2,656 research outputs found
Matching of analytical and numerical solutions for neutron stars of arbitrary rotation
We demonstrate the results of an attempt to match the two-soliton analytical
solution with the numerically produced solutions of the Einstein field
equations, that describe the spacetime exterior of rotating neutron stars, for
arbitrary rotation. The matching procedure is performed by equating the first
four multipole moments of the analytical solution to the multipole moments of
the numerical one. We then argue that in order to check the effectiveness of
the matching of the analytical with the numerical solution we should compare
the metric components, the radius of the innermost stable circular orbit
(), the rotation frequency and the
epicyclic frequencies . Finally we present some
results of the comparison.Comment: Contribution at the 13th Conference on Recent Developments in Gravity
(NEB XIII), corrected typo in of eq. 5 of the published versio
Faithful transformation of quasi-isotropic to Weyl-Papapetrou coordinates: A prerequisite to compare metrics
We demonstrate how one should transform correctly quasi-isotropic coordinates
to Weyl-Papapetrou coordinates in order to compare the metric around a rotating
star that has been constructed numerically in the former coordinates with an
axially symmetric stationary metric that is given through an analytical form in
the latter coordinates. Since a stationary metric associated with an isolated
object that is built numerically partly refers to a non-vacuum solution
(interior of the star) the transformation of its coordinates to Weyl-Papapetrou
coordinates, which are usually used to describe vacuum axisymmetric and
stationary solutions of Einstein equations, is not straightforward in the
non-vacuum region. If this point is \textit{not} taken into consideration, one
may end up to erroneous conclusions about how well a specific analytical metric
matches the metric around the star, due to fallacious coordinate
transformations.Comment: 18 pages, 2 figure
Correlating decoherence in transmon qubits: Low frequency noise by single fluctuators
We report on long-term measurements of a highly coherent, non-tunable
superconducting transmon qubit, revealing low-frequency burst noise in
coherence times and qubit transition frequency. We achieve this through a
simultaneous measurement of the qubit's relaxation and dephasing rate as well
as its resonance frequency. The analysis of correlations between these
parameters yields information about the microscopic origin of the intrinsic
decoherence mechanisms in Josephson qubits. Our results are consistent with a
small number of microscopic two-level systems located at the edges of the
superconducting film, which is further confirmed by a spectral noise analysis.Comment: 10 Pages, 6 figure
Fair Robust Assignment Using Redundancy
We study the consideration of fairness in redundant assignment for multi-agent task allocation. It has recently been shown that redundant assignment of agents to tasks provides robustness to uncertainty in task performance. However, the question of how to fairly assign these redundant resources across tasks remains unaddressed. In this paper, we present a novel problem formulation for fair redundant task allocation, in which we cast it as the optimization of worst-case task costs. Solving this problem optimally is NP-hard. Therefore, we exploit properties of supermodularity to propose a polynomial-time, near-optimal solution. Our algorithm provides a solution set that is α times larger than the optimal set size in order to guarantee a solution cost at least as good as the optimal target cost. We derive the sub- optimality bound on this cardinality relaxation, α. Additionally, we demonstrate that our algorithm performs near-optimally without the cardinality relaxation. We show the algorithm in simulations of redundant assignments of robots to goal nodes on transport networks with uncertain travel times. Empirically, our algorithm outperforms benchmarks, scales to large problems, and provides improvements in both fairness and average utility.We gratefully acknowledge the support from ARL Grant DCIST CRA W911NF-17-2-0181, NSF Grant CNS-1521617, ARO Grant W911NF-13-1- 0350, ONR Grants N00014-20-1-2822 and ONR grant N00014-20-S-B001, and Qualcomm Research. The first author acknowledges support from the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1845298
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Fair Robust Assignment Using Redundancy
We study the consideration of fairness in redundant assignment for multi-agent task allocation. It has recently been shown that redundant assignment of agents to tasks provides robustness to uncertainty in task performance. However, the question of how to fairly assign these redundant resources across tasks remains unaddressed. In this paper, we present a novel problem formulation for fair redundant task allocation, in which we cast it as the optimization of worst-case task costs. Solving this problem optimally is NP-hard. Therefore, we exploit properties of supermodularity to propose a polynomial-time, near-optimal solution. Our algorithm provides a solution set that is α times larger than the optimal set size in order to guarantee a solution cost at least as good as the optimal target cost. We derive the sub- optimality bound on this cardinality relaxation, α. Additionally, we demonstrate that our algorithm performs near-optimally without the cardinality relaxation. We show the algorithm in simulations of redundant assignments of robots to goal nodes on transport networks with uncertain travel times. Empirically, our algorithm outperforms benchmarks, scales to large problems, and provides improvements in both fairness and average utility.We gratefully acknowledge the support from ARL Grant DCIST CRA W911NF-17-2-0181, NSF Grant CNS-1521617, ARO Grant W911NF-13-1- 0350, ONR Grants N00014-20-1-2822 and ONR grant N00014-20-S-B001, and Qualcomm Research. The first author acknowledges support from the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1845298
Thermally induced magnetic relaxation in square artificial spin ice
The properties of natural and artificial assemblies of interacting elements,
ranging from Quarks to Galaxies, are at the heart of Physics. The collective
response and dynamics of such assemblies are dictated by the intrinsic
dynamical properties of the building blocks, the nature of their interactions
and topological constraints. Here we report on the relaxation dynamics of the
magnetization of artificial assemblies of mesoscopic spins. In our model
nano-magnetic system - square artificial spin ice - we are able to control the
geometrical arrangement and interaction strength between the magnetically
interacting building blocks by means of nano-lithography. Using time resolved
magnetometry we show that the relaxation process can be described using the
Kohlrausch law and that the extracted temperature dependent relaxation times of
the assemblies follow the Vogel-Fulcher law. The results provide insight into
the relaxation dynamics of mesoscopic nano-magnetic model systems, with
adjustable energy and time scales, and demonstrates that these can serve as an
ideal playground for the studies of collective dynamics and relaxations.Comment: 15 pages, 5 figure
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