In this paper, one of the simplest and most regular members of the family of the Meshless Local Petrov-Galerkin (MLPG) methods; namely MLPG5, is applied to analyze the thick-walled isotropic laminated cylinders under elasto-static pressure. A novel simple technique is proposed to eliminate a very important difficulty of the meshless methods to deal with material discontinuities regarding to the...

A truly Meshless Local Petrov-Galerkin (MLPG) method is developed for solving 3D elasto-static problems. Using the general MLPG concept, this method is derived through the local weak forms of the equilibrium equations, by using a test function, namely, the Heaviside step function. The Moving Least Squares (MLS) are chosen to construct the shape functions. The penalty approach is used to impose ...

Abstract We rigorously investigate the rapidly oscillating contributions in sinc-function representation of Dirac delta function and Fourier transform Coulomb potential. Beginning with a derivation standard integral Heaviside step function, we examine that contains sinc function. By contour integration, prove satisfies properties although it is divergent at nonzero points. This good pedagogical...

This paper is devoted to the study of inhomogeneous wave equation with singular (less than continuous) time dependent coefficients. Particular attention given role lower order terms and suitable Levi conditions are formulated in obtain a very weak solution as introduced [15]. Very solutions for this kind equations also investigated from numerical point view two toy models: Heaviside function de...

In this work, we study a quasilinear elliptic problem involving the 1-Laplacian operator, with discontinuous, superlinear and subcritical nonlinearity Heaviside function $H(\cdot - \beta )$ . Our approach is based on an analysis of associated p-Laplacian problem, followed by thorough asymptotic behaviour or such solutions as $p \to 1^+$ We also solutions, $\beta 0^+$ prove that it converges to ...

We analyze a time independent integral equation defined on a spatially extended domain which arises in the modelling of neuronal networks. In this paper, the coupling function is oscillatory and the firing rate is a smooth “heaviside-like” function. We will derive an associated fourth order ODE and establish that any bounded solution of the ODE is also a solution of the integral equation. We wi...

Different notions of entropy can be identified in different communities: (i) the thermodynamic sense, (ii) the information sense, (iii) the statistical sense, (iv) the disorder sense, and (v) the homogeneity sense. Especially the “disorder sense” and the “homogeneity sense” relate to and require the notion of space and time. One of the few prominent examples relating entropy to geometry and to ...

We propose the use of Heaviside transform with respect to the quark mass to investigate dynamical aspects of QCD. We show that at large momentum transfer the transformed propagator of massive quarks behaves softly and thus the dominant effect of explicit chiral symmetry breaking disappears through Heaviside transform. This suggests that the massless approximation would be more convenient to do ...