In this paper, we consider a neural field model comprised of two distinct populations of neurons, excitatory and inhibitory, for which both the velocities of action potential propagation and the time courses of synaptic processing are different. Using recently-developed techniques, we construct the Evans function characterising the stability of both stationary and travelling wave solutions, und...

A meshless method based on the local Petrov-Galerkin approach is proposed for the solution of steady-state and transient heat conduction problems in a continuously nonhomogeneous anisotropic medium. The Laplace transform is used to treat the time dependence of the variables for transient problems. The analyzed domain is covered by small subdomains with a simple geometry. A weak formulation for ...

In this paper, the orthogonal collocation technique is utilized to solve the Poppe method equations for heat and mass transfer in counter flowing wet-cooling towers. The six differential equations for unsaturated and supersaturated air from the Poppe method are simplified, yielding three differential equations that use the Heaviside function. The humidity ratio is demonstrated to be a finite po...

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 ...

A subdomain variational inequality and its meshless linear complementary formulation are developed in the present paper for solving two-dimensional contact problems. The subdomain variational inequality will be defined in detail. The meshless method is based on a local weighted residual method with the Heaviside step function as the weighting function over a local subdomain and radial basis fun...