1,326 research outputs found
Infinitesimal deformations of Poisson bi-vectors using the Kontsevich graph calculus
Let be a Poisson structure on a finite-dimensional affine real manifold.
Can be deformed in such a way that it stays Poisson? The language of
Kontsevich graphs provides a universal approach -- with respect to all affine
Poisson manifolds -- to finding a class of solutions to this deformation
problem. For that reasoning, several types of graphs are needed. In this paper
we outline the algorithms to generate those graphs. The graphs that encode
deformations are classified by the number of internal vertices ; for we present all solutions of the deformation problem. For , first reproducing the pentagon-wheel picture suggested at
by Kontsevich and Willwacher, we construct the heptagon-wheel cocycle that
yields a new unique solution without -loops and tadpoles at .Comment: International conference ISQS'25 on integrable systems and quantum
symmetries (6-10 June 2017 in CVUT Prague, Czech Republic). Introductory
paragraph I.1 follows p.3 in arXiv:1710.00658 [math.CO]; 13 pages, 3 figures,
2 table
Poisson brackets symmetry from the pentagon-wheel cocycle in the graph complex
Kontsevich designed a scheme to generate infinitesimal symmetries
of Poisson brackets
on all affine manifolds ; every such deformation is encoded
by oriented graphs on vertices and edges. In particular, these
symmetries can be obtained by orienting sums of non-oriented graphs on
vertices and edges. The bi-vector flow preserves the space of Poisson structures if
is a cocycle with respect to the vertex-expanding differential in the
graph complex.
A class of such cocycles is known to exist:
marked by , each of them contains a -gon wheel
with a nonzero coefficient. At the tetrahedron
itself is a cocycle; at the Kontsevich--Willwacher pentagon-wheel
cocycle consists of two graphs. We reconstruct the
symmetry and verify that
is a Poisson cocycle indeed:
via
.Comment: Int. workshop "Supersymmetries and quantum symmetries -- SQS'17"
(July 31 -- August 5, 2017 at JINR Dubna, Russia), 4+v pages, 2 figures, 1
tabl
Non-equilibrium hydrogen ionization in 2D simulations of the solar atmosphere
The ionization of hydrogen in the solar chromosphere and transition region
does not obey LTE or instantaneous statistical equilibrium because the
timescale is long compared with important hydrodynamical timescales, especially
of magneto-acoustic shocks. We implement an algorithm to compute
non-equilibrium hydrogen ionization and its coupling into the MHD equations
within an existing radiation MHD code, and perform a two-dimensional simulation
of the solar atmosphere from the convection zone to the corona. Analysis of the
simulation results and comparison to a companion simulation assuming LTE shows
that: a) Non-equilibrium computation delivers much smaller variations of the
chromospheric hydrogen ionization than for LTE. The ionization is smaller
within shocks but subsequently remains high in the cool intershock phases. As a
result, the chromospheric temperature variations are much larger than for LTE
because in non-equilibrium, hydrogen ionization is a less effective internal
energy buffer. The actual shock temperatures are therefore higher and the
intershock temperatures lower. b) The chromospheric populations of the hydrogen
n = 2 level, which governs the opacity of Halpha, are coupled to the ion
populations. They are set by the high temperature in shocks and subsequently
remain high in the cool intershock phases. c) The temperature structure and the
hydrogen level populations differ much between the chromosphere above
photospheric magnetic elements and above quiet internetwork. d) The hydrogen n
= 2 population and column density are persistently high in dynamic fibrils,
suggesting that these obtain their visibility from being optically thick in
Halpha also at low temperature.Comment: 10 pages, 4 figure
Identication of linear slow sausage waves in magnetic pores
The analysis of an 11-hour series of high resolution white light observations of a large pore in the sunspot group NOAA 7519, observed on 5 June 1993 with the Swedish Vacuum Solar Telescope at La Palma on Canary Islands, has been recently described by Dorotovič et al. (2002). Special attention was paid to the evolution of a filamentary region attached to the pore, to horizontal motions around the pore, and to small-scale morphological changes. One of the results, relevant to out work here, was the determination of temporal area evolution of the studied pore where the area itself showed a linear trend of decrease with time at an average rate of −0.23 Mm2h−1 during the entire observing period. Analysing the time series of the are of the pore, there is strong evidence that coupling between the solar interior and magnetic atmosphere can occur at various scales and that the referred decrease of the area may be connected with a decrease of the magnetic field strength according to the magnetic field-to-size relation. Periods of global acoustic, e.g. p-mode, driven waves are usually in the range of 5–10 minutes, and are favourite candidates for the coupling of interior oscillations with atmospheric dynamics. However, by assuming that magneto-acoustic gravity waves may be there too, and may act as drivers, the observed periodicities (frequencies) are expected to be much longer (smaller), falling well within the mMHz domain. In this work we determine typical periods of such range in the area evolution of the pore using wavelet analysis. The resulted periods are in the range of 20–70 minutes, suggesting that periodic elements of the temporal evolution of the area of this studied pore could be linked to, and considered as, observational evidence of linear low-frequency slow sausage (magneto-acoustic gravity) waves in magnetic pores. This would give us further evidence on the coupling of global solar oscillations to the overlaying magnetic atmosphere
Interaction and observation: categorical semantics of reactive systems trough dialgebras
We use dialgebras, generalising both algebras and coalgebras, as a complement
of the standard coalgebraic framework, aimed at describing the semantics of an
interactive system by the means of reaction rules. In this model, interaction
is built-in, and semantic equivalence arises from it, instead of being
determined by a (possibly difficult) understanding of the side effects of a
component in isolation. Behavioural equivalence in dialgebras is determined by
how a given process interacts with the others, and the obtained observations.
We develop a technique to inter-define categories of dialgebras of different
functors, that in particular permits us to compare a standard coalgebraic
semantics and its dialgebraic counterpart. We exemplify the framework using the
CCS and the pi-calculus. Remarkably, the dialgebra giving semantics to the
pi-calculus does not require the use of presheaf categories
Spectropolarimetry of the nova-like variable V1315 Aql
We present spectropolarimetric observations of the eclipsing nova-like variable V1315 Aql, obtained with the aim of determining whether the single-peaked uneclipsed lines observed in this and related nova-likes are the result of disc emission scattered into the line of sight by the wind. The data show linear polarization with a mean value of 0.11+-0.02%. There are no significant differences between the continuum and line polarizations and no significant variations with wavelength or binary phase. We argue that the measured polarization may be attributed to scattering in the interstellar medium and hence conclude that there is no evidence of polarization intrinsic to V1315 Aql. We discuss alternative models which promise to resolve the controversy surrounding these objects
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