2,939 research outputs found
Load-depth sensing of isotropic, linear viscoelastic materials using rigid axisymmetric indenters
An indentation experiment involves five variables: indenter shape, material
behavior of the substrate, contact size, applied load and indentation depth.
Only three variable are known afterwards, namely, indenter shape, plus load and
depth as function of time. As the contact size is not measured and the
determination of the material properties is the very aim of the test; two
equations are needed to obtain a mathematically solvable system.
For elastic materials, the contact size can always be eliminated once and for
all in favor of the depth; a single relation between load, depth and material
properties remains with the latter variable as unknown.
For viscoelastic materials where hereditary integrals model the constitutive
behavior, the relation between depth and contact size usually depends also on
the (time-dependent) properties of the material. Solving the inverse problem,
i.e., determining the material properties from the experimental data, therefore
needs both equations. Extending Sneddon's analysis of the indentation problem
for elastic materials to include viscoelastic materials, the two equations
mentioned above are derived. To find the time dependence of the material
properties the feasibility of Golden and Graham's method of decomposing
hereditary integrals (J.M. Golden and G.A.C. Graham. Boundary value problems in
linear viscoelasticity, Springer, 1988) is investigated and applied to a single
load-unload process and to sinusoidally driven stationary state indentation
processes.Comment: 116 pages, 29 figure
The dynamical distance and intrinsic structure of the globular cluster omega Centauri
We determine the dynamical distance D, inclination i, mass-to-light ratio M/L
and the intrinsic orbital structure of the globular cluster omega Cen, by
fitting axisymmetric dynamical models to the ground-based proper motions of van
Leeuwen et al. and line-of-sight velocities from four independent data-sets. We
correct the observed velocities for perspective rotation caused by the space
motion of the cluster, and show that the residual solid-body rotation component
in the proper motions can be taken out without any modelling other than
assuming axisymmetry. This also provides a tight constraint on D tan i.
Application of our axisymmetric implementation of Schwarzschild's orbit
superposition method to omega Cen reveals no dynamical evidence for a
significant radial dependence of M/L. The best-fit dynamical model has a
stellar V-band mass-to-light ratio M/L_V = 2.5 +/- 0.1 M_sun/L_sun and an
inclination i = 50 +/- 4 degrees, which corresponds to an average intrinsic
axial ratio of 0.78 +/- 0.03. The best-fit dynamical distance D = 4.8 +/- 0.3
kpc (distance modulus 13.75 +/- 0.13 mag) is significantly larger than obtained
by means of simple spherical or constant-anisotropy axisymmetric dynamical
models, and is consistent with the canonical value 5.0 +/- 0.2 kpc obtained by
photometric methods. The total mass of the cluster is (2.5 +/- 0.3) x 10^6
M_sun. The best-fit model is close to isotropic inside a radius of about 10
arcmin and becomes increasingly tangentially anisotropic in the outer region,
which displays significant mean rotation. This phase-space structure may well
be caused by the effects of the tidal field of the Milky Way. The cluster
contains a separate disk-like component in the radial range between 1 and 3
arcmin, contributing about 4% to the total mass.Comment: 37 pages (23 figures), accepted for publication in A&A, abstract
abridged, for PS and PDF file with full resolution figures, see
http://www.strw.leidenuniv.nl/~vdven/oc
Triaxial orbit-based modelling of the Milky Way Nuclear Star Cluster
We construct triaxial dynamical models for the Milky Way nuclear star cluster
using Schwarzschild's orbit superposition technique. We fit the stellar
kinematic maps presented in Feldmeier et al. (2014). The models are used to
constrain the supermassive black hole mass M_BH, dynamical mass-to-light ratio
M/L, and the intrinsic shape of the cluster. Our best-fitting model has M_BH =
(3.0 +1.1 -1.3)x10^6 M_sun, M/L = (0.90 +0.76 -0.08) M_sun/L_{sun,4.5micron},
and a compression of the cluster along the line-of-sight. Our results are in
agreement with the direct measurement of the supermassive black hole mass using
the motion of stars on Keplerian orbits. The mass-to-light ratio is consistent
with stellar population studies of other galaxies in the mid-infrared. It is
