This study explored the free vibration problem in relation to glass fiber reinforced polymer (GFRP) plates with central cutouts and free boundaries using theoretical, experimental, and numerical methods. The theoretical formulations were derived from the classical lamination plate theory. The rectangular cutout was mathematically modeled into the stiffness matrix of the plate by multiplying Hea...

Many tissue level models of neural networks are written in the language of nonlinear integro-differential equations. Analytical solutions have only been obtained for the special case that the nonlinearity is a Heaviside function. Thus the pursuit of even approximate solutions to such models is of interest to the broad mathematical neuroscience community. Here we develop one such scheme, for sta...

This artcile is concerned with thermal buckling and thermal induced free vibration analyses of PCPs (perforated composite plates) with simply supported edges applying a mathematical model. The stiffness and density of PCP are defined locally using Heaviside distribution functions. The governing equations are derived based on CLPT. The present solution gives reasonable results in comparison with...

A bstract We discuss peculiarities that arise in the computation of real-emission contributions to observables contain Heaviside functions. prominent example such a case is zero-jettiness soft function SCET, whose calculation at next-to-next-to-next-to-leading order perturbative QCD an interesting problem. Since distinguishes between emissions into different hemispheres, its definition involves...

We present a finite difference method for discretizing a Heaviside function H(u(~x)), where u is a level set function u : Rn 7→ R that is positive on a bounded region Ω ⊂ R. There are two variants of our algorithm, both of which are adapted from finite difference methods that we proposed for discretizing delta functions in [13–15]. We consider our approximate Heaviside functions as they are use...

In 1+1 dimensional hydrodynamics originally proposed by Landau, we derive a new potential and distribution function including Heaviside function and investigate its mathematical and physical properties. Using the original distribution derived by Landau, a distribution function found by Srivastava et al., our distribution function, and the Gaussian distribution proposed by Carruthers et al., we ...

In 1+1 dimensional hydrodynamics originally proposed by Landau, we derive a new potential and distribution function including Heaviside function and investigate its mathematical and physical properties. Using the original distribution derived by Landau, a distribution function found by Srivastava et al., our distribution function, and the Gaussian distribution proposed by Carruthers et al., we ...

The current study presents a mathematical modeling for sandwich panels with foam filled orthogonally rib-stiffened core using Heaviside distribution functions. The governing equations of the static problem have been derived based on classical lamination theory. The present model contains three displacement variables considering all of the stiffness coefficients. A closed form solution using Gal...