In the sense of distributions, derivative Heaviside unit step function $H(t)$ is a generalized Dirac-$\delta$ distribution. If velocity $V(t)$ flat plate impulsive, as $V(t)=H(t)$ (i.e., it suddenly set into motion with at $t=0^+$), then its acceleration $V'(t)=\delta(t)$. The distribution has no point values. However, when forcing term an ODE (in $t$), contributes to solution. recently publish...

We analyze a time independent integral equation defined on a spatially extended domain which arises in the modeling of neuronal networks. In our survey, 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 wil...

<b>Background:</b> Pulsed field ablation (PFA) is a new type of physical energy source in the fields tumor and atrial fibrillation ablation, based on irreversible electroporation with non-thermal, clear boundaries, selective killing, rapid advantages. PFA induces changes electrical conductivity zone, which can be described by step function used to predict zone. However, current rese...

Three kinds of fragile points methods based on Petrov-Galerkin weak-forms (PG-FPMs) are proposed for analyzing heat conduction problems in nonhomogeneous anisotropic media. This is a follow-up the previous study original FPM symmetric Galerkin weak-form. The trial function piecewise-continuous, written as local Taylor expansions at points. A modified radial basis function-based differential qua...

The Meshless Local Petrov-Galerkin (MLPG) method is one of the recently developed element-free methods. The method is convenient and can produce accurate results with continuous secondary variables, but is more computationally expensive than the finite element method. To overcome this disadvantage, a simple Heaviside test function is chosen. The computational effort is significantly reduced by ...

The symbiotic branching model describes the evolution of two interacting populations and if started with complementary Heaviside functions, the interface where both populations are present remains compact. In this paper, we show tightness of the diffusively rescaled solutions and thus provide a first step towards a scaling limit for the interface. The crucial estimate involves a mixed fourth mo...

The numerical integration of discontinuous functions is an abiding problem addressed by various authors. This subject gained even more attention in the context extended finite element method (XFEM), which exact crucial to obtaining reliable results. In this scope, equivalent polynomials represent effective circumvent while exploiting standard Gauss quadrature rule exactly integrate times step f...

This article is concerned with the rigorous validation of anomalous spreading speeds in a system of coupled Fisher-KPP equations of cooperative type. Anomalous spreading refers to a scenario wherein the coupling of two equations leads to faster spreading speeds in one of the components. The existence of these spreading speeds can be predicted from the linearization about the unstable state. We ...

If an oscillator is driven by a force that switches between two frequencies, the dynamics it exhibits depends on precise manner of switching. Here we take one-dimensional and consider scenarios in which switching occurs: (i) driving forces have different or (ii) as single forcing whose frequency values. The difference subtle, but entirely changes long term behaviour, concerns whether switch can...