21,618 research outputs found
Magnetohydrodynamic convectons
Numerical continuation is used to compute branches of spatially localized structures in convection in an imposed vertical magnetic field. In periodic domains with finite spatial period, these branches exhibit slanted snaking and consist of localized states of even and odd parity. The properties of these states are analysed and related to existing asymptotic approaches valid either at small amplitude (Cox and Matthews, Physica D, vol. 149, 2001, p. 210), or in the limit of small magnetic diffusivity (Dawes, J. Fluid Mech., vol. 570, 2007, p. 385). The transition to standard snaking with increasing domain size is explored
Local symmetry dynamics in one-dimensional aperiodic lattices
A unifying description of lattice potentials generated by aperiodic
one-dimensional sequences is proposed in terms of their local reflection or
parity symmetry properties. We demonstrate that the ranges and axes of local
reflection symmetry possess characteristic distributional and dynamical
properties which can be determined for every aperiodic binary lattice. A
striking aspect of such a property is given by the return maps of sequential
spacings of local symmetry axes, which typically traverse few-point symmetry
orbits. This local symmetry dynamics allows for a classification of inherently
different aperiodic lattices according to fundamental symmetry principles.
Illustrating the local symmetry distributional and dynamical properties for
several representative binary lattices, we further show that the renormalized
axis spacing sequences follow precisely the particular type of underlying
aperiodic order. Our analysis thus reveals that the long-range order of
aperiodic lattices is characterized in a compellingly simple way by its local
symmetry dynamics.Comment: 15 pages, 12 figure
The Pagoda Sequence: a Ramble through Linear Complexity, Number Walls, D0L Sequences, Finite State Automata, and Aperiodic Tilings
We review the concept of the number wall as an alternative to the traditional
linear complexity profile (LCP), and sketch the relationship to other topics
such as linear feedback shift-register (LFSR) and context-free Lindenmayer
(D0L) sequences. A remarkable ternary analogue of the Thue-Morse sequence is
introduced having deficiency 2 modulo 3, and this property verified via the
re-interpretation of the number wall as an aperiodic plane tiling
Refinement for Transition Systems with Responses
Motivated by the response pattern for property specifications and
applications within flexible workflow management systems, we report upon an
initial study of modal and mixed transition systems in which the must
transitions are interpreted as must eventually, and in which implementations
can contain may behaviors that are resolved at run-time. We propose Transition
Systems with Responses (TSRs) as a suitable model for this study. We prove that
TSRs correspond to a restricted class of mixed transition systems, which we
refer to as the action-deterministic mixed transition systems. We show that
TSRs allow for a natural definition of deadlocked and accepting states. We then
transfer the standard definition of refinement for mixed transition systems to
TSRs and prove that refinement does not preserve deadlock freedom. This leads
to the proposal of safe refinements, which are those that preserve deadlock
freedom. We exemplify the use of TSRs and (safe) refinements on a small
medication workflow.Comment: In Proceedings FIT 2012, arXiv:1207.348
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