In dentin restoration, collagen fiber network infiltration is an issue. Using data from the litterature, we have constructed a relevant numerical geometrical model of the network. The specificity of our model is that the fibers are taken into account implicitly using a regularized Heaviside function. This function is either used to set the viscosity or to localize the contact line where capilla...

We present a robust second-order accurate method for discretizing the multidimensional Heaviside and the Dirac delta functions on irregular domains. The method is robust in the following ways: (1) Integrations of source terms on a co-dimension one surface are independent of the underlying grid and therefore stable under perturbations of the domain’s boundary; (2) The method depends only on the ...

We discuss an optimal control problem of laser surface hardening of steel which is governed by a dynamical system consisting of a semilinear parabolic equation and an ordinary differential equation with a non differentiable right hand side function f+. To avoid the numerical and analytic difficulties posed by f+, it is regularized using a monotone Heaviside function and the regularized problem ...

Digital image watermarking is an important technique for the authentication of multimedia content and copyright protection. Conventional digital image watermarking techniques are often vulnerable to geometric distortions such as Rotation, Scaling, and Translation (RST). These distortions desynchronize the watermark information embedded in an image and thus disable watermark detection. To solve ...

We recently reported on a method for measuring orbital angular momentum (OAM) states of light based on the transformation of helically phased beams to tilted plane waves [Phys. Rev. Lett.105, 153601 (2010)]. Here we consider the performance of such a system for superpositions of OAM states by measuring the modal content of noninteger OAM states and beams produced by a Heaviside phase plate.

This paper proposes a subtractive geometry projection topology optimization approach to simulate the multi-axis machining process and remove material from initial design domain. Each geometric primitive is described by plane extrusion operation based on 2D closed cubic spline curve controlled boundary points. The reference for 3D can freely rotate translate in space optimization. then projected...

Abstract This paper proposes a novel density-based method for structural design considering restrictions of multi-axis machining processes. A new mathematical formulation based on Heaviside function is presented to transform the field into geometry which can be manufactured by process. The developed 5-axis machining, also applied 2.5D milling restriction. filter techniques are incorporated effe...

In Lp-spaces with p an integer from [1, infinity) there exists a best approximation mapping to the set of functions computable by Heaviside perceptron networks with n hidden units; however for p an integer from (1, infinity) such best approximation is not unique and cannot be continuous.