arXiv subjects

David Cohen

Publications and source records attributed to David Cohen.

At least 37 records · Page 2Linked to original sources

arXiv2021

Towards optomechanical parametric instabilities prediction in ground-based gravitational wave detectors

Increasing the laser power is essential to improve the sensitivity of interferometric gravitational wave detectors. However, optomechanical parametric instabilities can set a limit to that power. It is of major importance to understand and characterize the many parameters and effects that influence these instabilities. Here, we model with a high degree of precision the optical and mechanical modes that are involved in these parametric instabilities, such that our model can become predictive. As an example, we perform simulations for the Advanced Virgo interferometer (O3 configuration). In particular we compute mechanical modes losses by combining both on-site measurements and finite element analysis with unprecedented level of detail and accuracy. We also study the influence on optical modes and parametric gains of mirror finite size effects, and mirror deformations due to thermal absorption. We show that these effects play an important role if transverse optical modes of order higher than four are involved in the instability process.

astro-ph.IM↗

arXiv2021

Drift-preserving numerical integrators for stochastic Poisson systems

We perform a numerical analysis of a class of randomly perturbed {H}amiltonian systems and {P}oisson systems. For the considered additive noise perturbation of such systems, we show the long time behavior of the energy and quadratic Casimirs for the exact solution. We then propose and analyze a drift-preserving splitting scheme for such problems with the following properties: exact drift preservation of energy and quadratic Casimirs, mean-square order of convergence one, weak order of convergence two. These properties are illustrated with numerical experiments.

math.NA↗

arXiv2021

Numerical approximation and simulation of the stochastic wave equation on the sphere

Solutions to the stochastic wave equation on the unit sphere are approximated by spectral methods. Strong, weak, and almost sure convergence rates for the proposed numerical schemes are provided and shown to depend only on the smoothness of the driving noise and the initial conditions. Numerical experiments confirm the theoretical rates. The developed numerical method is extended to stochastic wave equations on higher-dimensional spheres and to the free stochastic Schrödinger equation on the unit sphere.

math.NA↗

arXiv2020

Strong rates of convergence of a splitting scheme for Schrödinger equations with nonlocal interaction cubic nonlinearity and white noise dispersion

We analyse a splitting integrator for the time discretization of the Schrödinger equation with nonlocal interaction cubic nonlinearity and white noise dispersion. We prove that this time integrator has order of convergence one in the $p$-th mean sense, for any $p\geq1$ in some Sobolev spaces. We prove that the splitting schemes preserves the $L^2$-norm, which is a crucial property for the proof of the strong convergence result. Finally, numerical experiments illustrate the performance of the proposed numerical scheme.

math.NA↗

arXiv2020

Lie-Trotter Splitting for the Nonlinear Stochastic Manakov System

This article analyses the convergence of the Lie-Trotter splitting scheme for the stochastic Manakov equation, a system arising in the study of pulse propagation in randomly birefringent optical fibers. First, we prove that the strong order of the numerical approximation is 1/2 if the nonlinear term in the system is globally Lipschitz. Then, we show that the splitting scheme has convergence order 1/2 in probability and almost sure order 1/2- in the case of a cubic nonlinearity. We provide several numerical experiments illustrating the aforementioned results and the efficiency of the Lie-Trotter splitting scheme. Finally, we numerically investigate the possible blowup of solutions for some power-law nonlinearities.

math.AP↗

arXiv2020

High order numerical integrators for single integrand Stratonovich SDEs

We show that applying any deterministic B-series method of order $p_d$ with a random step size to single integrand SDEs gives a numerical method converging in the mean-square and weak sense with order $\lfloor p_d/2\rfloor$.As an application, we derive high order energy-preserving methods for stochastic Poisson systems as well as further geometric numerical schemes for this wide class of Stratonovich SDEs.

