884 research outputs found
On post-Lie algebras, Lie--Butcher series and moving frames
Pre-Lie (or Vinberg) algebras arise from flat and torsion-free connections on
differential manifolds. They have been studied extensively in recent years,
both from algebraic operadic points of view and through numerous applications
in numerical analysis, control theory, stochastic differential equations and
renormalization. Butcher series are formal power series founded on pre-Lie
algebras, used in numerical analysis to study geometric properties of flows on
euclidean spaces. Motivated by the analysis of flows on manifolds and
homogeneous spaces, we investigate algebras arising from flat connections with
constant torsion, leading to the definition of post-Lie algebras, a
generalization of pre-Lie algebras. Whereas pre-Lie algebras are intimately
associated with euclidean geometry, post-Lie algebras occur naturally in the
differential geometry of homogeneous spaces, and are also closely related to
Cartan's method of moving frames. Lie--Butcher series combine Butcher series
with Lie series and are used to analyze flows on manifolds. In this paper we
show that Lie--Butcher series are founded on post-Lie algebras. The functorial
relations between post-Lie algebras and their enveloping algebras, called
D-algebras, are explored. Furthermore, we develop new formulas for computations
in free post-Lie algebras and D-algebras, based on recursions in a magma, and
we show that Lie--Butcher series are related to invariants of curves described
by moving frames.Comment: added discussion of post-Lie algebroid
Fingerprint-enhanced capacitive-piezoelectric flexible sensing skin to discriminate static and dynamic tactile stimuli
nspired by the structure and functions of the human skin, a highly sensitive capacitive‐piezoelectric flexible sensing skin with fingerprint‐like patterns to detect and discriminate between spatiotemporal tactile stimuli including static and dynamic pressures and textures is presented. The capacitive‐piezoelectric tandem sensing structure is embedded in the phalange of a 3D‐printed robotic hand, and a tempotron classifier system is used for tactile exploration. The dynamic tactile sensor, interfaced with an extended gate configuration to a common source metal oxide semiconductor field effect transistor (MOSFET), exhibits a sensitivity of 2.28 kPa−1. The capacitive sensing structure has nonlinear characteristics with sensitivity varying from 0.25 kPa−1 in the low‐pressure range (<100 Pa) to 0.002 kPa−1 in high pressure (≈2.5 kPa). The output from the presented sensor under a closed‐loop tactile scan, carried out with an industrial robotic arm, is used as latency‐coded spike trains in a spiking neural network (SNN) tempotron classifier system. With the capability of performing a real‐time binary naturalistic texture classification with a maximum accuracy of 99.45%, the presented bioinspired skin finds applications in robotics, prosthesis, wearable sensors, and medical devices
Protostellar clusters in intermediate-mass (IM) star forming regions
The transition between the low density groups of T Tauri stars and the high
density clusters around massive stars occurs in the intermediate-mass (IM)
range (M2--8 M). High spatial resolution studies of IM young
stellar objects (YSO) can provide important clues to understand the clustering
in massive star forming regions.
Aims: Our aim is to search for clustering in IM Class 0 protostars. The high
spatial resolution and sensitivity provided by the new A configuration of the
Plateau de Bure Interferometer (PdBI) allow us to study the clustering in these
nearby objects.
Methods: We have imaged three IM Class 0 protostars (Serpens-FIRS 1, IC 1396
N, CB 3) in the continuum at 3.3 and 1.3mm using the PdBI. The sources have
been selected with different luminosity to investigate the dependence of the
clustering process on the luminosity of the source.
Results: Only one millimeter (mm) source is detected towards the low
luminosity source Serpens--FIRS 1. Towards CB 3 and IC1396 N, we detect two
compact sources separated by 0.05 pc. The 1.3mm image of IC 1396 N, which
provides the highest spatial resolution, reveal that one of these cores is
splitted in, at least, three individual sources.Comment: 4 pages, 3 figures, accepted for publication in Astronomy and
Astrophysics Letters (Special Feature IRAM/PdB
Evolution of the polarization of the optical afterglow of the gamma-ray burst GRB 030329
We report 31 polarimetric observations of the afterglow of GRB 030329 with
high signal-to-noise and high sampling frequency. We establish the polarization
light curve, detect sustained polarization at the percent level, and find
significant variability of polarization degree and angle. The data imply that
the afterglow magnetic field has small coherence length and is mostly random,
probably generated by turbulence.Comment: Nature 426 (13. Nov. 2003), 2 figure
Spin and Statistics and First Principles
It was shown in the early Seventies that, in Local Quantum Theory (that is
the most general formulation of Quantum Field Theory, if we leave out only the
unknown scenario of Quantum Gravity) the notion of Statistics can be grounded
solely on the local observable quantities (without assuming neither the
commutation relations nor even the existence of unobservable charged field
operators); one finds that only the well known (para)statistics of Bose/Fermi
type are allowed by the key principle of local commutativity of observables. In
this frame it was possible to formulate and prove the Spin and Statistics
Theorem purely on the basis of First Principles.
