294,409 research outputs found
Detection of flux emergence, splitting, merging, and cancellation of network field. I Splitting and Merging
Frequencies of magnetic patch processes on supergranule boundary, namely flux
emergence, splitting, merging, and cancellation, are investigated through an
automatic detection. We use a set of line of sight magnetograms taken by the
Solar Optical Telescope (SOT) on board Hinode satellite. We found 1636 positive
patches and 1637 negative patches in the data set, whose time duration is 3.5
hours and field of view is 112" \times 112". Total numbers of magnetic
processes are followed: 493 positive and 482 negative splittings, 536 positive
and 535 negative mergings, 86 cancellations, and 3 emergences. Total numbers of
emergence and cancellation are significantly smaller than those of splitting
and merging. Further, frequency dependences of merging and splitting processes
on flux content are investigated. Merging has a weak dependence on flux content
only with a power- law index of 0.28. Timescale for splitting is found to be
independent of parent flux content before splitting, which corresponds to \sim
33 minutes. It is also found that patches split into any flux contents with a
same probability. This splitting has a power-law distribution of flux content
with an index of -2 as a time independent solution. These results support that
the frequency distribution of flux content in the analyzed flux range is
rapidly maintained by merging and splitting, namely surface processes. We
suggest a model for frequency distributions of cancellation and emergence based
on this idea.Comment: 32 pages, 10 figures, 1 table, accepted to Ap
Dominated Pesin theory: convex sum of hyperbolic measures
In the uniformly hyperbolic setting it is well known that the set of all
measures supported on periodic orbits is dense in the convex space of all
invariant measures. In this paper we consider the converse question, in the
non-uniformly hyperbolic setting: assuming that some ergodic measure converges
to a convex combination of hyperbolic ergodic measures, what can we deduce
about the initial measures?
To every hyperbolic measure whose stable/unstable Oseledets splitting
is dominated we associate canonically a unique class of periodic
orbits for the homoclinic relation, called its \emph{intersection class}. In a
dominated setting, we prove that a measure for which almost every measure in
its ergodic decomposition is hyperbolic with the same index such as the
dominated splitting is accumulated by ergodic measures if, and only if, almost
all such ergodic measures have a common intersection class.
We provide examples which indicate the importance of the domination
assumption.Comment: final version, new co-author, to appear in: Israel Journal of
Mathematic
Algebraic Relations Between Harmonic Sums and Associated Quantities
We derive the algebraic relations of alternating and non-alternating finite
harmonic sums up to the sums of depth~6. All relations for the sums up to
weight~6 are given in explicit form. These relations depend on the structure of
the index sets of the harmonic sums only, but not on their value. They are
therefore valid for all other mathematical objects which obey the same
multiplication relation or can be obtained as a special case thereof, as the
harmonic polylogarithms. We verify that the number of independent elements for
a given index set can be determined by counting the Lyndon words which are
associated to this set. The algebraic relations between the finite harmonic
sums can be used to reduce the high complexity of the expressions for the
Mellin moments of the Wilson coefficients and splitting functions significantly
for massless field theories as QED and QCD up to three loop and higher orders
in the coupling constant and are also of importance for processes depending on
more scales. The ratio of the number of independent sums thus obtained to the
number of all sums for a given index set is found to be with the
depth of the sum independently of the weight. The corresponding counting
relations are given in analytic form for all classes of harmonic sums to
arbitrary depth and are tabulated up to depth .Comment: 39 pages LATEX, 1 style fil
Generalized Heegaard splittings and the disk complex
Let be an orientable, irreducible -manifold and
a weakly reducible, unstabilized Heegaard
splitting of of genus at least three. In this article, we define an
equivalent relation on the set of the generalized Heegaard splittings
obtained by weak reductions and find special subsets of the disk complex
named by the "equivalent clusters", where we can find a
canonical function from the set of equivalent clusters to the set of the
equivalent classes for the relation . As an application, we prove that if
is topologically minimal and the topological index of is at least
three, then there is a -simplex in formed by two weak
reducing pairs such that the equivalent classes of the generalized Heegaard
splittings obtained by weak reductions along the weak reducing pairs for the
relation are different. In the last section, we prove is a
bijection if the genus of is three. Using it, we prove there is a canonical
function from the set of components of
to the set of the isotopy classes of the generalized Heegaard splittings
obtained by weak reductions and describe what is.Comment: 40 pages, 5 figures, This article is the generalization of the
authour's previous article arXiv:1412.2228 to arbitrarily high genus case
On well-rounded sublattices of the hexagonal lattice
We produce an explicit parameterization of well-rounded sublattices of the
hexagonal lattice in the plane, splitting them into similarity classes. We use
this parameterization to study the number, the greatest minimal norm, and the
highest signal-to-noise ratio of well-rounded sublattices of the hexagonal
lattice of a fixed index. This investigation parallels earlier work by
Bernstein, Sloane, and Wright where similar questions were addressed on the
space of all sublattices of the hexagonal lattice. Our restriction is motivated
by the importance of well-rounded lattices for discrete optimization problems.
Finally, we also discuss the existence of a natural combinatorial structure on
the set of similarity classes of well-rounded sublattices of the hexagonal
lattice, induced by the action of a certain matrix monoid.Comment: 21 pages (minor correction to the proof of Lemma 2.1); to appear in
Discrete Mathematic
Paired accelerated arames: The perfect interferometer with everywhere smooth wave amplitudes
Rindler's acceleration-induced partitioning of spacetime leads to a
nature-given interferometer. It accomodates quantum mechanical and wave
mechanical processes in spacetime which in (Euclidean) optics correspond to
wave processes in a ``Mach-Zehnder'' interferometer: amplitude splitting,
reflection, and interference. These processes are described in terms of
amplitudes which behave smoothly across the event horizons of all four Rindler
sectors. In this context there arises quite naturally a complete set of
orthonormal wave packet histories, one of whose key properties is their
"explosivity index". In the limit of low index values the wave packets trace
out fuzzy world lines. By contrast, in the asymptotic limit of high index
values, there are no world lines, not even fuzzy ones. Instead, the wave packet
histories are those of entities with non-trivial internal collapse and
explosion dynamics. Their details are described by the wave processes in the
above-mentioned Mach-Zehnder interferometer. Each one of them is a double slit
interference process. These wave processes are applied to elucidate the
amplification of waves in an accelerated inhomogeneous dielectric. Also
discussed are the properties and relationships among the transition amplitudes
of an accelerated finite-time detector.Comment: 38 pages, RevTex, 10 figures, 4 mathematical tutorials. Html version
of the figures and of related papers available at
http://www.math.ohio-state.edu/~gerlac
A low-order automatic domain splitting approach for nonlinear uncertainty mapping
This paper introduces a novel method for the automatic detection and handling
of nonlinearities in a generic transformation. A nonlinearity index that
exploits second order Taylor expansions and polynomial bounding techniques is
first introduced to rigorously estimate the Jacobian variation of a nonlinear
transformation. This index is then embedded into a low-order automatic domain
splitting algorithm that accurately describes the mapping of an initial
uncertainty set through a generic nonlinear transformation by splitting the
domain whenever some imposed linearity constraints are non met. The algorithm
is illustrated in the critical case of orbital uncertainty propagation, and it
is coupled with a tailored merging algorithm that limits the growth of the
domains in time by recombining them when nonlinearities decrease. The low-order
automatic domain splitting algorithm is then combined with Gaussian mixtures
models to accurately describe the propagation of a probability density
function. A detailed analysis of the proposed method is presented, and the
impact of the different available degrees of freedom on the accuracy and
performance of the method is studied
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