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An Optimization Based Empirical Mode Decomposition Scheme for Images
Get PDFBidimensional empirical mode decompositions (BEMD) have been developed to decompose any bivariate function or image
additively into multiscale components, so-called intrinsic mode functions (IMFs), which are approximately orthogonal to each other with respect to the inner product. In this paper, a novel optimization problem is designed to achieve this decomposition which takes into account important features desired of the BEMD. Specifically, we propose a data-adapted iterative method which we call Opt-BEMD which minimizes in each iteration a smoothness functional subject to inequality constraints involving the strictly local extrema of the image. In this way, the method constructs a sparse data-adapted basis for the input function as well as an envelope in a mathematically stringent sense. Moreover, we propose an ensemble version of Opt-BEMD to strengthen its performance when applied to noise-contaminated images or images with only few extrema
On atomistic-to-continuum couplings without ghost forces in three dimensions
Get PDFIn this paper we construct energy based numerical methods free of ghost forces in three dimen- sional lattices arising in crystalline materials. The analysis hinges on establishing a connection of the coupled system to conforming finite elements. Key ingredients are: (i) a new representation of discrete derivatives related to long range interactions of atoms as volume integrals of gradients of piecewise linear functions over bond volumes, and (ii) the construction of an underlying globally continuous function representing the coupled modeling method
A variational approximation scheme for radial polyconvex elasticity that preserves the positivity of Jacobians
No full textReflection and refraction of an Airy beam at a dielectric interface
Get PDFReflection and refraction of a finite-power Airy beam at the interface between two dielectric media are investigated analytically and numerically. The formulation takes into account the paraxial nature of the optical beams to derive convenient field evolution equations in coordinate frames moving along Snell’s refraction and reflection axes. Through numerical simulations, the self-accelerating dynamics of the Airy-like refracted and reflected beams are observed. Of special interest are the cases of critical incidence at Brewster and total-internal-reflection (TIR) angles. In the former case, we find that the reflected beam achieves to self-heal despite the severe supression of a part of its spectrum, while, in the latter case, the beam remains nearly unaffected except for the Goos-Hänchen shift. The self-accelerating quality persists even if the beam is trapped by multiple TIRs inside a dielectric film. Grazing incidence of an Airy beam at the interface between two media with close refractive indices is also investigated revealing that the interface can act as a filter cepending on the beam scale and tilt. We finally consider reverse refraction and perfect imaging of an Airy beam into a left-handed medium
Large Shear Rate Behaviour For the Hébraud-Lequeux Model
Get PDFThe Hébraud-Lequeux model is a model describing the flow of soft glassy material in a simple shear flow configuration. It is given by a kinetic/Fokker-Planck type of equation whose coefficients depend on the shear rate of the experiment. In this paper we want to study what happens to the stationary solutions of this model when the shear rate is asymptotically large. In order to that, we expand the solution of the equation using singular perturbation tools. In the end, we rigorously prove the estimate of Hébraud and Lequeux that the material asymptotically behaves as a Newtonian fluid
On a uniform estimate for positive solutions of semilinear elliptic equations
Get PDFWe consider semilinear elliptic equations with Dirichlet boundary conditions in a Lipschitz, possibly unbounded, domain. Under suitable assumptions on the nonlinearity, we deduce a condition on the size of the domain that implies the existence of a positive solution satisfying a uniform pointwise estimate. Here, uniform means that the estimate is independent of the domain. Besides of its simplicity, the main advantage of our approach is that we can remove a restrictive assumption on the nonlinearity that was imposed in a recent paper. Moreover, we can remove a non-degeneracy condition that was assumed in the latter paper