possible that we underestimate M_BH and overestimate the cluster's triaxiality
due to observational effects. The spatially semi-resolved kinematic data and
extinction within the nuclear star cluster bias the observations to the near
side of the cluster, and may appear as a compression of the nuclear star
cluster along the line-of-sight. We derive a total dynamical mass for the Milky
Way nuclear star cluster of M_MWNSC = (2.1 +-0.7)x10^7 M_sun within a sphere
with radius r = 2 x r_eff = 8.4 pc. The best-fitting model is tangentially
anisotropic in the central r = 0.5-2 pc of the nuclear star cluster, but close
to isotropic at larger radii. Our triaxial models are able to recover complex
kinematic substructures in the velocity map.Comment: 14 pages, 10 figures. Accepted for publication in MNRA
General solution of the Jeans equations for triaxial galaxies with separable potentials
The Jeans equations relate the second-order velocity moments to the density
and potential of a stellar system. For general three-dimensional stellar
systems, there are three equations and six independent moments. By assuming
that the potential is triaxial and of separable Staeckel form, the mixed
moments vanish in confocal ellipsoidal coordinates. Consequently, the three
Jeans equations and three remaining non-vanishing moments form a closed system
of three highly-symmetric coupled first-order partial differential equations in
three variables. These equations were first derived by Lynden-Bell, over 40
years ago, but have resisted solution by standard methods. We present the
general solution here.
We consider the two-dimensional limiting cases first. We solve their Jeans
equations by a new method which superposes singular solutions. The singular
solutions, which are new, are standard Riemann-Green functions. The
two-dimensional solutions are applied to non-axisymmetric discs, oblate and
prolate spheroids, and also to the scale-free triaxial limit. We then extend
the method of singular solutions to the triaxial case, and obtain a full
solution. The general solution can be expressed in terms of complete
(hyper)elliptic integrals which can be evaluated in a straightforward way, and
provides the full set of second moments which can support a triaxial density
distribution in a separable triaxial potential. (abridged)Comment: 28 pages (7 figures), LaTeX MN2e, accepted for publication in MNRA
Space Motions of the Dwarf Spheroidal Galaxies Draco and Sculptor based on HST Proper Motions with ~10-year Time Baseline
We present new proper motion (PM) measurements of the dwarf spheroidal
galaxies (dSphs) Draco and Sculptor using multi-epoch images obtained with the
Hubble Space Telescope ACS/WFC. Our PM results have uncertainties far lower
than previous measurements, even made with the same instrument. The PM results
for Draco and Sculptor are (mu_W,mu_N)_Dra =
(-0.0562+/-0.0099,-0.1765+/-0.0100) mas/yr and (mu_W,mu_N)_Scl =
(-0.0296+/-0.0209,-0.1358 +/-0.0214) mas/yr. The implied Galactocentric
velocity vectors for Draco and Sculptor have radial and tangential components:
(V_rad,V_tan)_Dra = (-88.6,161.4) +/- (4.4,5.6) km/s; and (V_rad,V_tan)_Scl =
(72.6,200.2) +/- (1.3,10.8) km/s. We study the detailed orbital history of both
Draco and Sculptor via numerical orbit integrations. Orbital periods of Draco
and Sculptor are found to be 1-2 and 2-5 Gyrs, respectively, accounting for
uncertainties in the MW mass. We also study the influence of the Large
Magellanic Cloud (LMC) on the orbits of Draco and Sculptor. Overall, the
inclusion of the LMC increases the scatter in the orbital results. Based on our
calculations, Draco shows a rather wide range of orbital parameters depending
on the MW mass and inclusion/exclusion of the LMC, but Sculptor's orbit is very
well constrained with its most recent pericentric approach to the MW being
0.3-0.4 Gyr ago. Our new PMs imply that the orbital trajectories of both Draco
and Sculptor are confined within the Disk of Satellites (DoS), better so than
implied by earlier PM measurements, and likely rule out the possibility that
these two galaxies were accreted together as part of a tightly bound group.Comment: 17 pages, 8 figures, 6 tables. Accepted for publication in Ap
Dark Matter Fraction in Disk-Like Galaxies Over the Past 10 Gyr
We present an observational study of the dark matter fraction in star-forming
disk-like galaxies up to redshift , selected from publicly
available integral field spectroscropic surveys, namely KMOS3D}, KGES, and
KROSS. We provide novel observational evidence, showing that at a fixed