math.NA↗

arXiv2020

Exponential integrators for the stochastic Manakov equation

This article presents and analyses an exponential integrator for the stochastic Manakov equation, a system arising in the study of pulse propagation in randomly birefringent optical fibers. We first prove that the strong order of the numerical approximation is $1/2$ if the nonlinear term in the system is globally Lipschitz-continuous. Then, we use this fact to prove that the exponential integrator has convergence order $1/2$ in probability and almost sure order $1/2$, in the case of the cubic nonlinear coupling which is relevant in optical fibers. Finally, we present several numerical experiments in order to support our theoretical findings and to illustrate the efficiency of the exponential integrator as well as a modified version of it.

math.NA↗

arXiv2020

Drift-preserving numerical integrators for stochastic Hamiltonian systems

The paper deals with numerical discretizations of separable nonlinear Hamiltonian systems with additive noise. For such problems, the expected value of the total energy, along the exact solution, drifts linearly with time. We present and analyze a time integrator having the same property for all times. Furthermore, strong and weak convergence of the numerical scheme along with efficient multilevel Monte Carlo estimators are studied. Finally, extensive numerical experiments illustrate the performance of the proposed numerical scheme.

math.NA↗

arXiv2019

KELT-23Ab: A Hot Jupiter Transiting a Near-Solar Twin Close to the TESS and JWST Continuous Viewing Zones

We announce the discovery of KELT-23Ab, a hot Jupiter transiting the relatively bright ($V=10.3$) star BD+66 911 (TYC 4187-996-1), and characterize the system using follow-up photometry and spectroscopy. A global fit to the system yields host-star properties of $T_{eff}=5900\pm49 K$, $M_*=0.945^{+0.060}_{-0.054} M_{\odot}$, $R_*=0.995\pm0.015 R_{\odot}$, $L_*=1.082^{+0.051}_{-0.048} L_{\odot}$, log$g_{*}=4.418^{+0.026}_{-0.025}$ (cgs), and $\left[{\rm Fe}/{\rm H}\right]=-0.105\pm0.077$. KELT-23Ab is a hot Jupiter with mass $M_P=0.938^{+0.045}_{-0.042} M_{\rm J}$, radius $R_P=1.322\pm0.025 R_{\rm J}$, and density $ρ_P=0.504^{+0.038}_{-0.035}$ g cm$^{-3}$. Intense insolation flux from the star has likely caused KELT-23Ab to become inflated. The time of inferior conjunction is $T_0=2458149.40776\pm0.00091~\rm {BJD_{TDB}}$ and the orbital period is $P=2.255353^{+0.000031}_{-0.000030}$ days. There is strong evidence that KELT-23A is a member of a long-period binary star system with a less luminous companion, and due to tidal interactions, the planet is likely to spiral into its host within roughly a Gyr. This system has one of the highest positive ecliptic latitudes of all transiting planet hosts known to date, placing it near the Transiting Planet Survey Satellite and James Webb Space Telescope continuous viewing zones. Thus we expect it to be an excellent candidate for long-term monitoring and follow-up with these facilities.

astro-ph.EP↗

arXiv2019

Exponential Integrators for Stochastic Maxwell's Equations Driven by Itô Noise

This article presents explicit exponential integrators for stochastic Maxwell's equations driven by both multiplicative and additive noises. By utilizing the regularity estimate of the mild solution, we first prove that the strong order of the numerical approximation is $\frac 12$ for general multiplicative noise. Combing a proper decomposition with the stochastic Fubini's theorem, the strong order of the proposed scheme is shown to be $1$ for additive noise. Moreover, for linear stochastic Maxwell's equation with additive noise, the proposed time integrator is shown to preserve exactly the symplectic structure, the evolution of the energy as well as the evolution of the divergence in the sense of expectation. Several numerical experiments are presented in order to verify our theoretical findings.

