solutions of the
first type have facets at the extremum points, while in solutions of the second
type the facets are replaced by cusps. Interactions between steps of opposite
signs determine whether a system is of the first or second type. Finally, we
relate our model to an actual experiment and find good agreement between a
measured AFM snapshot and a solution of our continuum model.Comment: 18 pages, 6 figures in 9 eps file
On computational irreducibility and the predictability of complex physical systems
Using elementary cellular automata (CA) as an example, we show how to
coarse-grain CA in all classes of Wolfram's classification. We find that
computationally irreducible (CIR) physical processes can be predictable and
even computationally reducible at a coarse-grained level of description. The
resulting coarse-grained CA which we construct emulate the large-scale behavior
of the original systems without accounting for small-scale details. At least
one of the CA that can be coarse-grained is irreducible and known to be a
universal Turing machine.Comment: 4 pages, 2 figures, to be published in PR
Origin Gaps and the Eternal Sunshine of the Second-Order Pendulum
The rich experiences of an intentional, goal-oriented life emerge, in an
unpredictable fashion, from the basic laws of physics. Here I argue that this
unpredictability is no mirage: there are true gaps between life and non-life,
mind and mindlessness, and even between functional societies and groups of
Hobbesian individuals. These gaps, I suggest, emerge from the mathematics of
self-reference, and the logical barriers to prediction that self-referring
systems present. Still, a mathematical truth does not imply a physical one: the
universe need not have made self-reference possible. It did, and the question
then is how. In the second half of this essay, I show how a basic move in
physics, known as renormalization, transforms the "forgetful" second-order
equations of fundamental physics into a rich, self-referential world that makes
possible the major transitions we care so much about. While the universe runs
in assembly code, the coarse-grained version runs in LISP, and it is from that
the world of aim and intention grows.Comment: FQXI Prize Essay 2017. 18 pages, including afterword on
Ostrogradsky's Theorem and an exchange with John Bova, Dresden Craig, and
Paul Livingsto
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
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