arXiv subjects

Josselin Garnier

Publications and source records attributed to Josselin Garnier.

At least 91 records · Page 5Linked to original sources

arXiv2020

Multiscale analysis of spectral broadening of acoustic waves by a turbulent shear layer

We consider the scattering of acoustic waves emitted by an active source above a plane turbulent shear layer. The layer is modeled by a moving random medium with small spatial and temporal fluctuations of its mean velocity, and constant density and speed of sound. We develop a multi-scale perturbative analysis for the acoustic pressure field transmitted by the layer and derive its power spectral density when the correlation function of the velocity fluctuations is known. Our aim is to compare the proposed analytical model with some experimental results obtained for jet flows in open wind tunnels. We start with the Euler equations for an ideal fluid flow and linearize them about an ambient, unsteady inhomogeneous flow. We study the transmitted pressure field without fluctuations of the ambient flow velocity to obtain the Green's function of the unperturbed medium with constant characteristics. Then we use a Lippmann-Schwinger equation to derive an analytical expression of the transmitted pressure field, as a function of the velocity fluctuations within the layer. Its power spectral density is subsequently computed invoking a stationary-phase argument, assuming in addition that the source is time-harmonic and the layer is thin. We finally study the influence of the source tone frequency and ambient flow velocity on the power spectral density of the transmitted pressure field and compare our results with other analytical models and experimental data.

physics.flu-dyn↗

arXiv2020

Intensity fluctuations in random waveguides

An asymptotic analysis of wave propagation in randomly perturbed waveguides is carried out in order to identify the effective Markovian dynamics of the guided mode powers. The main result consists in a quantification of the fluctuations of the mode powers and wave intensities that increase exponentially with the propagation distance. The exponential growth rate is studied in detail so as to determine its dependence with respect to the waveguide geometry, the statistics of the random perturbations, and the operating wavelength.

math.AP↗

arXiv2019

Multiplexing schemes for optical communication through atmospheric turbulence

A central question in free-space optical communications is how to improve the transfer of information between a transmitter and receiver. The capacity of the communication channel can be increased by multiplexing of independent modes using either: (1) the MIMO (Multiple-Input-Multiple- Output) approach, where the communication is done with modes obtained from the singular value decomposition of the transfer matrix from the transmitter array to the receiver array, or (2) the OAM (Orbital Angular Momentum) approach, which uses vortex beams that carry angular momenta. In both cases, the number of usable modes is limited by the finite aperture of the transmitter and receiver, and the effect of the turbulent atmosphere. The goal of this paper is twofold: First, we show that the MIMO and OAM multiplexing schemes are closely related. Specifically, in the case of circular apertures, the usable singular modes of the transfer matrix are essentially the same as the commonly used Laguerre-Gauss vortex beams, provided these have a special radius that depends on the wavelength, the distance from the transmitter to the receiver and the ratio of the radii of their apertures. Second, we study the effect of atmospheric turbulence on the communication modes using the phase screen method put in the mathematical framework of beam propagation in random media.

eess.SP↗

arXiv2019

How a moving passive observer can perceive its environment ? The Unruh effect revisited

We consider a point-like observer that moves in a medium illuminated by noise sources with Lorentz-invariant spectrum. We show that the autocorrelation function of the signal recorded by the observer allows it to perceive its environment. More precisely, we consider an observer with constant acceleration (along a Rindler trajectory) and we exploit the recent work on the emergence of the Green's function from the cross correlation of signals transmitted by noise sources. First we recover the result that the signal recorded by the observer has a constant Wigner transform, i.e. a constant local spectrum, when the medium is homogeneous (this is the classical analogue of the Unruh effect). We complete that result by showing that the Rindler trajectory is the only straight-line trajectory that satisfies this property. We also show that, in the presence of an obstacle in the form of an infinite perfect mirror, the Wigner transform is perturbed when the observer comes into the neighborhood of the obstacle. The perturbation makes it possible for the observer to determine its position relative to the obstacle once the entire trajectory has been traversed.

