4,078 research outputs found
Relativistic surfatron process for Landau resonant electrons in radiation belts
Recent theoretical studies of the nonlinear wave-particle interactions for
relativistic particles have shown that Landau resonant orbits could be
efficiently accelerated along the mean background magnetic field for
propagation angles in close proximity to a critical propagation
associated with a Hopf--Hopf bifurcation condition. In this
report, we extend previous studies to reach greater modeling capacities for the
study of electrons in radiation belts by including longitudinal wave effects
and inhomogeneous magnetic fields. We find that even though both effects can
limit the surfatron acceleration of electrons in radiation belts, gains in
energy of the order of 100 keV, taking place on the order of ten milliseconds,
are sufficiently strong for the mechanism to be relevant to radiation belt
dynamics.Comment: Published in Nonlinear Processes of Geophysics but available in here
without some random typos introduced by publishe
Sparse Array DFT Beamformers for Wideband Sources
Sparse arrays are popular for performance optimization while keeping the
hardware and computational costs down. In this paper, we consider sparse arrays
design method for wideband source operating in a wideband jamming environment.
Maximizing the signal-to-interference plus noise ratio (MaxSINR) is adopted as
an optimization objective for wideband beamforming. Sparse array design problem
is formulated in the DFT domain to process the source as parallel narrowband
sources. The problem is formulated as quadratically constraint quadratic
program (QCQP) alongside the weighted mixed -norm squared
penalization of the beamformer weight vector. The semidefinite relaxation (SDR)
of QCQP promotes sparse solutions by iteratively re-weighting beamformer based
on previous iteration. It is shown that the DFT approach reduces the
computational cost considerably as compared to the delay line approach, while
efficiently utilizing the degrees of freedom to harness the maximum output SINR
offered by the given array aperture
Equivariant semidefinite lifts and sum-of-squares hierarchies
A central question in optimization is to maximize (or minimize) a linear
function over a given polytope P. To solve such a problem in practice one needs
a concise description of the polytope P. In this paper we are interested in
representations of P using the positive semidefinite cone: a positive
semidefinite lift (psd lift) of a polytope P is a representation of P as the
projection of an affine slice of the positive semidefinite cone
. Such a representation allows linear optimization problems
over P to be written as semidefinite programs of size d. Such representations
can be beneficial in practice when d is much smaller than the number of facets
of the polytope P. In this paper we are concerned with so-called equivariant
psd lifts (also known as symmetric psd lifts) which respect the symmetries of
the polytope P. We present a representation-theoretic framework to study
equivariant psd lifts of a certain class of symmetric polytopes known as
orbitopes. Our main result is a structure theorem where we show that any
equivariant psd lift of size d of an orbitope is of sum-of-squares type where
the functions in the sum-of-squares decomposition come from an invariant
subspace of dimension smaller than d^3. We use this framework to study two
well-known families of polytopes, namely the parity polytope and the cut
polytope, and we prove exponential lower bounds for equivariant psd lifts of
these polytopes.Comment: v2: 30 pages, Minor changes in presentation; v3: 29 pages, New
structure theorem for general orbitopes + changes in presentatio
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