53 research outputs found
Spherically symmetric Einstein-Maxwell theory and loop quantum gravity corrections
Effects of inverse triad corrections and (point) holonomy corrections,
occuring in loop quantum gravity, are considered on the properties of
Reissner-Nordstr\"om black holes. The version of inverse triad corrections with
unmodified constraint algebra reveals the possibility of occurrence of three
horizons (over a finite range of mass) and also shows a mass threshold beyond
which the inner horizon disappears. For the version with modified constraint
algebra, coordinate transformations are no longer a good symmetry. The
covariance property of spacetime is regained by using a \emph{quantum} notion
of mapping from phase space to spacetime. The resulting quantum effects in both
versions of these corrections can be associated with renormalization of either
mass, charge or wave function. In neither of the versions, Newton's constant is
renormalized. (Point) Holonomy corrections are shown to preclude the undeformed
version of constraint algebra as also a static solution, though
time-independent solutions exist. A possible reason for difficulty in
constructing a covariant metric for these corrections is highlighted.
Furthermore, the deformed algebra with holonomy corrections is shown to imply
signature change.Comment: 38 pages, 9 figures, matches published versio
Classical and Quantum Gravitational Collapse in d-dim AdS Spacetime I. Classical Solutions
We study the collapse of a spherically symmetric dust distribution in
-dimensional AdS spacetime. We investigate the role of dimensionality, and
the presence of a negative cosmological constant, in determining the formation
of trapped surfaces and the end state of gravitational collapse. We obtain the
self-similar solution for the case of zero cosmological constant, and show that
one cannot construct a self-similar solution when a cosmological constant is
included.Comment: 19 pages, sections on surface gravity removed, section on self
similar solution expanded, appendix removed, references added. To appear in
Phys. Rev.
Electron-phonon interaction contribution to the total energy of group IV semiconductor polymorphs: evaluation and implications
In density functional theory (DFT) based total energy studies, the van der
Waals (vdW) and zero-point vibrational energy (ZPVE) correction terms are
included to obtain energy differences between polymorphs. We introduce a new
correction term, due to electron-phonon interactions (EPI). We rely on Allen's
general formalism, which goes beyond the Quasi-Harmonic Approximation (QHA), to
include the free energy contributions due to quasiparticle interactions. We
show that, for semiconductors and insulators, the EPI contributions to the free
energies of electrons and phonons are constant terms. Using Allen's formalism
in combination with the Allen-Heine theory for EPI corrections, we calculate
the zero-point EPI corrections to the total energy for cubic and hexagonal
polytypes of Carbon, Silicon and Silicon Carbide. The EPI corrections alter the
energy differences between polytypes. In SiC polytypes, the EPI correction term
is more sensitive to crystal structure than the vdW and ZPVE terms and is thus
essential in determining their energy differences. It clearly establishes that
the cubic SiC-3C is metastable and hexagonal SiC-4H is the stable polytype. Our
results are consistent with the experimental results of Kleykamp. Our study
enables the inclusion of EPI corrections as a separate term in the free energy
expression. This opens the way to beyond the QHA by including the contribution
of EPI on all thermodynamic properties.Comment: Submitted for publication. 32 pages and 2 figure
Lemaitre-Tolman-Bondi collapse from the perspective of loop quantum gravity
Lemaitre-Tolman-Bondi models as specific spherically symmetric solutions of
general relativity simplify in their reduced form some of the mathematical
ingredients of black hole or cosmological applications. The conditions imposed
in addition to spherical symmetry turn out to take a simple form at the
kinematical level of loop quantum gravity, which allows a discussion of their
implications at the quantum level. Moreover, the spherically symmetric setting
of inhomogeneity illustrates several non-trivial properties of lattice
refinements of discrete quantum gravity. Nevertheless, the situation at the
dynamical level is quite non-trivial and thus provides insights to the anomaly
problem. At an effective level, consistent versions of the dynamics are
presented which implement the conditions together with the dynamical
constraints of gravity in an anomaly-free manner. These are then used for
analytical as well as numerical investigations of the fate of classical
singularities, including non-spacelike ones, as they generically develop in
these models. None of the corrections used here resolve those singularities by
regular effective geometries. However, there are numerical indications that the
collapse ends in a tamer shell-crossing singularity prior to the formation of
central singularities for mass functions giving a regular conserved mass
density. Moreover, we find quantum gravitational obstructions to the existence
of exactly homogeneous solutions within this class of models. This indicates
that homogeneous models must be seen in a wider context of inhomogeneous
solutions and their reduction in order to provide reliable dynamical
conclusions.Comment: 56 pages, 42 figure
The International Workshop on Osteoarthritis Imaging Knee MRI Segmentation Challenge: A Multi-Institute Evaluation and Analysis Framework on a Standardized Dataset
Purpose: To organize a knee MRI segmentation challenge for characterizing the
semantic and clinical efficacy of automatic segmentation methods relevant for
monitoring osteoarthritis progression.
Methods: A dataset partition consisting of 3D knee MRI from 88 subjects at
two timepoints with ground-truth articular (femoral, tibial, patellar)
cartilage and meniscus segmentations was standardized. Challenge submissions
and a majority-vote ensemble were evaluated using Dice score, average symmetric
surface distance, volumetric overlap error, and coefficient of variation on a
hold-out test set. Similarities in network segmentations were evaluated using
pairwise Dice correlations. Articular cartilage thickness was computed per-scan
and longitudinally. Correlation between thickness error and segmentation
metrics was measured using Pearson's coefficient. Two empirical upper bounds
for ensemble performance were computed using combinations of model outputs that
consolidated true positives and true negatives.
Results: Six teams (T1-T6) submitted entries for the challenge. No
significant differences were observed across all segmentation metrics for all
tissues (p=1.0) among the four top-performing networks (T2, T3, T4, T6). Dice
correlations between network pairs were high (>0.85). Per-scan thickness errors
were negligible among T1-T4 (p=0.99) and longitudinal changes showed minimal
bias (<0.03mm). Low correlations (<0.41) were observed between segmentation
metrics and thickness error. The majority-vote ensemble was comparable to top
performing networks (p=1.0). Empirical upper bound performances were similar
for both combinations (p=1.0).
Conclusion: Diverse networks learned to segment the knee similarly where high
segmentation accuracy did not correlate to cartilage thickness accuracy. Voting
ensembles did not outperform individual networks but may help regularize
individual models.Comment: Submitted to Radiology: Artificial Intelligence; Fixed typo
Micro force sensor with piezoresistive amorphous carbon strain gauge
In this contribution we report for the first time on the successful integration of amorphous carbon (a-C) as a piezoresistive strain gauge into a silicon micro cantilever force sensor. Sputter-deposited a-C layers showing excellent tribological properties contain a percentage of nearly 20% of tetrahedral sp3 carbon bonds as observed by optical absorption and Raman spectroscopy. Temperature-dependent transport measurements revealed hopping conduction between conducting sp2 carbon sites embedded in the insulating skeletal matrix of sp3 bonds. Changing their distance by strain a change of resistivity could be expected, which was investigated with layers sputter-deposited on a silicon membrane and structured by the lift-off technique using photo resist. Cantilevers comprising a-C strain gauges were etched out of this membrane using tetra methyl ammonium hydroxide (TMAH) and potassium hydroxide (KOH) solutions in a bulk silicon micromachining process. Realised prototypes were tested by applying a variable load to the cantilever free end. We found linear characteristics of the strain gauge resistance versus the applied force in the range of 0 to ±600 µN revealing piezoresistive gauge factors of a-C within 36-46
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