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Due to the influence of equipment instability and surveying environment, scattering echoes and other factors, it is sometimes difficult to obtain high-quality sub-bottom profile (SBP) images by traditional denoising methods. In this paper, a novel SBP image denoising method is developed for obtaining underlying clean images based on a non-local low-rank framework. Firstly, to take advantage of the inherent layering structures of the SBP image, a direction image is obtained and used as a guidance image. Secondly, the robust guidance weight for accurately selecting the similar patches is given. A novel denoising method combining the weight and a non-local low-rank filtering framework is proposed. Thirdly, after discussing the filtering parameter settings, the proposed method is tested in actual measurements of sub-bottom, both in deep water and shallow water. Experimental results validate the excellent performance of the proposed method. Finally, the proposed method is verified and compared with other methods quantificationally based on the synthetic images and has achieved the total average peak signal-to-noise ratio (PSNR) of 21.77 and structural similarity index (SSIM) of 0.573, which is far better than other methods.

The main goal of this work is to prove the existence of three different solutions (one positive, one negative and one with nonconstant sign) for the equation $(-\Delta_p)^s u= |u|^{p^{*}_s -2} u +\lambda f(x,u)$ in a bounded domain with Dirichlet condition, where $(-\Delta_p)^s$ is the well known $p$-fractional Laplacian and $p^*_s=\frac{np}{n-sp}$ is the critical Sobolev exponent for the non local case. The proof is based in the extension of the Concentration Compactness Principle for the $p$-fractional Laplacian and Ekeland's variational Principle., Comment: 10 pages. arXiv admin note: text overlap with arXiv:0808.3143, arXiv:0912.3465

The aim of the present work is to investigate the mechanical behaviour of orthotropic masonry subjected to localized loads in the context of both ’implicit’/’weak’ and ’explicit’/’strong’ non-local continuum models. To look for possible correspondences and differences, the solutions of Cosserat (micropolar) and integral form of Eringen models, obtained by employing finite element method, are compared. The resulting displacement and stress fields highlight the diffusive character of micropolar model, and the capability of Eringen model in avoiding stress singularities.

The formation of desiccation cracks in unsaturated soils as a discontinuity phenomenon can compromise the integrity of civil infrastructure on unsaturated soils. Because of the singularity at such discontinuities, the mathematical modeling of desiccation cracking is challenging. In this study, we apply a coupled nonlocal peridynamic poroelastic framework to model desiccation cracking in unsaturated soils. The soil skeleton is modeled by a nonlocal peridynamic elastic solid. A peridynamic equivalence of the generalized Darcy&rsquo, s law is utilized to model unsaturated fluid flow. Cracking is determined by a critical stretch criterion between material points as well as an energy criterion. We present numerical simulations of desiccation cracking in soil bars and thin soil discs for one-dimensional cracking and two-dimensional cracking networks, respectively. The numerical results have demonstrated that the proposed nonlocal mathematical framework is a promising and robust method for modeling desiccation cracking in unsaturated soils.

This paper reviews the emergence of non-local flow phenomena in granular materials and discusses a range of models that have been proposed to integrate an intrinsic length-scale into granular rheology. The frameworks discussed include micro-polar modeling, kinetic theory, three particular order-parameter-based models, and strongly non-local integral-based models. An extensive commentary is included discussing the current capabilities of these existing models as well as their implementational ease, physical motivation, and breadth of predictive ability.

In this study, a new peridynamic Mindlin plate formulation is presented which is suitable for the analysis of functionally graded materials. The governing equations of peridynamic formulation are obtained by using Euler-Lagrange equations in conjunction with Taylor&rsquo, s expansion. To validate the new formulation, three different numerical benchmark problems are considered for a Mindlin plate subjected to simply supported, fully clamped and mixed (clamped-simply supported) boundary conditions. Peridynamic results are compared against results from finite element analysis and a good agreement is observed between the two methods.

