19 research outputs found
Growth and Decay in Life-Like Cellular Automata
We propose a four-way classification of two-dimensional semi-totalistic
cellular automata that is different than Wolfram's, based on two questions with
yes-or-no answers: do there exist patterns that eventually escape any finite
bounding box placed around them? And do there exist patterns that die out
completely? If both of these conditions are true, then a cellular automaton
rule is likely to support spaceships, small patterns that move and that form
the building blocks of many of the more complex patterns that are known for
Life. If one or both of these conditions is not true, then there may still be
phenomena of interest supported by the given cellular automaton rule, but we
will have to look harder for them. Although our classification is very crude,
we argue that it is more objective than Wolfram's (due to the greater ease of
determining a rigorous answer to these questions), more predictive (as we can
classify large groups of rules without observing them individually), and more
accurate in focusing attention on rules likely to support patterns with complex
behavior. We support these assertions by surveying a number of known cellular
automaton rules.Comment: 30 pages, 23 figure
Quantum Mechanics Model on K\"ahler conifold
We propose an exactly-solvable model of the quantum oscillator on the class
of K\"ahler spaces (with conic singularities), connected with two-dimensional
complex projective spaces. Its energy spectrum is nondegenerate in the orbital
quantum number, when the space has non-constant curvature. We reduce the model
to a three-dimensional system interacting with the Dirac monopole. Owing to
noncommutativity of the reduction and quantization procedures, the Hamiltonian
of the reduced system gets non-trivial quantum corrections. We transform the
reduced system into a MIC-Kepler-like one and find that quantum corrections
arise only in its energy and coupling constant. We present the exact spectrum
of the generalized MIC-Kepler system. The one-(complex) dimensional analog of
the suggested model is formulated on the Riemann surface over the complex
projective plane and could be interpreted as a system with fractional spin.Comment: 5 pages, RevTeX format, some misprints heve been correcte
Localization dynamics in a binary two-dimensional cellular automaton: the Diffusion Rule
We study a two-dimensional cellular automaton (CA), called Diffusion Rule
(DR), which exhibits diffusion-like dynamics of propagating patterns. In
computational experiments we discover a wide range of mobile and stationary
localizations (gliders, oscillators, glider guns, puffer trains, etc), analyze
spatio-temporal dynamics of collisions between localizations, and discuss
possible applications in unconventional computing.Comment: Accepted to Journal of Cellular Automat
Is symmetry identity?
Wigner found unreasonable the "effectiveness of mathematics in the natural
sciences". But if the mathematics we use to describe nature is simply a coded
expression of our experience then its effectiveness is quite reasonable. Its
effectiveness is built into its design. We consider group theory, the logic of
symmetry. We examine the premise that symmetry is identity; that group theory
encodes our experience of identification. To decide whether group theory
describes the world in such an elemental way we catalogue the detailed
correspondence between elements of the physical world and elements of the
formalism. Providing an unequivocal match between concept and mathematical
statement completes the case. It makes effectiveness appear reasonable. The
case that symmetry is identity is a strong one but it is not complete. The
further validation required suggests that unexpected entities might be
describable by the irreducible representations of group theory
An Observational Overview of Solar Flares
We present an overview of solar flares and associated phenomena, drawing upon
a wide range of observational data primarily from the RHESSI era. Following an
introductory discussion and overview of the status of observational
capabilities, the article is split into topical sections which deal with
different areas of flare phenomena (footpoints and ribbons, coronal sources,
relationship to coronal mass ejections) and their interconnections. We also
discuss flare soft X-ray spectroscopy and the energetics of the process. The
emphasis is to describe the observations from multiple points of view, while
bearing in mind the models that link them to each other and to theory. The
present theoretical and observational understanding of solar flares is far from
complete, so we conclude with a brief discussion of models, and a list of
missing but important observations.Comment: This is an article for a monograph on the physics of solar flares,
inspired by RHESSI observations. The individual articles are to appear in
Space Science Reviews (2011