Signal to Noise Ratio estimation in passive correlation-based imaging

We consider imaging with passive arrays of sensors using as illumination ambient noise sources. The first step for imaging under such circumstances is the computation of the cross correlations of the recorded signals, which have attracted a lot of attention recently because of their numerous applications in seismic imaging, volcano monitoring, and petroleum prospecting. Here, we use these cross correlations for imaging reflectors with travel-time migration. While the resolution of the image obtained this way has been studied in detail, an analysis of the signal-to-noise ratio (SNR) is presented in this paper along with numerical simulations that support the theoretical results. It is shown that the SNR of the image inherits the SNR of the computed cross correlations and therefore it is proportional to the square root of the bandwidth of the noise sources times the recording time. Moreover, the SNR of the image is proportional to the array size. This means that the image can be stabilized by increasing the size of the array when the recorded signals are not of long duration, which is important in applications such as non-destructive testing

Evolution PDEs and augmented eigenfunctions. I finite interval

The so-called unified method expresses the solution of an initial-boundary value problem for an evolution PDE in the finite interval in terms of an integral in the complex Fourier (spectral) plane. Simple initial-boundary value problems, which will be referred to as problems of type~I, can be solved via a classical transform pair. For example, the Dirichlet problem of the heat equation can be solved in terms of the transform pair associated with the Fourier sine series. Such transform pairs can be constructed via the spectral analysis of the associated spatial operator. For more complicated initial-boundary value problems, which will be referred to as problems of type~II, there does \emph{not} exist a classical transform pair and the solution \emph{cannot} be expressed in terms of an infinite series. Here we pose and answer two related questions: first, does there exist a (non-classical) transform pair capable of solving a type~II problem, and second, can this transform pair be constructed via spectral analysis? The answer to both of these questions is positive and this motivates the introduction of a novel class of spectral entities. We call these spectral entities augmented eigenfunctions, to distinguish them from the generalised eigenfunctions introduced in the sixties by Gel'fand and his co-authors

The problem of dynamic cavitation in nonlinear elasticity

The notion of singular limiting induced from continuum solutions (slic-solutions) is applied to the problem of cavitation in nonlinear elasticity, in order to re-assess an example of non-uniqueness of entropic weak solutions (with polyconvex energy) due to a forming cavity

Inversions of Statistical Parameters of an Acoustic Signal in Range-dependent Environments with Applications in Ocean Acoustic Tomography

The paper presents an application of a method for the characterization of underwater acoustic signals based on the statistics of their wavelet transform sub-band coefficients in range-dependent environments. As it was illustrated in previous works, this statistical characterization scheme is a very efficient tool for obtaining observables to be exploited in problems of ocean acoustic tomography and geoacoustic inversion, when range-independent environments are considered. Now the scheme is applied in range-dependent environments for the estimation of range-dependent features in shallow water. A simple denoising strategy, also presented in the paper, is shown to enhance the quality of the inversion results, as it helps to keep the signal characterization to the energy significant part of it. The results presented for typical test cases are encouraging and indicative of the potential of the method for the treatment of inverse problems in acoustical oceanography

Structure and Dynamics of Poly(methyl-methacrylate)/Graphene systems through Atomistic Molecular Dynamics Simulations

The main goal of the present work is to examine the effect of graphene layers on the sructural and dynamical properties of polymer systems. We study hybrid poly(methyl methacrylate) (PMMA)/graphene interfacial systems, through detailed atomistic molecular dynamics (MD) simulations. In order to characterize the interface, various properties related to density, structure and dynamics of polymer chains are calculated, as a function of the distance from the substrate. A series of different hybrid systems, with width ranging between [2.60 – 13.35] nm, are being modeled. In addition, we compare the properties of the macromolecular chains to the properties of the orresponding bulk system at the same temperature. We observe a strong effect of graphene layers on both structure and dynamics of the PMMA chains. Furthermore the PMMA/graphene interface is characterized by different length scales, depending on the actual property we probe: Density of PMMA polymer chains is larger than the bulk value, for polymer chains close to graphene layers up to distances of about [1.0-1.5]nm. Chain conformations are perturbed for distances up to about 2-3 radius of gyration from graphene. Segmental dynamics of PMMA is much slower close to the solid layers up to about [2-3]nm. Finally terminal-chain dynamics is slower, compared to the bulk one, up to distances of about 5-7 radius of gyration