math.AP↗

arXiv2019

High-Resolution Interferometric Synthetic Aperture Imaging in scattering media

The goal of synthetic aperture imaging is to estimate the reflectivity of a remote region of interest by processing data gathered with a moving sensor which emits periodically a signal and records the backscattered wave. We introduce and analyze a high-resolution interferometric method for synthetic aperture imaging through an unknown scattering medium which distorts the wave. The method builds on the coherent interferometric (CINT) approach which uses empirical cross-correlations of the measurements to mitigate the distortion, at the expense of a loss of resolution of the image. The new method shows that, while mitigating the wave distortion, it is possible to obtain a robust and sharp estimate of the modulus of the Fourier transform of the reflectivity function. A high-resolution image can then be obtained by a phase retrieval algorithm.

eess.IV↗

arXiv2019

Emergence of Turbulent Epochs in Oil Prices

Oil price data have a complicated multi-scale structure that may vary with time. We use time-frequency analysis to identify the main features of these variations and, in particular, the regime shifts. The analysis is based on a wavelet-based decomposition and analysis of the associated scale spectrum. The joint estimation of the local Hurst exponent and volatility is the key to detect and identify regime shifting and switching of the oil price. The framework involves in particular modeling in terms of a process of `multi-fractional' type so that both the roughness and the volatility of the price process may vary with time. Special epochs then emerge as a result of these degrees of freedom, moreover, as a result of the special type of spectral estimator used. These special epochs are discussed and related to historical events. Some of them are not detected by standard analysis based on maximum likelihood estimation. The paper presents a novel algorithm for robust detection of such special epochs and multi-fractional behavior in financial or other types of data. In the financial context insight about such behavior of the asset price is important to evaluate financial contracts involving the asset.

q-fin.ST↗

arXiv2019

Chaos and Order in the Bitcoin Market

The bitcoin price has surged in recent years and it has also exhibited phases of rapid decay. In this paper we address the question to what extent this novel cryptocurrency market can be viewed as a classic or semi-efficient market. Novel and robust tools for estimation of multi-fractal properties are used to show that the bitcoin price exhibits a very interesting multi-scale correlation structure. This structure can be described by a power-law behavior of the variances of the returns as functions of time increments and it can be characterized by two parameters, the volatility and the Hurst exponent. These power-law parameters, however, vary in time. A new notion of generalized Hurst exponent is introduced which allows us to check if the multi-fractal character of the underlying signal is well captured. It is moreover shown how the monitoring of the power-law parameters can be used to identify regime shifts for the bitcoin price. A novel technique for identifying the regimes switches based on a goodness of fit of the local power-law parameters is presented. It automatically detects dates associated with some known events in the bitcoin market place. A very surprising result is moreover that, despite the wild ride of the bitcoin price in recent years and its multi-fractal and non-stationary character, this price has both local power-law behaviors and a very orderly correlation structure when it is observed on its entire period of existence.

q-fin.ST↗

arXiv2018

Acoustic and geoacoustic inverse problems in randomly perturbed shallow-water environments

The main goal of this paper is to estimate the regional acoustic and geoacoustic shallow-water environment from data collected by a vertical hydrophone array and transmitted by distant time-harmonic point sources. We aim at estimating the statistical properties of the random fluctuations of the index of refraction in the water column and the characteristics of the sea bottom. We first explain from first principles how acoustic wave propagation can be expressed as Markovian dynamics for the complex mode amplitudes of the sound pressure, which makes it possible to express the cross moments of the sound pressure in terms of the parameters to be estimated. We then show how the estimation problem can be formulated as a nonlinear inverse problem using this formulation, that can be solved by minimization of a misfit function. We apply this method to experimental data collected by the ALMA system (Acoustic Laboratory for Marine Applications).

math.AP↗

arXiv2018

Wave propagation in randomly perturbed weakly coupled waveguides

We present an analysis of wave propagation in a two step-index, parallel waveguide system. The goal is to quantify the effect of scattering at randomly perturbed interfaces between the guiding layers of high index of refraction and the host medium. The analysis is based on the expansion of the solution of the wave equation in a complete set of guided, radiation and evanescent modes with amplitudes that are random fields, due to scattering. We obtain a detailed characterization of these amplitudes and thus quantify the transfer of power between the two waveguides in terms of their separation distance. The results show that, no matter how small the fluctuations of the interfaces are, they have significant effect at sufficiently large distance of propagation, which manifests in two ways: The first effect is well known and consists of power leakage from the guided modes to the radiation ones. The second effect consists of blurring of the periodic transfer of power between the waveguides and the eventual equipartition of power. Its quantification is the main practical result of the paper.

