2,451 research outputs found
Stability of domain walls coupled to Abelian gauge fields
Rozowsky, Volkas and Wali recently found interesting numerical solutions to
the field equations for a gauged U1xU1 scalar field model. Their solutions
describe a reflection-symmetric domain wall with scalar fields and coupled
gauge configurations that interpolate between constant magnetic fields on one
side of the wall and exponentially decaying ones on the other side. This
corresponds physically to an infinite sheet of supercurrent confined to the
domain wall with a linearly rising gauge potential on one side and Meissner
suppression on the other. While it was shown that these static solutions
satisfied the field equations, their stability was left unresolved. In this
paper, we analyse the normal modes of perturbations of the static solutions to
demonstrate their perturbative stability.Comment: 9 pages, 9 figure
Bug propagation and debugging in asymmetric software structures
Software dependence networks are shown to be scale-free and asymmetric. We
then study how software components are affected by the failure of one of them,
and the inverse problem of locating the faulty component. Software at all
levels is fragile with respect to the failure of a random single component.
Locating a faulty component is easy if the failures only affect their nearest
neighbors, while it is hard if the failures propagate further.Comment: 4 pages, 4 figure
Computational Processes and Incompleteness
We introduce a formal definition of Wolfram's notion of computational process
based on cellular automata, a physics-like model of computation. There is a
natural classification of these processes into decidable, intermediate and
complete. It is shown that in the context of standard finite injury priority
arguments one cannot establish the existence of an intermediate computational
process
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
A Concrete View of Rule 110 Computation
Rule 110 is a cellular automaton that performs repeated simultaneous updates
of an infinite row of binary values. The values are updated in the following
way: 0s are changed to 1s at all positions where the value to the right is a 1,
while 1s are changed to 0s at all positions where the values to the left and
right are both 1. Though trivial to define, the behavior exhibited by Rule 110
is surprisingly intricate, and in (Cook, 2004) we showed that it is capable of
emulating the activity of a Turing machine by encoding the Turing machine and
its tape into a repeating left pattern, a central pattern, and a repeating
right pattern, which Rule 110 then acts on. In this paper we provide an
explicit compiler for converting a Turing machine into a Rule 110 initial
state, and we present a general approach for proving that such constructions
will work as intended. The simulation was originally assumed to require
exponential time, but surprising results of Neary and Woods (2006) have shown
that in fact, only polynomial time is required. We use the methods of Neary and
Woods to exhibit a direct simulation of a Turing machine by a tag system in
polynomial time
On the boundaries of solvability and unsolvability in tag systems. Theoretical and Experimental Results
Several older and more recent results on the boundaries of solvability and
unsolvability in tag systems are surveyed. Emphasis will be put on the
significance of computer experiments in research on very small tag systems
The clash of symmetries in a Randall-Sundrum-like spacetime
We present a toy model that exhibits clash-of-symmetries style Higgs field
kink configurations in a Randall-Sundrum-like spacetime. The model has two
complex scalar fields Phi_{1,2}, with a sextic potential obeying global
U(1)xU(1) and discrete Phi_1 Phi_2 interchange symmetries. The scalar
fields are coupled to 4+1 dimensional gravity endowed with a bulk cosmological
constant. We show that the coupled Einstein-Higgs field equations have an
interesting analytic solution provided the sextic potential adopts a particular
form. The 4+1 metric is shown to be that of a smoothed-out Randall-Sundrum type
of spacetime. The thin-brane Randall-Sundrum limit, whereby the Higgs field
kinks become step functions, is carefully defined in terms of the fundamental
parameters in the action. The ``clash of symmetries'' feature, defined in
previous papers, is manifested here through the fact that both of the U(1)
symmetries are spontaneously broken at all non-asymptotic points in the extra
dimension . One of the U(1)'s is asymptotically restored as w --> -infinity,
with the other U(1) restored as w --> +infinity. The spontaneously broken
discrete symmetry ensures topological stability. In the gauged version of this
model we find new flat-space solutions, but in the warped metric case we have
been unable to find any solutions with nonzero gauge fields.Comment: 15 pages, 5 figures; minor changes including added references and an
updated figure; to appear in Phys Rev
Multi-Head Finite Automata: Characterizations, Concepts and Open Problems
Multi-head finite automata were introduced in (Rabin, 1964) and (Rosenberg,
1966). Since that time, a vast literature on computational and descriptional
complexity issues on multi-head finite automata documenting the importance of
these devices has been developed. Although multi-head finite automata are a
simple concept, their computational behavior can be already very complex and
leads to undecidable or even non-semi-decidable problems on these devices such
as, for example, emptiness, finiteness, universality, equivalence, etc. These
strong negative results trigger the study of subclasses and alternative
characterizations of multi-head finite automata for a better understanding of
the nature of non-recursive trade-offs and, thus, the borderline between
decidable and undecidable problems. In the present paper, we tour a fragment of
this literature
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