The process of ‘Evolutionary Diffusion’, i.e. reproduction with local mutation but without selection in a biological population, resembles standard Diffusion in many ways. However, Evolutionary Diffusion allows the formation of localized peaks that undergo drift, even in the infinite population limit. We relate a microscopic evolution model to a stochastic model which we solve fully. This allow...

A new, wide class of relativistic stochastic processes is introduced. All relativistic processes considered so far in the literature are members of this class. For each process, the stochastic equations of motion are obtained in an arbitrary Lorentz frame. The associated Kolmogorov equation is also derived for the first time, in both (3 + 1)and manifestly covariant forms.

Spherical pellets of antimony sulphide were dissolved in 1 molar sodium hydroxide solutions at different temperatures. It was found that the shrinking core with ash layer model could satisfactorily explain the dissolution process. Using this model it was found that initially the rate controlling step is a chemical reaction with activation energy of 10.2 kJ/mol. As the ash layer builds up, diffu...

We consider the problem of depth estimation from multiple images based on the defocus cue. For a Gaussian defocus blur, the observations can be shown to be the solution of a deterministic but inhomogeneous diffusion process. However, the diffusion process does not sufficiently address the case in which the Gaussian kernel is deformed. This deformation happens due to several factors like self-oc...

To address the air pollution diffusing problem, a visualization algorithm based on fluid diffusion physical model and volume rendering is proposed to simulate the diffusion process epically for the urgent pollution accidents. The diffusion model is based on the simplified heat diffusion equation and the basic vortex constraint. The texture mapping based volume rendering method is adapted to han...

We propose the point process model as the Poissonian-like stochastic sequence with slowly diffusing mean rate and adjust the parameters of the model to the empirical data of trading activity for 26 stocks traded on NYSE. The proposed scaled stochas-tic differential equation provides the universal description of the trading activities with the same parameters applicable for all stocks.

Diffusion equations are mathematical models which explain how the concentration of one or more substances distributed in space is altered by a diffusion process which causes the substances to spread out over a surface in space. For a normal diffusion process, the flux of particles into one region must be the sum of particle flux flowing out of the surrounding regions. From Fick’s first law, thi...

Purpose: discuss actual application value of the diffusion theory in massive electric vehicle charging load; Method: introduce single vehicle charging process, extend it to charging process of two and multiple electric vehicles, abstract physical process of parallel charging of electric vehicles, introduce energy block concept and diffusion theory, and establish diffusion charging model of elec...

At present paper, we establish the existence of pullback $mathcal{D}$-attractor for the process associated with non-autonomous partly dissipative reaction-diffusion equation in $L^2(mathbb{R}^n)times L^2(mathbb{R}^n)$. In order to do this, by energy equation method we show that the process, which possesses a pullback $mathcal{D}$-absorbing set, is pullback $widehat{D}_0$-asymptotically compact.