The critical behavior of a non-local scalar field theory is studied. This theory has a non-local quartic interaction term which involves a real power -\beta of the Laplacian. The parameter \beta can be tuned so as to make that interaction marginal for any dimension. The lowest order Feynman diagrams corresponding to coupling constant renormalization, mass renormalization, and field renormalization are computed. In all cases a non-trivial IR fixed point is obtained. Remarkably, for dimensions different from 4, field renormalization is required at the one-loop level. For d=4, the theory reduces to the usual local \phi^{4} field theory and field renormalization is required starting at the the two-loop level. The critical exponents \nu and \eta are computed for dimensions 2,3,4 and 5. For dimensions greater than four, the critical exponent \eta turns out to be negative for \epsilon>0, which indicates a violation of the unitarity bounds., Comment: 12 pages, 5 figures

Thoroughly mixing immiscible fluids creates droplets of one phase dispersed in a continuum of the other phase. In such emulsions, the individual droplets have rather mundane mechanical behavior. However, densely confining these suspended droplets generates a packing of particles with a spectacular diversity of mechanical behavior whose origins we are only beginning to understand. This mini review serves to survey a non-exhaustive range of experimental dense slow flow emulsion work. To embed these works in the context of the flow behavior of other structured fluids, we also discuss briefly the related non-local flow modeling attempts as one of the approaches that has been used successfully in describing emulsion flow properties and other materials.

We study—experimentally,theoretically, and numerically—nonlinear excitations in lattices ofmagnetswithlong-rangeinteractions. We examinebreather solutions, whichare spatially localized and periodicin time, in a chain with algebraically-decaying interactions.Itwas established two decades ago(Flach1998Phys. Rev.E58R4116)that lattices with long-range interactions can have breather solutions inwhich the spatial decay ofthe tailshas a crossover from exponential to algebraic decay.Inthis article, werevisitthis problem inthe setting ofa chain of repelling magnets with a massdefect and verify, bothnumerically and experimentally, theexistence of breatherswith such a crossover., New Journal of Physics, 21, ISSN:1367-2630

On a two-dimensional quasicrystal, a Penrose tiling, we simulate for the first time a game of life dynamics governed by non-local rules. Quasicrystals have inherently non-local order since any local patch, the emperor, forces the existence of a large number of tiles at all distances, the empires. Considering the emperor and its local patch as a quasiparticle, in this case a glider, its empire represents its field and the interaction between quasiparticles can be modeled as the interaction between their empires. Following a set of rules, we model the walk of life in different setups and we present examples of self-interaction and two-particle interactions in several scenarios. This dynamic is influenced by both higher dimensional representations and local choice of hinge variables. We discuss our results in the broader context of particle physics and quantum field theory, as a first step in building a geometrical model that bridges together higher dimensional representations, quasicrystals and fundamental particles interactions.

Old and recent experiments show that there is a direct response to the heating power of transport observed in modulated ECH experiments both in tokamaks and stellarators. This is most apparent for modulated experiments in the Large Helical Device (LHD) and in Wendelstein 7 advanced stellarator (W7-AS). In this paper we show that: (1) this power dependence can be reproduced by linear models and as such hysteresis (in flux) has no relationship to hysteresis as defined in the literature; (2) observations of 'hysteresis' (in flux) and a direct response to power can be perfectly reproduced by introducing an error in the estimated deposition profile as long as the errors redistribute the heat over a large radius; (3) non-local models depending directly on the heating power can also explain the experimentally observed Lissajous curves (hysteresis); (4) how non-locality and deposition errors can be recognized in experiments and how they affect estimates of transport coefficients; (5) from a linear perturbation transport experiment, it is not possible to discern deposition errors from non-local fast transport components (mathematically equivalent). However, when studied over different operating points non-linear-non-local transport models can be derived which should be distinguishable from errors in the deposition profile. To show all this, transport needs to be analyzed by separating the transport in a slow (diffusive) time-scale and a fast (heating/non-local) time-scale, which can only be done in the presence of perturbations.

