In this paper we study one-dimensional Fisher-Kolmogorov equation with density dependent non-linear diffusion. We choose the diffusion as a function of cell density such that it is high in highly cell populated areas and it is small in the regions of fewer cells. The Fisher equation with non-linear diffusion is known as modified Fisher equation. We study the travelling wave solution of modified...

The work studies wave activity in spatial systems, which exhibit nonlocal spatial interactions at the presence of a finite propagation speed. We find analytically propagation delay-induced wave instabilities for various local excitatory and lateral inhibitory spatial interactions. The final numerical simulation confirms the analytical results.

We present a theoretical analysis of intracellular calcium waves propagated by calcium feedback at the inositol 1,4,5-trisphosphate (IP3) receptor. The model includes essential features of calcium excitability, but is still analytically tractable. Formulas are derived for the wave speed, amplitude, and width. The calculations take into account cytoplasmic Ca buffering, the punctate nature of th...

We show that the boundary conditions entering in the definition of the self-adjoint operator ∆ describing the Laplacian plus a finite number of point interactions are local if and only if the corresponding wave equation φ̈ = ∆φ has finite speed of propagation.

Fossil Fuels are always considered as environmental pollutants. On the other hand, the political and economic situations highly affect the price of these fuels. Offshore wind and wave, as renewable energy sources, represent the better alternatives for electricity generation. Therefore, it is necessary that wind speeds effectively be estimated due to the absence of field measurements of the wind...

this paper was aimed to report the 3d finite element analysis simulation of laser welding process of ti6al4v 1.7 mm sheets in butt joint in order to predict the temperature distribution, hardness, and weld geometry. the butt-joint welds were made using co2 laser with the maximum power of 2.2 kw in the continuous wave mode. a part of the experimental work was carried out to verify the weld geome...

In this paper we study the propagation of singularity for Schrödingertype equations with variable coefficients. We introduce a new notion of wave propagation set, the homogeneous wave front set, and it propagates along straight lines with finite speed away from x 6= 0. Then we show that it is related to the wave front set in a natural way. These results may be considered as a refinement of the ...

We introduce and study the Dunkl symmetric systems. We prove the wellposedness results for the Cauchy problem for these systems. Eventually we describe the finite speed of it. Next the semi-linear Dunkl-wave equations are also studied.

in this paper, a new algorithm for studying elastic wave propagation in the phononic crystals is presented. at first, the displacement-based forms of elastic wave equations are derived and then the forms are discretized using finite difference method. so the new algorithm is called the displacement-based finite difference time domain (dbfdtd). three numerical examples are computed with this met...