Selective imaging of extended reflectors in a two-dimensional waveguide

We consider the problem of selective imaging extended reflectors in waveguides using the response matrix of the scattered field obtained with an active array. Selective imaging amounts to being able to focus at the edges of a reflector which typically give raise to weaker echoes than those coming from its main body. To this end, we propose a selective imaging method that uses projections on low rank subspaces of a weighted modal projection of the array response matrix, $\widehat{\mathbb{P}}(\omega)$. We analyze theoretically our imaging method for a simplified model problem where the scatterer is a vertical one-dimensional perfect reflector. In this case, we show that the rank of $\widehat{\mathbb{P}}(\omega)$ equals the size of the reflector devided by the cross-range array resolution which is $\lambda/2$ for an array spanning the whole depth of the waveguide. We also derive analytic expressions for the singular vectors of $\widehat{\mathbb{P}}(\omega)$ which allows us to show how selective imaging can be achieved. Our numerical simulations are in very good agreement with the theory and illustrate the robustness of our imaging functional for reflectors of various shapes

Dynamics of various Polymer/Graphene Interfacial Systems through Atomistic Molecular Dynamics Simulations

The current work refers to a simulation study on hybrid polymer/graphene interfacial systems. We explore the effect of graphene on the mobility of polymers, by studying three well known and widely used polymers, polyethylene (PE), polystyrene (PS) and poly(methyl-methacrylate) (PMMA). Qualitative and quantitative differences in the dynamic properties of the polymer chains in particular at the polymer/graphene interface are detected. Results concerning both the segmental and the terminal dynamics render PE much faster than the other two polymers, PS follows, while PMMA is the slowest one. Clear spatial dynamic heterogeneity has been observed for all model systems, with different dynamical behavior of the adsorbed polymer segments. The segmental relaxation time of polymer (τseg) as a function of the distance from graphene shows an abrupt decrease beyond the first adsorption layer for PE, as a result of its the well-ordered layered structure close to graphene, though a more gradual decay for PS and PMMA. The distribution of the relaxation times of adsorbed segments was also found to be broader than the bulk ones for all three polymer/graphene systems

Monitoring the sea environment using acoustics the role of the acoustical observatories

The presentation deals with theoretical factors and technical specifications pertinent to the design of an acoustical observatory for the monitoring of the marine environment. Two types of observatories are mentioned, namely active and passive. Among the various cases of active observatories, the ones related to ocean acoustic tomography are presented in some detail and the inverse problem of retrieving information from measured acoustic data is explained. Some basic issues related to the type of measurements that should be made for optimal use of the acoustic field are also given with related references. Finally, the basic features of passive observatories are underlined without going into details

Analytic Regularity and GPC Approximation for Control Problems Constrained by Linear Parametric Elliptic and Parabolic PDEs

This paper deals with linear-quadratic optimal control problems constrained by a parametric or stochastic elliptic or parabolic PDE. We address the (difficult) case that the state equation depends on a countable number of parameters i.e., on $\sigma_j$ with $j\in\N$, and that the PDE operator may depend non-affinely on the parameters. We consider tracking-type functionals and distributed as well as boundary controls. Building on recent results in [CDS1, CDS2], we show that the state and the control are analytic as functions depending on these parameters $\sigma_j$. We establish sparsity of generalized polynomial chaos (gpc) expansions of both, state and control, in terms of the stochastic coordinate sequence $\sigma = (\sigma_j)_{j\ge 1}$ of the random inputs, and prove convergence rates of best $N$-term truncations of these expansions. Such truncations are the key for subsequent computations since they do {\em not} assume that the stochastic input data has a finite expansion. In the follow-up paper [KS2], we explain two methods how such best $N$-term truncations can practically be computed, by greedy-type algorithms as in [SG, Gi1], or by multilevel Monte-Carlo methods as in [KSS]. The sparsity result allows in conjunction with adaptive wavelet Galerkin schemes for sparse, adaptive tensor discretizations of control problems constrained by linear elliptic and parabolic PDEs developed in [DK, GK, K], see [KS2]