4,359 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
Understanding the central kinematics of globular clusters with simulated integrated-light IFU observations
The detection of intermediate mass black holes in the centres of globular
clusters is highly controversial, as complementary observational methods often
deliver significantly different results. In order to understand these
discrepancies, we develop a procedure to simulate integral field unit (IFU)
observations of globular clusters: Simulating IFU Star Cluster Observations
(SISCO). The input of our software are realistic dynamical models of globular
clusters that are then converted in a spectral data cube. We apply SISCO to
Monte Carlo cluster simulations from Downing et al. (2010), with a realistic
number of stars and concentrations. Using independent realisations of a given
simulation we are able to quantify the stochasticity intrinsic to the problem
of observing a partially resolved stellar population with integrated-light
spectroscopy. We show that the luminosity-weighted IFU observations can be
strongly biased by the presence of a few bright stars that introduce a scatter
in the velocity dispersion measurements up to 40% around the expected
value, preventing any sound assessment of the central kinematic and a sensible
interpretation of the presence/absence of an intermediate mass black hole.
Moreover, we illustrate that, in our mock IFU observations, the average
kinematic tracer has a mass of 0.75 solar masses, only slightly lower
than the mass of the typical stars examined in studies of resolved
line-of-sight velocities of giant stars. Finally, in order to recover unbiased
kinematic measurements we test different masking techniques that allow us to
remove the spaxels dominated by bright stars, bringing the scatter down to a
level of only a few percent. The application of SISCO will allow to investigate
state-of-the-art simulations as realistic observations.Comment: 13 pages, 9 figures, 1 table. Accepted for publication in MNRA
Three flow regimes of viscous jet falling onto a moving surface
A stationary viscous jet falling from an oriented nozzle onto a moving
surface is studied, both theoretically and experimentally. We distinguish three
flow regimes and classify them by the convexity of the jet shape (concave,
vertical and convex). The fluid is modeled as a Newtonian fluid, and the model
for the flow includes viscous effects, inertia and gravity. By studying the
characteristics of the conservation of momentum for a dynamic jet, the boundary
conditions for each flow regime are derived, and the flow regimes are
characterized in terms of the process and material parameters. The model is
solved by a transformation into an algebraic equation. We make a comparison
between the model and experiments, and obtain qualitative agreement
Falling of a viscous jet onto a moving surface
We analyze the stationary flow of a jet of Newtonian fluid that is drawn by
gravity onto a moving surface. The situation is modeled by a third-order ODE on
a domain of unknown length and with an additional integral condition; by
solving part of the equation explicitly we can reformulate the problem as a
first-order ODE, again with an integral constraint. We show that there are two
flow regimes, and characterize the associated regions in the three-dimensional
parameter space in terms of an easily calculable quantity. In a qualitative
sense the results from the model are found to correspond with experimental
observations.Comment: 16 pages, 11 figure
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
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