49 research outputs found
The Hess-Appelrot system and its nonholonomic analogs
This paper is concerned with the nonholonomic Suslov problem and its
generalization proposed by Chaplygin. The issue of the existence of an
invariant measure with singular density (having singularities at some points of
phase space) is discussed
Hamiltonization of Elementary Nonholonomic Systems
In this paper, we develop the Chaplygin reducing multiplier method; using
this method, we obtain a conformally Hamiltonian representation for three
nonholonomic systems, namely, for the nonholonomic oscillator, for the
Heisenberg system, and for the Chaplygin sleigh. Furthermore, in the case of an
oscillator and the nonholonomic Chaplygin sleigh, we show that the problem
reduces to the study of motion of a mass point (in a potential field) on a
plane and, in the case of the Heisenberg system, on the sphere. Moreover, we
consider an example of a nonholonomic system (suggested by Blackall) to which
one cannot apply the reducing multiplier method
Topology and bifurcations in nonholonomic mechanics
This paper develops topological methods for qualitative analysis of the behavior of nonholonomic dynamical systems. Their application is illustrated by considering a new integrable system of nonholonomic mechanics, called a nonholonomic hinge. Although this system is nonholonomic, it can be represented in Hamiltonian form with a Lie–Poisson bracket of rank two. This Lie–Poisson bracket is used to perform stability analysis of fixed points. In addition, all possible types of integral manifolds are found and a classification of trajectories on them is presented
SDSS-IV MaNGA : constraints on the conditions for star formation in galaxy discs
Funding: Leverhulme Trust Early Career Fellowship (AW)Regions of disc galaxies with widespread star formation tend to be both gravitationally unstable and self-shielded against ionizing radiation, whereas extended outer discs with little or no star formation tend to be stable and unshielded on average. We explore what drives the transition between these two regimes, specifically whether discs first meet the conditions for self-shielding (parameterized by dust optical depth, τ) or gravitational instability (parameterized by a modified version of Toomre’s instability parameters, Qthermal, which quantifies the stability of a gas disc that is thermally supported at T = 104 K). We first introduce a new metric formed by the product of these quantities, Qthermalτ, which indicates whether the conditions for disk instability or self-shielding are easier to meet in a given region of a galaxy, and we discuss how Qthermalτ can be constrained even in the absence of direct gas information. We then analyse a sample of 13 galaxies with resolved gas measurements and find that on average galaxies will reach the threshold for disk instabilities (Qthermal 1). Using integral field spectroscopic observations of a sample of 236 galaxies from the MaNGA survey, we find that the value of Qthermalτ in star-forming discs is consistent with similar behavior. These results support a scenario where disc fragmentation and collapse occurs before self-shielding, suggesting that gravitational instabilities are the primary condition for widespread star formation in galaxy discs. Our results support similar conclusions based on recent galaxy simulations.PostprintPeer reviewe
Tracing chemical evolution over the extent of the Milky Way's Disk with APOGEE Red Clump Stars
We employ the first two years of data from the near-infrared, high-resolution
SDSS-III/APOGEE spectroscopic survey to investigate the distribution of
metallicity and alpha-element abundances of stars over a large part of the
Milky Way disk. Using a sample of ~10,000 kinematically-unbiased red-clump
stars with ~5% distance accuracy as tracers, the [alpha/Fe] vs. [Fe/H]
distribution of this sample exhibits a bimodality in [alpha/Fe] at intermediate
metallicities, -0.9<[Fe/H]<-0.2, but at higher metallicities ([Fe/H]=+0.2) the
two sequences smoothly merge. We investigate the effects of the APOGEE
selection function and volume filling fraction and find that these have little
qualitative impact on the alpha-element abundance patterns. The described
abundance pattern is found throughout the range 5<R<11 kpc and 0<|Z|<2 kpc
across the Galaxy. The [alpha/Fe] trend of the high-alpha sequence is
surprisingly constant throughout the Galaxy, with little variation from region
to region (~10%). Using simple galactic chemical evolution models we derive an
average star formation efficiency (SFE) in the high-alpha sequence of ~4.5E-10
1/yr, which is quite close to the nearly-constant value found in
molecular-gas-dominated regions of nearby spirals. This result suggests that
the early evolution of the Milky Way disk was characterized by stars that
shared a similar star formation history and were formed in a well-mixed,
turbulent, and molecular-dominated ISM with a gas consumption timescale (1/SFE)
of ~2 Gyr. Finally, while the two alpha-element sequences in the inner Galaxy
can be explained by a single chemical evolutionary track this cannot hold in
the outer Galaxy, requiring instead a mix of two or more populations with
distinct enrichment histories.Comment: 18 pages, 17 figures. Accepted for publication in Ap