1,483 research outputs found
On nonlinear Alfv\'en-cyclotron waves in multi-species plasma
Large-amplitude Alfv\'en waves are ubiquitous in space plasmas and a main
component of magnetohydrodynamic (MHD) turbulence in the heliosphere. As pump
waves they are prone to parametric instability by which they can generate
cyclotron and acoustic daughter waves. Here we revisit a related process within
the framework of the multi-fluid equations for a plasma consisting of many
species. The nonlinear coupling of the Alfv\'en wave to acoustic waves is
studied, and a set of compressive and coupled wave equations for the transverse
magnetic field and longitudinal electric field is derived for waves propagating
along the mean-field direction. It turns out that slightly compressive Alfv\'en
waves exert, through induced gyro-radius and kinetic-energy modulations, an
electromotive force on the particles in association with a longitudinal
electric field, which has a potential that is given by the gradient of the
transverse kinetic energy of the particles gyrating about the mean field. This
in turn drives electric fluctuations (sound and ion-acoustic waves) along the
mean magnetic field, which can nonlinearly react back on the transverse
magnetic field. Mutually coupled Alfv\'en-cyclotron-acoustic waves are thus
excited, a nonlinear process that can drive a cascade of wave energy in the
plasma and may generate compressive microturbulence. These driven electric
fluctuations might have consequences for the dissipation of MHD turbulence and,
thus, for the heating and acceleration of particles in the solar wind.Comment: 19 pages, accepted by Journal of Plasma Physics, in press, Link:
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=7908294&fulltextType=RA&fileId=S002237781000054
The performance of arm locking in LISA
For the laser interferometer space antenna (LISA) to reach it's design
sensitivity, the coupling of the free running laser frequency noise to the
signal readout must be reduced by more than 14 orders of magnitude. One
technique employed to reduce the laser frequency noise will be arm locking,
where the laser frequency is locked to the LISA arm length. This paper details
an implementation of arm locking, studies orbital effects, the impact of errors
in the Doppler knowledge, and noise limits. The noise performance of arm
locking is calculated with the inclusion of the dominant expected noise
sources: ultra stable oscillator (clock) noise, spacecraft motion, and shot
noise. Studying these issues reveals that although dual arm locking [A. Sutton
& D. A Shaddock, Phys. Rev. D 78, 082001 (2008).] has advantages over single
(or common) arm locking in terms of allowing high gain, it has disadvantages in
both laser frequency pulling and noise performance. We address this by
proposing a hybrid sensor, retaining the benefits of common and dual arm
locking sensors. We present a detailed design of an arm locking controller and
perform an analysis of the expected performance when used with and without
laser pre-stabilization. We observe that the sensor phase changes beneficially
near unity-gain frequencies of the arm-locking controller, allowing a factor of
10 more gain than previously believed, without degrading stability. We show
that the LISA frequency noise goal can be realized with arm locking and
Time-Delay Interferometry only, without any form of pre-stabilization.Comment: 28 pages, 36 figure
On uniformization of compact Kähler manifolds with negative first chern class by bounded symmetric domains
Includes bibliographical references.We consider two complementary problems: given a compact Kähler manifold with negative first Chern Class, when is its universal cover a Bounded Symmetric Domain? And if it is, which Bounded Symmetric Domain is it? Existing literature is discussed, with particular attention given to two recent papers of Catanese and Di Scala ([CDS12] and [CDS]) which answer both questions first for Bounded Symmetric Domains of Tube Type, and then for all Bounded Symmetric Domains without Ball Factors. Using work of Yau and others on ball quotients we extend the main result of [CDS] to all bounded Symmetric Domains, including those with ball factors, thus answering the two questions posed in full generality
Adapting Zeroth Order Algorithms for Comparison-Based Optimization
Comparison-Based Optimization (CBO) is an optimization paradigm that assumes
only very limited access to the objective function f(x). Despite the growing
relevance of CBO to real-world applications, this field has received little
attention as compared to the adjacent field of Zeroth-Order Optimization (ZOO).
In this work we propose a relatively simple method for converting ZOO
algorithms to CBO algorithms, thus greatly enlarging the pool of known
algorithms for CBO. Via PyCUTEst, we benchmarked these algorithms against a
suite of unconstrained problems. We then used hyperparameter tuning to
determine optimal values of the parameters of certain algorithms, and utilized
visualization tools such as heat maps and line graphs for purposes of
interpretation. All our code is available at
https://github.com/ishaslavin/Comparison_Based_Optimization.Comment: Pending review at SIUR
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