math.NA↗

arXiv2017

A fully discrete approximation of the one-dimensional stochastic heat equation

A fully discrete approximation of the one-dimensional stochastic heat equation driven by multiplicative space-time white noise is presented. The standard finite difference approximation is used in space and a stochastic exponential method is used for the temporal approximation. Observe that the proposed exponential scheme does not suffer from any kind of CFL-type step size restriction. When the drift term and the diffusion coefficient are assumed to be globally Lipschitz, this explicit time integrator allows for error bounds in $L^q(Ω)$, for all $q\geq2$, improving some existing results in the literature. On top of this, we also prove almost sure convergence of the numerical scheme. In the case of non-globally Lipschitz coefficients, we provide sufficient conditions under which the numerical solution converges in probability to the exact solution. Numerical experiments are presented to illustrate the theoretical results.

math.NA↗

arXiv2017

High Resolution FDMA MIMO Radar

Traditional multiple input multiple output radars, which transmit orthogonal coded waveforms, suffer from range-azimuth resolution trade-off. In this work, we adopt a frequency division multiple access (FDMA) approach that breaks this conflict. We combine narrow individual bandwidth for high azimuth resolution and large overall total bandwidth for high range resolution. We process all channels jointly to overcome the FDMA range resolution limitation to a single bandwidth, and address range-azimuth coupling using a random array configuration.

eess.SP↗

arXiv2017

Geometric numerical integrators for Hunter-Saxton-like equations

We present novel geometric numerical integrators for Hunter--Saxton-like equations by means of new multi-symplectic formulations and known Hamiltonian structures of the problems. We consider the Hunter--Saxton equation, the modified Hunter--Saxton equation, and the two-component Hunter--Saxton equation. Multi-symplectic discretisations based on these new formulations of the problems are exemplified by means of the explicit Euler box scheme, and Hamiltonian-preserving discretisations are exemplified by means of the discrete variational derivative method. We explain and justify the correct treatment of boundary conditions in a unified manner. This is necessary for a proper numerical implementation of these equations and was never explicitly clarified in the literature before, to the best of our knowledge. Finally, numerical experiments demonstrate the favourable behaviour of the proposed numerical integrators.

math.NA↗

arXiv2016

On the Existence of Synchrostates in Multichannel EEG Signals during Face-perception Tasks

Phase synchronisation in multichannel EEG is known as the manifestation of functional brain connectivity. Traditional phase synchronisation studies are mostly based on time average synchrony measures hence do not preserve the temporal evolution of the phase difference. Here we propose a new method to show the existence of a small set of unique phase synchronised patterns or "states" in multi-channel EEG recordings, each "state" being stable of the order of ms, from typical and pathological subjects during face perception tasks. The proposed methodology bridges the concepts of EEG microstates and phase synchronisation in time and frequency domain respectively. The analysis is reported for four groups of children including typical, Autism Spectrum Disorder (ASD), low and high anxiety subjects - a total of 44 subjects. In all cases, we observe consistent existence of these states - termed as synchrostates - within specific cognition related frequency bands (beta and gamma bands), though the topographies of these synchrostates differ for different subject groups with different pathological conditions. The inter-synchrostate switching follows a well-defined sequence capturing the underlying inter-electrode phase relation dynamics in stimulus- and person-centric manner. Our study is motivated from the well-known EEG microstate exhibiting stable potential maps over the scalp. However, here we report a similar observation of quasi-stable phase synchronised states in multichannel EEG. The existence of the synchrostates coupled with their unique switching sequence characteristics could be considered as a potentially new field over contemporary EEG phase synchronisation studies.

