14,389 research outputs found
Synchronization in a ring of pulsating oscillators with bidirectional couplings
We study the dynamical behavior of an ensemble of oscillators interacting
through short range bidirectional pulses. The geometry is 1D with periodic
boundary conditions. Our interest is twofold. To explore the conditions
required to reach fully synchronization and to invewstigate the time needed to
get such state. We present both theoretical and numerical results.Comment: Revtex, 4 pages, 2 figures. To appear in Int. J. Bifurc. and Chao
Quadratic Maps in Two Variables on Arbitrary Fields
Let be a field of characteristic different from and , and
let be a vector space of dimension over . The generic
classification of homogeneous quadratic maps under the action
of the linear group of , is given and efficient computational criteria to
recognize equivalence are provided.Comment: 12 pages, no figure
A bottom-up approach to the strong CP problem
The strong CP problem is one of many puzzles in the theoretical description
of elementary particle physics that still lacks an explanation. While top-down
solutions to that problem usually comprise new symmetries or fields or both, we
want to present a rather bottom-up perspective. The main problem seems to be
how to achieve small CP violation in the strong interactions despite large CP
violation in weak interactions. Observation of CP violation is exclusively
through the Higgs--Yukawa interactions. In this paper, we show that with
minimal assumptions on the structure of mass (Yukawa) matrices they do not
contribute to the strong CP problem and thus we can provide a pathway to a
solution of the strong CP problem within the structures of the Standard Model
and no extension at the electroweak scale is needed. However, to address the
flavor puzzle, models based on minimal SU(3) flavor groups leading to the
proposed flavor matrices are favored. Though we refrain from an explicit a UV
completion of the Standard Model, we provide a simple requirement those models
should have to intrinsically not show a strong CP problem.Comment: 12 pages; v2: extended discussion, title changed to be more genera
Collision, explosion and collapse of homoclinic classes
Homoclinic classes of generic -diffeomorphisms are maximal transitive
sets and pairwise disjoint. We here present a model explaining how two
different homoclinic classes may intersect, failing to be disjoint. For that we
construct a one-parameter family of diffeomorphisms with
hyperbolic points and having nontrivial homoclinic classes, such that,
for , the classes of and are disjoint, for , they are equal,
and, for , their intersection is a saddle-node.Comment: This is the final version, accepted in 200
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