Numerical simulations of the Fourier transformed Vlasov-Maxwell system in higher dimensions --- Theory and applications

We present a review of recent developments of simulations of the Vlasov-Maxwell system of equations using a Fourier transform method in velocity space. In this method, the distribution functions for electrons and ions are Fourier transformed in velocity space, and the resulting set of equations are solved numerically. In the original Vlasov equation, phase mixing may lead to an oscillatory behavior and sharp gradients of the distribution function in velocity space, which is problematic in simulations where it can lead to unphysical electric fields and instabilities and to the recurrence effect where parts of the initial condition recur in the simulation. The particle distribution function is in general smoother in the Fourier transformed velocity space, which is desirable for the numerical approximations. By designing outflow boundary conditions in the Fourier transformed velocity space, the highest oscillating terms are allowed to propagate out through the boundary and are removed from the calculations, thereby strongly reducing the numerical recurrence effect. The outflow boundary conditions in higher dimensions including electromagnetic effects are discussed. The Fourier transform method is also suitable to solve the Fourier transformed Wigner equation, which is the quantum mechanical analogue of the Vlasov equation for classical particles.Comment: 41 pages, 19 figures. To be published in Transport Theory and Statistical Physics. Proceedings of the VLASOVIA 2009 Workshop, CIRM, Luminy, Marseilles, France, 31 August - 4 September 200

A well-posedness theory in measures for some kinetic models of collective motion

We present existence, uniqueness and continuous dependence results for some kinetic equations motivated by models for the collective behavior of large groups of individuals. Models of this kind have been recently proposed to study the behavior of large groups of animals, such as flocks of birds, swarms, or schools of fish. Our aim is to give a well-posedness theory for general models which possibly include a variety of effects: an interaction through a potential, such as a short-range repulsion and long-range attraction; a velocity-averaging effect where individuals try to adapt their own velocity to that of other individuals in their surroundings; and self-propulsion effects, which take into account effects on one individual that are independent of the others. We develop our theory in a space of measures, using mass transportation distances. As consequences of our theory we show also the convergence of particle systems to their corresponding kinetic equations, and the local-in-time convergence to the hydrodynamic limit for one of the models

Vlasov scaling for stochastic dynamics of continuous systems

We describe a general scheme of derivation of the Vlasov-type equations for Markov evolutions of particle systems in continuum. This scheme is based on a proper scaling of corresponding Markov generators and has an algorithmic realization in terms of related hierarchical chains of correlation functions equations. Several examples of the realization of the proposed approach in particular models are presented.Comment: 23 page

Vlasov equation for long-range interactions on a lattice

We show that, in the continuum limit, the dynamics of Hamiltonian systems defined on a lattice with long-range couplings is well described by the Vlasov equation. This equation can be linearized around the homogeneous state and a dispersion relation, that depends explicitly on the Fourier modes of the lattice, can be derived. This allows one to compute the stability thresholds of the homogeneous state, which turn out to depend on the mode number. When this state is unstable, the growth rates are also function of the mode number. Explicit calculations are performed for the $\alpha$-HMF model with $0 \leq \alpha <1$, for which the zero mean-field mode is always found to dominate the exponential growth. The theoretical predictions are successfully compared with numerical simulations performed on a finite lattice

First narrow-band search for continuous gravitational waves from known pulsars in advanced detector data

Spinning neutron stars asymmetric with respect to their rotation axis are potential sources of continuous gravitational waves for ground-based interferometric detectors. In the case of known pulsars a fully coherent search, based on matched filtering, which uses the position and rotational parameters obtained from electromagnetic observations, can be carried out. Matched filtering maximizes the signalto- noise (SNR) ratio, but a large sensitivity loss is expected in case of even a very small mismatch between the assumed and the true signal parameters. For this reason, narrow-band analysis methods have been developed, allowing a fully coherent search for gravitational waves from known pulsars over a fraction of a hertz and several spin-down values. In this paper we describe a narrow-band search of 11 pulsars using data from Advanced LIGO’s first observing run. Although we have found several initial outliers, further studies show no significant evidence for the presence of a gravitational wave signal. Finally, we have placed upper limits on the signal strain amplitude lower than the spin-down limit for 5 of the 11 targets over the bands searched; in the case of J1813-1749 the spin-down limit has been beaten for the first time. For an additional 3 targets, the median upper limit across the search bands is below the spin-down limit. This is the most sensitive narrow-band search for continuous gravitational waves carried out so far

Identification and mitigation of narrow spectral artifacts that degrade searches for persistent gravitational waves in the first two observing runs of Advanced LIGO