In the present paper, the material parameters of the isotropic relaxed micromorphic model derived for a specific metamaterial in a previous contribution are used to model its transmission properties. Specifically, the reflection and transmission coefficients at an interface between a homogeneous solid and the chosen metamaterial are analyzed by using both the relaxed micromorphic model and a direct FEM implementation of the detailed microstructure. The obtained results show an excellent agreement between the transmission spectra derived via our enriched continuum model and those issued by the direct FEM simulation. Such excellent agreement validates the indirect measure of the material parameters and opens the way towards an efficient meta-structural design., Comment: The paper has been already accepted in Mathematics and Mechanics of Solids as it is

International audience; We have determined the magnetic ground state of the half-metal CrO 2 based on 1s2p Resonant Inelastic X-ray Scattering Magnetic Circular Dichroism (RIXS-MCD) experiments. The two-dimensional RIXS-MCD map displays the 1s X-ray absorption spectrum combined with the 1s2p X-ray emission decay, where there is a large MCD contrast in the final state involving the 2p core hole. Our measurements show that the Cr K pre-edge structure is dominated by dipolar contributions and the quadrupole peak is invisible in direct K pre-edge absorption. Using RIXS-MCD, we reveal that the quadrupole 1s3d pre-edge has a large MCD contrast, which appears at lower energy with respect to the K pre-edge maximum. We use crystal field multiplet calculations to model the excitonic RIXS-MCD spectral shape in tetragonal (D 4h) symmetry. The RIXS-MCD is strongly sensitive to the ground state distortion of the Cr 4+ sites. The calculations of the RIXS-MCD maps suggest that the 3d spin–orbit interaction is fully quenched (3d = 0 meV) and the ground state electron configuration must contain a 3 B 2g (D 4h) contribution, which is required to explain the appearance of the Magnetic Circular Dichroism (MCD) in the Cr K pre-edge. This is in apparent contrast with the compressed tetragonal distortion.

Reconstructing images from multi-view projections is a crucial task both in the computer vision community and in the medical imaging community, and dynamic positron emission tomography (PET) is no exception. Unfortunately, image quality is inevitably degraded by the limitations of photon emissions and the trade-off between temporal and spatial resolution. In this paper, we develop a novel tensor based nonlocal low-rank framework for dynamic PET reconstruction. Spatial structures are effectively enhanced not only by nonlocal and sparse features, but momentarily by tensor-formed low-rank approximations in the temporal realm. Moreover, the total variation is well regularized as a complementation for denoising. These regularizations are efficiently combined into a Poisson PET model and jointly solved by distributed optimization. The experiments demonstrated in this paper validate the excellent performance of the proposed method in dynamic PET.

This paper presents an incremental-secant mean-field homogenization (MFH) procedure for composites made of elasto-plastic constituents exhibiting damage. During the damaging process of one phase, the proposed method can account for the resulting unloading of the other phase, ensuring an accurate prediction of the scheme. When strain softening of materials is involved, classical finite element formulations lose solution uniqueness and face the strain localization problem. To avoid this issue the model is formulated in a so-called implicit gradient-enhanced approach, with a view toward macro-scale simulations. The method is then used to predict the behavior of composites whose matrix phases exhibit strain softening, and is shown to be accurate compared to unit cell simulations and experimental results. Then the convergence of the method upon strain softening, with respect to the mesh size, is demonstrated on a notched composite ply. Finally, applications consisting in a stacking plate, successively without and with a hole, are given as illustrations of the possibility of the method to be used in a multiscale framework.© 2013 Elsevier Ltd. All rights reserved.

The first author gratefully acknowledges the hospitality and the support provided by the Insti- tut de Mathématiques de Marseille during the completion of this work.; International audience; We first consider an elastic thin heterogeneous cylinder of radius of order ε: the interior of the cylinder is occupied by a stiff material (fiber) that is surrounded by a soft material (matrix). By assuming that the elasticity tensor of the fiber does not scale with ε and that of the matrix scales with ε2, we prove that the one dimensional model is a nonlocal system.We then consider a reference configuration domain filled out by periodically distributed rods similar to those described above. We prove that the homogenized model is a second order nonlocal problem.In particular, we show that the homogenization problem is directly connected to the 3D–1D dimensional reduction problem.