physics.med-ph↗

arXiv2016

SUMMeR: Sub-Nyquist MIMO Radar

Multiple input multiple output (MIMO) radar exhibits several advantages with respect to traditional radar array systems in terms of flexibility and performance. However, MIMO radar poses new challenges for both hardware design and digital processing. In particular, achieving high azimuth resolution requires a large number of transmit and receive antennas. In addition, the digital processing is performed on samples of the received signal, from each transmitter to each receiver, at its Nyquist rate, which can be prohibitively large when high resolution is needed. Overcoming the rate bottleneck, sub-Nyquist sampling methods have been proposed that break the link between radar signal bandwidth and sampling rate. In this work, we extend these methods to MIMO configurations and propose a sub-Nyquist MIMO radar (SUMMeR) system that performs both time and spatial compression. We present a range-azimuth-Doppler recovery algorithm from sub-Nyquist samples obtained from a reduced number of transmitters and receivers, that exploits the sparsity of the recovered targets' parameters. This allows us to achieve reduction in the number of deployed antennas and the number of samples per receiver, without degrading the time and spatial resolutions. Simulations illustrate the detection performance of SUMMeR for different compression levels and shows that both time and spatial resolution are preserved, with respect to classic Nyquist MIMO configurations. We also examine the impact of design parameters, such as antennas' locations and carrier frequencies, on the detection performance, and provide guidelines for their choice.

cs.IT↗

arXiv2016

Cognitive Sub-Nyquist Hardware Prototype of a Collocated MIMO Radar

We present the design and hardware implementation of a radar prototype that demonstrates the principle of a sub-Nyquist collocated multiple-input multiple-output (MIMO) radar. The setup allows sampling in both spatial and spectral domains at rates much lower than dictated by the Nyquist sampling theorem. Our prototype realizes an X-band MIMO radar that can be configured to have a maximum of 8 transmit and 10 receive antenna elements. We use frequency division multiplexing (FDM) to achieve the orthogonality of MIMO waveforms and apply the Xampling framework for signal recovery. The prototype also implements a cognitive transmission scheme where each transmit waveform is restricted to those pre-determined subbands of the full signal bandwidth that the receiver samples and processes. Real-time experiments show reasonable recovery performance while operating as a 4x5 thinned random array wherein the combined spatial and spectral sampling factor reduction is 87.5% of that of a filled 8x10 array.

cs.IT↗

arXiv2016

X-ray emission from magnetic massive stars

Magnetically confined winds of early-type stars are expected to be sources of bright and hard X-rays. To clarify the systematics of the observed X-ray properties, we have analyzed a large series of Chandra and XMM observations, corresponding to all available exposures of known massive magnetic stars (over 100 exposures covering ~60% of stars compiled in the catalog of Petit et al. 2013). We show that the X-ray luminosity is strongly correlated with the stellar wind mass-loss-rate, with a power-law form that is slightly steeper than linear for the majority of the less luminous, lower-Mdot B stars and flattens for the more luminous, higher-Mdot O stars. As the winds are radiatively driven, these scalings can be equivalently written as relations with the bolometric luminosity. The observed X-ray luminosities, and their trend with mass-loss rates, are well reproduced by new MHD models, although a few overluminous stars (mostly rapidly rotating objects) exist. No relation is found between other X-ray properties (plasma temperature, absorption) and stellar or magnetic parameters, contrary to expectations (e.g. higher temperature for stronger mass-loss rate). This suggests that the main driver for the plasma properties is different from the main determinant of the X-ray luminosity. Finally, variations of the X-ray hardnesses and luminosities, in phase with the stellar rotation period, are detected for some objects and they suggest some temperature stratification to exist in massive stars' magnetospheres.

astro-ph.SR↗

arXiv2016

Exponential integrators for stochastic Schrödinger equations driven by Ito noise

We study an explicit exponential scheme for the time discretisation of stochastic Schrödinger equations driven by additive or multiplicative Ito noise. The numerical scheme is shown to converge with strong order $1$ if the noise is additive and with strong order $1/2$ for multiplicative noise. In addition, if the noise is additive, we show that the exact solutions of our problems satisfy trace formulas for the expected mass, energy, and momentum (i.e., linear drifts in these quantities). Furthermore, we inspect the behaviour of the numerical solutions with respect to these trace formulas. Several numerical simulations are presented and confirm our theoretical results.

math.NA↗