Searches are under way in Advanced LIGO and Virgo data for persistent gravitational waves from continuous sources, e.g. rapidly rotating galactic neutron stars, and stochastic sources, e.g. relic gravitational waves from the Big Bang or superposition of distant astrophysical events such as mergers of black holes or neutron stars. These searches can be degraded by the presence of narrow spectral artifacts (lines) due to instrumental or environmental disturbances. We describe a variety of methods used for finding, identifying and mitigating these artifacts, illustrated with particular examples. Results are provided in the form of lists of line artifacts that can safely be treated as non-astrophysical. Such lists are used to improve the efficiencies and sensitivities of continuous and stochastic gravitational wave searches by allowing vetoes of false outliers and permitting data cleaning

Identification and mitigation of narrow spectral artifacts that degrade searches for persistent gravitational waves in the first two observing runs of Advanced LIGO

Searches are under way in Advanced LIGO and Virgo data for persistent gravitational waves from continuous sources, e.g. rapidly rotating galactic neutron stars, and stochastic sources, e.g. relic gravitational waves from the Big Bang or superposition of distant astrophysical events such as mergers of black holes or neutron stars. These searches can be degraded by the presence of narrow spectral artifacts (lines) due to instrumental or environmental disturbances. We describe a variety of methods used for finding, identifying and mitigating these artifacts, illustrated with particular examples. Results are provided in the form of lists of line artifacts that can safely be treated as non-astrophysical. Such lists are used to improve the efficiencies and sensitivities of continuous and stochastic gravitational wave searches by allowing vetoes of false outliers and permitting data cleaning.P.B. Covas … H. Cao … W. Kim … E.J. King … J. Munch … D.J. Ottaway … P.J. Veitch … et al. (LSC Instrument Authors

Identification and mitigation of narrow spectral artifacts that degrade searches for persistent gravitational waves in the first two observing runs of Advanced LIGO

Searches are under way in Advanced LIGO and Virgo data for persistent gravitational waves from continuous sources, e.g. rapidly rotating galactic neutron stars, and stochastic sources, e.g. relic gravitational waves from the Big Bang or superposition of distant astrophysical events such as mergers of black holes or neutron stars. These searches can be degraded by the presence of narrow spectral artifacts (lines) due to instrumental or environmental disturbances. We describe a variety of methods used for finding, identifying and mitigating these artifacts, illustrated with particular examples. Results are provided in the form of lists of line artifacts that can safely be treated as non-astrophysical. Such lists are used to improve the efficiencies and sensitivities of continuous and stochastic gravitational wave searches by allowing vetoes of false outliers and permitting data cleaning

Search for post-merger gravitational waves from the remnant of the binary neutron star merger GW170817

In Advanced LIGO, detection and astrophysical source parameter estimation of the binary black hole merger GW150914 requires a calibrated estimate of the gravitational-wave strain sensed by the detectors. Producing an estimate from each detector's differential arm length control loop readout signals requires applying time domain filters, which are designed from a frequency domain model of the detector's gravitational-wave response. The gravitational-wave response model is determined by the detector's opto-mechanical response and the properties of its feedback control system. The measurements used to validate the model and characterize its uncertainty are derived primarily from a dedicated photon radiation pressure actuator, with cross-checks provided by optical and radio frequency references. We describe how the gravitational-wave readout signal is calibrated into equivalent gravitational-wave-induced strain and how the statistical uncertainties and systematic errors are assessed. Detector data collected over 38 calendar days, from September 12 to October 20, 2015, contain the event GW150914 and approximately 16 of coincident data used to estimate the event false alarm probability. The calibration uncertainty is less than 10% in magnitude and 10 degrees in phase across the relevant frequency band 20 Hz to 1 kHz

Identification and mitigation of narrow spectral artifacts that degrade searches for persistent gravitational waves in the first two observing runs of Advanced LIGO

Searches are under way in Advanced LIGO and Virgo data for persistent gravitational waves from continuous sources, e.g. rapidly rotating galactic neutron stars, and stochastic sources, e.g. relic gravitational waves from the Big Bang or superposition of distant astrophysical events such as mergers of black holes or neutron stars. These searches can be degraded by the presence of narrow spectral artifacts (lines) due to instrumental or environmental disturbances. We describe a variety of methods used for finding, identifying and mitigating these artifacts, illustrated with particular examples. Results are provided in the form of lists of line artifacts that can safely be treated as non-astrophysical. Such lists are used to improve the efficiencies and sensitivities of continuous and stochastic gravitational wave searches by allowing vetoes of false outliers and permitting data cleaning.Comment: 21 page