International audience; Simulating damage and failure of metallic or composite structures often fails when using standard finite element discretizations and a Newton-Raphson solving procedure. The difficulties arise from an uncontrolled mesh dependency caused by damage localization, to structural instabilities and to an increase of computational costs. The first problem can be overcome by using non-local damage constitutive equations together with a specific finite element model. The second problem can then be solved with an arc-length method which manages instabilities and snap-backs. They are caused by the loss of strength-carrying capacity of the damaged material. Finally, the whole computational scheme is parallelized. The main contribution of this paper consists in bringing together the three numerical techniques: non-local material model; piloting and parallel computations. The resulting numerical scheme allows to go beyond the overly simplistic cases often encountered in the literature. It allows robust industrial simulations with a high number of degrees of freedom, both in two and three dimensions, and deepened studies involving a large number of simulations.

We combine experimental and theoretical methods to assess the effect of a set of point mutations on c7A, a highly mechanostable type I cohesin module from scaffoldin CipA from Clostridium thermocellum. We propose a novel robust and computationally expedient theoretical method to determine the effects of point mutations on protein structure and stability. We use all-atom simulations to predict structural shifts with respect to the native protein and then analyze the mutants using a coarse-grained model. We examine transitions in contacts between residues and find that changes in the contact map usually involve a non-local component that can extend up to 50 Å. We have identified mutations that may lead to a substantial increase in mechanical and thermodynamic stabilities by making systematic substitutions into alanine and phenylalanine in c7A. Experimental measurements of the mechanical stability and circular dichroism data agree qualitatively with the predictions provided the thermal stability is calculated using only the contacts within the secondary structures., We thank D. V. Laurents for his help with CD measurements and their analysis. This research has been supported by the ERA-NET grant ERA-IB (No. EIB.12.022) (FiberFuel) and the European Framework Programme VII NMP Grant No. 604530-2 (CellulosomePlus) and by PLGrid Infrastructure. It was also co-financed by the Polish Ministry of Science and Higher Education from the resources granted for the years 2014-2017 in support of international scientific projects. D.T. acknowledges Science Foundation Ireland (SFI) for financial support under Grant No. 15/CDA/3491 and M.Ch., M.G., and D.T. acknowledge computing resources at the SFI/Higher Education Authority Irish Centre for High-End Computing (ICHEC).

International audience; This article introduces a new image segmentation method that makes use of non-local comparisons between pairs of patches of features. A non-local energy is defined by summing the interactions between pairs of patches inside and outside the segmented domain. A maximum radius of interaction can be adapted to fit the amount of variation of the features inside and outside the region to segment. This non-local energy is minimized using a level set approach. The corresponding curve evolution defines a non-local active contour that converges to a local minimum of our energy. In contrast to previous segmentation methods, this approach only requires a local homogeneity of the features inside and outside the region to segment. This does not impose a global homogeneity as required by region-based segmentation methods. This comparison principle is also less sensitive to initialization than edge-based approaches. We instantiate this novel framework using patches of intensity or color values as well as Gabor features. This allows us to segment regions with smoothly varying intensity or colors as well as well as complicated textures with a spatially varying local orientation.

International audience; Anisotropic damage thermodynamics framework allows to model the concrete-like mate- rials behavior and in particular their dissymmetric tension/compression response. To deal with dynamics applications such as impact, it is furthermore necessary to take into account the strain rate effect observed experimentally. This is done in the present work by means of anisotropic visco-damage, by introducing a material strain rate effect in the cases of posi- tive hydrostatic stresses only. The proposed delay-damage law assumes no viscous effect in compression as the consideration of inertia effects proves sufficient to model the apparent material strength increase. High-rate dynamics applications imply to deal with wave prop- agation and reflection which can generate alternated loading in the impacted structure. In order to do so, the key concept of active damage is defined and introduced within both the damage criterion and the delay-damage evolution law. At the structural level, strain localization often leads to spurious mesh dependency. Three-dimensional Finite Element computations of dynamic tensile tests by spalling are presented, with visco-damage and either without or with non-local enhancement. Delay- damage, as introduced, regularizes the solution in fast dynamics. The location of the macro-crack initiated is found influenced by non-local regularization. The strain rate range in which each enhancement, delay-damage or non-local enhancement, has a regularizing effect is studied.