math.AP↗

arXiv2018

Efficient Seismic fragility curve estimation by Active Learning on Support Vector Machines

Fragility curves which express the failure probability of a structure, or critical components, as function of a loading intensity measure are nowadays widely used (i) in Seismic Probabilistic Risk Assessment studies, (ii) to evaluate impact of construction details on the structural performance of installations under seismic excitations or under other loading sources such as wind. To avoid the use of parametric models such as lognormal model to estimate fragility curves from a reduced number of numerical calculations, a methodology based on Support Vector Machines coupled with an active learning algorithm is proposed in this paper. In practice, input excitation is reduced to some relevant parameters and, given these parameters, SVMs are used for a binary classification of the structural responses relative to a limit threshold of exceedance. Since the output is not only binary, this is a score, a probabilistic interpretation of the output is exploited to estimate very efficiently fragility curves as score functions or as functions of classical seismic intensity measures.

cs.LG↗

arXiv2018

A ghost imaging modality in a random waveguide

We study the imaging of a penetrable scatterer, aka target, in a waveguide with randomly perturbed boundary. The target is located between a partially coherent source which transmits the wave, and a detector which measures the spatially integrated energy flux of the wave. The imaging is impeded by random boundary scattering effects that accumulate as the wave propagates. We consider a very large distance (range) between the target and the detector, where that cumulative scattering is so strong that it distributes the energy evenly among the components (modes) of the wave. Conventional imaging is impossible in this equipartition regime. Nevertheless, we show that the target can be located with a ghost imaging modality. This forms an image using the cross-correlation of the measured energy flux, integrated over the aperture of the detector, with the time and space resolved energy flux in a reference waveguide, at the search range. We consider two reference waveguides: The waveguide with unperturbed boundary, in which we can calculate the energy flux, and the actual random waveguide, before the presence of the target, in which the energy flux should be measured. We analyze the ghost imaging modality from first principles and show that it can be efficient in a random waveguide geometry in which there is both strong modal dispersion and mode coupling induced by scattering, provided that the standard ghost imaging function is modified and integrated over a suitable time offset window in order to compensate for dispersion and diffusion. The analysis quantifies the resolution of the image in terms of the source and detector aperture, the range offset between the source and the target, and the duration of the measurements.

math.AP↗

arXiv2018

Imaging through a scattering medium by speckle intensity correlations

In this paper we analyze an imaging technique based on intensity speckle correlations over incident field position proposed in [J. A. Newmann and K. J. Webb, Phys. Rev. Lett. 113, 263903 (2014)]. Its purpose is to reconstruct a field incident on a strongly scattering random medium. The thickness of the complex medium is much larger than the scattering mean free path so that the wave emerging from the random section forms an incoherent speckle pattern. Our analysis clarifies the conditions under which the method can give a good reconstruction and characterizes its performance. The analysis is carried out in the white-noise paraxial regime, which is relevant for the applications in optics that motivated the original paper.

math.AP↗

arXiv2018

Wave propagation and imaging in moving random media

We present a study of sound wave propagation in a time dependent random medium and an application to imaging. The medium is modeled by small temporal and spatial random fluctuations in the wave speed and density, and it moves due to an ambient flow. We develop a transport theory for the energy density of the waves, in a forward scattering regime, within a cone (beam) of propagation with small opening angle. We apply the transport theory to the inverse problem of estimating a stationary wave source from measurements at a remote array of receivers. The estimation requires knowledge of the mean velocity of the ambient flow and the second-order statistics of the random medium. If these are not known, we show how they may be estimated from additional measurements gathered at the array, using a few known sources. We also show how the transport theory can be used to estimate the mean velocity of the medium. If the array has large aperture and the scattering in the random medium is strong, this estimate does not depend on the knowledge of the statistics of the random medium.