In a subsequent stage it has been possible to prove the existence of a
unique, canonical algebra of local field operators obeying ordinary Bose/Fermi
commutation relations at spacelike separations. In this general guise the Spin
- Statistics Theorem applies to Theories (on the four dimensional Minkowski
space) where only massive particles with finite mass degeneracy can occur. Here
we describe the underlying simple basic ideas, and briefly mention the
subsequent generalisations; eventually we comment on the possible validity of
the Spin - Statistics Theorem in presence of massless particles, or of
violations of locality as expected in Quantum Gravity.Comment: Survey based on a talk given at the Meeting on "Theoretical and
experimental aspects of the spin - statistics connection and related
symmetries", Trieste, Italy - October 21-25, 200
Overview of (pro-)Lie group structures on Hopf algebra character groups
Character groups of Hopf algebras appear in a variety of mathematical and
physical contexts. To name just a few, they arise in non-commutative geometry,
renormalisation of quantum field theory, and numerical analysis. In the present
article we review recent results on the structure of character groups of Hopf
algebras as infinite-dimensional (pro-)Lie groups. It turns out that under mild
assumptions on the Hopf algebra or the target algebra the character groups
possess strong structural properties. Moreover, these properties are of
interest in applications of these groups outside of Lie theory. We emphasise
this point in the context of two main examples: The Butcher group from
numerical analysis and character groups which arise from the Connes--Kreimer
theory of renormalisation of quantum field theories.Comment: 31 pages, precursor and companion to arXiv:1704.01099, Workshop on
"New Developments in Discrete Mechanics, Geometric Integration and
Lie-Butcher Series", May 25-28, 2015, ICMAT, Madrid, Spai
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Looking at the bright side of the ρ Ophiuchi dark cloud. Far infrared spectrophotometric observations of the ρ Oph cloud with the ISO-LWS
We present far infrared (45-195 μm) spectrophotometric observations with the ISO-LWS of the active star forming ρOph main cloud (L 1688). The [CII] 158 μm and [OI] 63 μm lines were detected at each of the 33 positions observed, whereas the [OI] 145 μm line was clearly seen toward twelve. The principal observational result is that the [CII] 158 μm line fluxes exhibit a clear correlation with projected distance from the dominant stellar source in the field (HD 147889). We interpret this in terms of PDR-type emission from the surface layers of the ρOph cloud. The observed [CII] 158 μm/[OI] 63 μm flux ratios are larger than unity everywhere. A comparison of the [CII] 158 μm line emission and the FIR dust continuum fluxes yields estimates of the efficiency at which the gas in the cloud converts stellar to [CII] 158 μm photons (χCII≳0.5%).
We first develop an empirical model, which provides us with a three dimensional view of the far and bright side of the dark ρOph cloud, showing that the cloud surface towards the putative energy source is concave. This model also yields quantitative estimates of the incident flux of ultraviolet radiation (G0 ~ 101 - 102) and of the degree of clumpiness/texture of the cloud surface (filling of the 80" beam ~0.2).
Subsequently, we use theoretical models of PDRS to derive the particle density, n(H), and the temperature structures, for Tgas and Tdust, in the surface layers of the ρOph cloud. Tgas is relatively low, ~60 K, but higher than Tdust ( ~30 K), and densities are generally found within the interval (1-3) 104 cm-3 . These PDR models are moderately successful in explaining the LWS observations. They correctly predict the [OI] 63 μm and [CII] 158 μm line intensities and the observed absence of any molecular line emission. The models do fail, however, to reproduce the observed small [OI] 63 μm/[OI] 145 μm ratios. We examine several possible explanations, but are unable to uniquely identify (or to disentangle) the cause(s) of this discrepancy.
From pressure equilibrium arguments we infer that the total mass of the ρOph main cloud (2pc2) is ~2 500 M⊙, which implies that the star formation efficiency to date is ≲4%, significantly lower than previous estimates
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