redshift, the dark matter fraction gradually increases with radius, indicating
that the outskirts of galaxies are dark matter dominated, similarly to local
star-forming disk galaxies. This observed dark matter fraction exhibits a
decreasing trend with increasing redshift. However, on average, the fraction
within the effective radius (upto outskirts) remains above 50\%, similar to
locals. Furthermore, we investigated the relationships between the dark matter,
baryon surface density, and circular velocity of galaxies. We observe a
decreasing trend in the dark matter fraction as baryon surface densities
increase, which is consistent across all stellar masses, redshift ranges, and
radii, with a scatter of 0.13 dex. On the other hand, the correlation between
the circular velocity at the outermost radius and the dark matter fraction
within this radius has a relatively low scatter (0.11 dex), but its slope
varies with stellar mass and with redshift, providing observational evidence of
the dynamical evolution of the interplay between the baryonic and dark matter
distributions with cosmic time. We observe that low stellar mass galaxies
() undergo a higher degree of
evolution, which may be attributed to the hierarchical merging of galaxies.Comment: Comments are welcom
Heat Kernel Asymptotics on Homogeneous Bundles
We consider Laplacians acting on sections of homogeneous vector bundles over
symmetric spaces. By using an integral representation of the heat semi-group we
find a formal solution for the heat kernel diagonal that gives a generating
function for the whole sequence of heat invariants. We argue that the obtained
formal solution correctly reproduces the exact heat kernel diagonal after a
suitable regularization and analytical continuation.Comment: 29 pages, Proceedings of the 2007 Midwest Geometry Conference in
Honor of Thomas P. Branso
The wall shear rate distribution for flow in random sphere packings
The wall shear rate distribution P(gamma) is investigated for pressure-driven
Stokes flow through random arrangements of spheres at packing fractions 0.1 <=
phi <= 0.64. For dense packings, P(gamma) is monotonic and approximately
exponential. As phi --> 0.1, P(gamma) picks up additional structure which
corresponds to the flow around isolated spheres, for which an exact result can
be obtained. A simple expression for the mean wall shear rate is presented,
based on a force-balance argument.Comment: 4 pages, 3 figures, 1 table, RevTeX 4; significantly revised with
significantly extended scop
A study of rotating globular clusters - the case of the old, metal-poor globular cluster NGC 4372
Aims: We present the first in-depth study of the kinematic properties and
derive the structural parameters of NGC 4372 based on the fit of a Plummer
profile and a rotating, physical model. We explore the link between internal
rotation to different cluster properties and together with similar studies of
more GCs, we put these in the context of globular cluster formation and
evolution. Methods: We present radial velocities for 131 cluster member stars
measured from high-resolution FLAMES/GIRAFFE observations. Their membership to
the GC is additionally confirmed from precise metallicity estimates. Using this
kinematic data set we build a velocity dispersion profile and a systemic
rotation curve. Additionally, we obtain an elliptical number density profile of
NGC 4372 based on optical images using a MCMC fitting algorithm. From this we
derive the cluster's half-light radius and ellipticity as r_h=3.4'+/-0.04' and
e=0.08+/-0.01. Finally, we give a physical interpretation of the observed
morphological and kinematic properties of this GC by fitting an axisymmetric,
differentially rotating, dynamical model. Results: Our results show that NGC
4372 has an unusually high ratio of rotation amplitude to velocity dispersion
(1.2 vs. 4.5 km/s) for its metallicity. This, however, puts it in line with two
other exceptional, very metal-poor GCs - M 15 and NGC 4590. We also find a mild
flattening of NGC 4372 in the direction of its rotation. Given its old age,
this suggests that the flattening is indeed caused by the systemic rotation
rather than tidal interactions with the Galaxy. Additionally, we estimate the
dynamical mass of the GC M_dyn=2.0+/-0.5 x 10^5 M_Sun based on the dynamical
model, which constrains the mass-to-light ratio of NGC 4372 between 1.4 and 2.3
M_Sun/L_Sun, representative of an old, purely stellar population.Comment: Accepted for publication in A&A, 12 pages, 14 figures, 2 table
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