math.AP↗

arXiv2018

Option pricing under fast-varying long-memory stochastic volatility

Recent empirical studies suggest that the volatility of an underlying price process may have correlations that decay slowly under certain market conditions. In this paper, the volatility is modeled as a stationary process with long-range correlation properties in order to capture such a situation, and we consider European option pricing. This means that the volatility process is neither a Markov process nor a martingale. However, by exploiting the fact that the price process is still a semimartingale and accordingly using the martingale method, we can obtain an analytical expression for the option price in the regime where the volatility process is fast mean-reverting. The volatility process is modeled as a smooth and bounded function of a fractional Ornstein-Uhlenbeck process. We give the expression for the implied volatility, which has a fractional term structure.

q-fin.PR↗

arXiv2018

Option Pricing under Fast-varying and Rough Stochastic Volatility

Recent empirical studies suggest that the volatilities associated with financial time series exhibit short-range correlations. This entails that the volatility process is very rough and its autocorrelation exhibits sharp decay at the origin. Another classic stylistic feature often assumed for the volatility is that it is mean reverting. In this paper it is shown that the price impact of a rapidly mean reverting rough volatility model coincides with that associated with fast mean reverting Markov stochastic volatility models. This reconciles the empirical observation of rough volatility paths with the good fit of the implied volatility surface to models of fast mean reverting Markov volatilities. Moreover, the result conforms with recent numerical results regarding rough stochastic volatility models. It extends the scope of models for which the asymptotic results of fast mean reverting Markov volatilities are valid. The paper concludes with a general discussion of fractional volatility asymptotics and their interrelation. The regimes discussed there include fast and slow volatility factors with strong or small volatility fluctuations and with the limits not commuting in general. The notion of a characteristic term structure exponent is introduced, this exponent governs the implied volatility term structure in the various asymptotic regimes.

q-fin.PR↗

arXiv2018

Mean Field Model for Collective Motion Bistability

We consider the Czirók model for collective motion of locusts along a one-dimensional torus. In the model, each agent's velocity locally interacts with other agents' velocities in the system, and there is also exogenous randomness to each agent's velocity. The interaction tends to create the alignment of collective motion. By analyzing the associated nonlinear Fokker-Planck equation, we obtain the condition for the existence of stationary order states and the conditions for their linear stability. These conditions depend on the noise level, which should be strong enough, and on the interaction between the agent's velocities, which should be neither too small, nor too strong. We carry out the fluctuation analysis of the interacting system and describe the large deviation principle to calculate the transition probability from one order state to the other. Numerical simulations confirm our analytical findings.

math.AP↗

arXiv2018

Non-invasive imaging through random media

When waves propagate through a strongly scattering medium the energy is transferred to the incoherent wave part by scattering. The wave intensity then forms a random speckle pattern seemingly without much useful information. However, a number of recent physical experiments show how one can extract useful information from this speckle pattern. Here we present the mathematical analysis that explains the quite stunning performance of such a scheme for speckle imaging. Our analysis identifies a scaling regime where the scheme works well. This regime is the white-noise paraxial regime, which leads to the Ito-Schrodinger model for the wave amplitude. The results presented in this paper conform with the sophisticated physical intuition that has motivated these schemes, but give a more detailed characterization of the performance. The analysis gives a description of (i) the information that can be extracted and with what resolution (ii) the statistical stability or signal-to-noise ratio with which the information can be extracted.

physics.optics↗

arXiv2017

Efficient sequential experimental design for surrogate modeling of nested codes

Thanks to computing power increase, the certification and the conception of complex systems relies more and more on simulation. To this end, predictive codes are needed, which have generally to be evaluated in a huge number of input points. When the computational cost of these codes is high, surrogate models are introduced to emulate the response of these codes. In this paper, we consider the situation when the system response can be modeled by two nested computer codes. By two nested computer codes, we mean that some inputs of the second code are outputs of the first code. More precisely, the idea is to propose sequential designs to improve the accuracy of the nested code's predictor by exploiting the nested structure of the codes. In particular, a selection criterion is proposed to allow the modeler to choose the code to call, depending on the expected learning rate and the computational cost of each code. The sequential designs are based on the minimization of the prediction variance, so adaptations of the Gaussian process formalism are proposed for this particular configuration in order to quickly evaluate the mean and the variance of the predictor. The proposed methods are then applied to examples.

stat.ME↗