246,045 research outputs found
On the Burer-Monteiro method for general semidefinite programs
Consider a semidefinite program (SDP) involving an positive
semidefinite matrix . The Burer-Monteiro method uses the substitution to obtain a nonconvex optimization problem in terms of an
matrix . Boumal et al. showed that this nonconvex method provably solves
equality-constrained SDPs with a generic cost matrix when , where is the number of constraints. In this note we extend
their result to arbitrary SDPs, possibly involving inequalities or multiple
semidefinite constraints. We derive similar guarantees for a fixed cost matrix
and generic constraints. We illustrate applications to matrix sensing and
integer quadratic minimization.Comment: 10 page
Nanoscale temperature measurements using non-equilibrium Brownian dynamics of a levitated nanosphere
Einstein realised that the fluctuations of a Brownian particle can be used to
ascertain properties of its environment. A large number of experiments have
since exploited the Brownian motion of colloidal particles for studies of
dissipative processes, providing insight into soft matter physics, and leading
to applications from energy harvesting to medical imaging. Here we use
optically levitated nanospheres that are heated to investigate the
non-equilibrium properties of the gas surrounding them. Analysing the sphere's
Brownian motion allows us to determine the temperature of the centre-of-mass
motion of the sphere, its surface temperature and the heated gas temperature in
two spatial dimensions. We observe asymmetric heating of the sphere and gas,
with temperatures reaching the melting point of the material. This method
offers new opportunities for accurate temperature measurements with spatial
resolution on the nanoscale, and a new means for testing non-equilibrium
thermodynamicsComment: 5 pages, 4 figures, supplementary material available upon reques
Insights from Asteroseismology of Massive Stars: The Need for Additional Angular Momentum Transport Mechanisms
In massive stars, rotation and oscillatory waves can have a tight interplay.
In order to assess the importance of additional angular momentum transport
mechanisms other than rotation, we compare the asteroseismic properties of a
uniformly rotating model and a differentially rotating one. Accordingly, we
employ the observed period spacing of 36 dipole g-modes in the Kepler
M target KIC 7760680 to discriminate between these two models. We favor
the uniformly rotating model, which fully satisfies all observational
constraints. Therefore, efficient angular momentum transport by additional
mechanisms such as internal gravity waves, heat-driven modes and magnetic field
is needed during early main sequence evolution of massive stars.Comment: Proceedings of "Seismology of the Sun and the Distant Stars 2016".
Editors: M\'ario J. P. F. G. Monteiro, Margarida S. Cunha, Jo\~ao Miguel T.
Ferreir
Observation of Scaling Violations in Scaled Momentum Distributions at HERA
Charged particle production has been measured in deep inelastic scattering
(DIS) events over a large range of and using the ZEUS detector. The
evolution of the scaled momentum, , with in the range 10 to 1280
, has been investigated in the current fragmentation region of the Breit
frame. The results show clear evidence, in a single experiment, for scaling
violations in scaled momenta as a function of .Comment: 21 pages including 4 figures, to be published in Physics Letters B.
Two references adde
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