We study the dynamics of three-dimensional Fisher fronts in the presence of density fluctuations. To this end we simulate the Fisher equation subject to stochastic internal noise, and study how the front moves and roughens as a function of the number of particles in the system, N. Our results suggest that the macroscopic behavior of the system is driven by the microscopic dynamics at its leadin...

In this paper, we analyze the impact of compression with complex random matrices on Fisher information and the Cramér-Rao Bound (CRB) for estimating unknown parameters in the mean value function of a complex multivariate normal distribution. We consider the class of random compression matrices whose distribution is right-unitarily invariant. The compression matrix whose elements are i.i.d. stan...

We have solved the Burgers-Fisher (BF) type equations, with time-dependent coefficients of convection and reaction terms, by using the auxiliary equation method. A class of solitary wave solutions are obtained, and some of which are derived for the first time. We have studied the effect of variable coefficients on physical parameters (amplitude and velocity) of solitary wave solutions. In some ...

It has been shown that the transition to the saturation regime of high energy QCD is similar to the formation of the front of a traveling wave. In particular, it can be verified that Balitsky-Kovchegov (BK) evolution equation reduces, after some approximations, to the nonlinear Fisher and Kolmogorov-Petrovsky-Piscounov (FKPP) equation, well-known from statistical physics. In these proceedings, ...

In this paper, we originate results with finite difference schemes to approximate the solution of the classical Fisher Kolmogorov Petrovsky Piscounov (KPP) equation from population dynamics. Fisher’s equation describes a balance between linear diffusion and nonlinear reaction. Numerical example illustrates the efficiency of the proposed schemes, also the Neumann stability analysis reveals that ...

Motivated by a phenomenon of phase transition in a model of alignment of selfpropelled particles, we obtain a kinetic mean-field equation which is nothing more than the Smoluchowski equation on the sphere with dipolar potential. In this self-contained article, using only basic tools, we analyze the dynamics of this equation in any dimension. We first prove global wellposedness of this equation,...

We perform an asymptotic analysis of models of population dynamics with a fractional Laplacian and local or nonlocal reaction terms. The first part of the paper is devoted to the long time/long range rescaling of the fractional Fisher-KPP equation. This rescaling is based on the exponential speed of propagation of the population. In particular we show that the only role of the fractional Laplac...

In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE) through substitution is converted into a nonlinear ordinary differential equation (NODE). The travelling wave solution i...

During a wound-healing cell migration assay experiment, cells are observed to detach and undergo mitosis before reattaching as a pair of cells on the substrate. During experiments with mice 3T3 fibroblasts, cell detachment can be confined to the wavefront region or it can occur over the whole wave profile. A multi-species continuum approach to modelling a wound-healing assay is taken to account...

The Tsallis entropy and Fisher information entropy (matrix) are very important quantities expressing information measures in nonextensive systems. Stationary and dynamical properties of the information entropies have been investigated in the N -unit coupled Langevin model subjected to additive and multiplicative white noise, which is one of typical nonextensive systems. We have made detailed, a...