86 research outputs found
Brownian Motion of Black Holes in Dense Nuclei
We evaluate the Brownian motion of a massive particle ( black hole ) at the center of a galaxy using N-body simulations. Our galaxy models have power-law central density cusps like those observed at the centers of elliptical galaxies. The simulations show that the black hole achieves a steady-state kinetic energy that is substantially different than would be predicted based on the properties of the galaxy model in the absence of the black hole. The reason appears to be that the black hole responds to stars whose velocities have themselves been raised by the presence of the black hole. Over a wide range of density slopes and black hole masses, the black hole’s mean kinetic energy is equal to what would be predicted under the assumption that it is in energy equipartition with stars lying within a distance ∼ rh/2 from it, where rh is the black hole’s influence radius. The dependence of the Brownian velocity on black hole mass is approximately hV2i µ M−1/(3−g) BH with g the power-law index of the stellar density profile, r µ r−g. This is less steep than the M−1 BH dependence predicted in a model where the effect of the black hole on the stellar velocities is ignored. The influence of a stellar mass spectrum on the black hole’s Brownian motion is also evaluated and found to be consistent with predictions from Chandrasekhar’s theory. We use these results to derive a probability function for the mass of the Milky Way black hole based on a measurement of its proper motion velocity. Interesting constraints on MBH will require a velocity resolution exceeding 0.5 km s−1 (Refer to PDF file for exact formulas)
Determination of the Defining Boundary in Nuclear Magnetic Resonance Diffusion Experiments
While nuclear magnetic resonance diffusion experiments are widely used to
resolve structures confining the diffusion process, it has been elusive whether
they can exactly reveal these structures. This question is closely related to
X-ray scattering and to Kac's "hear the drum" problem. Although the shape of
the drum is not "hearable", we show that the confining boundary of closed pores
can indeed be detected using modified Stejskal-Tanner magnetic field gradients
that preserve the phase information and enable imaging of the average pore in a
porous medium with a largely increased signal-to-noise ratio.Comment: 13 pages, 2 figure
Brownian Motion of Black Holes in Dense Nuclei
We evaluate the Brownian motion of a massive particle ("black hole") at the
center of a galaxy using N-body simulations. Our galaxy models have power-law
central density cusps like those observed at the centers of elliptical
galaxies. The simulations show that the black hole achieves a steady-state
kinetic energy that is substantially different than would be predicted based on
the properties of the galaxy model in the absence of the black hole. The reason
appears to be that the black hole responds to stars whose velocities have
themselves been raised by the presence of the black hole. Over a wide range of
density slopes and black hole masses, the black hole's mean kinetic energy is
equal to what would be predicted under the assumption that it is in energy
equipartition with stars lying within a distance ~r_h/2 from it, where r_h is
the black hole's influence radius. The dependence of the Brownian velocity on
black hole mass is approximately ~ 1/M^{1/(3-gamma)} with gamma the
power-law index of the stellar density profile, rho~1/r^gamma. This is less
steep than the 1/M dependence predicted in a model where the effect of the
black hole on the stellar velocities is ignored. The influence of a stellar
mass spectrum on the black hole's Brownian motion is also evaluated and found
to be consistent with predictions from Chandrasekhar's theory. We use these
results to derive a probability function for the mass of the Milky Way black
hole based on a measurement of its proper motion velocity. Interesting
constraints on M will require a velocity resolution exceeding 0.5 km/s.Comment: 11 pages, uses emulateapj.st
NeXtQSM -- A complete deep learning pipeline for data-consistent quantitative susceptibility mapping trained with hybrid data
Deep learning based Quantitative Susceptibility Mapping (QSM) has shown great
potential in recent years, obtaining similar results to established
non-learning approaches. Many current deep learning approaches are not data
consistent, require in vivo training data or solve the QSM problem in
consecutive steps resulting in the propagation of errors. Here we aim to
overcome these limitations and developed a framework to solve the QSM
processing steps jointly. We developed a new hybrid training data generation
method that enables the end-to-end training for solving background field
correction and dipole inversion in a data-consistent fashion using a
variational network that combines the QSM model term and a learned regularizer.
We demonstrate that NeXtQSM overcomes the limitations of previous deep learning
methods. NeXtQSM offers a new deep learning based pipeline for computing
quantitative susceptibility maps that integrates each processing step into the
training and provides results that are robust and fast
Revealing Hidden Potentials of the q-Space Signal in Breast Cancer
Mammography screening for early detection of breast lesions currently suffers
from high amounts of false positive findings, which result in unnecessary
invasive biopsies. Diffusion-weighted MR images (DWI) can help to reduce many
of these false-positive findings prior to biopsy. Current approaches estimate
tissue properties by means of quantitative parameters taken from generative,
biophysical models fit to the q-space encoded signal under certain assumptions
regarding noise and spatial homogeneity. This process is prone to fitting
instability and partial information loss due to model simplicity. We reveal
unexplored potentials of the signal by integrating all data processing
components into a convolutional neural network (CNN) architecture that is
designed to propagate clinical target information down to the raw input images.
This approach enables simultaneous and target-specific optimization of image
normalization, signal exploitation, global representation learning and
classification. Using a multicentric data set of 222 patients, we demonstrate
that our approach significantly improves clinical decision making with respect
to the current state of the art.Comment: Accepted conference paper at MICCAI 201
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