in this article using the inverse laplace transform, we show analytical solutions for the generalized mass transfers with (and without) a chemical reaction. these transfers have been expressed as the couette flow with the fractional derivative of the caputo sense. also, using the hankel contour for the bromwich's integral, the solutions are given in terms of the generalized airy functions.

The extended Airy kernel describes the space-time correlation functions for the Airy process, which is the limiting process for a polynuclear growth model. The Airy functions themselves are given by integrals in which the exponents have a cubic singularity, arising from the coalescence of two saddle points in an asymptotic analysis. Pearcey functions are given by integrals in which the exponent...

We demonstrate a new type of soliton formation arising from the interaction of multiple two-dimensional Airy beams in a nonlinear medium. While in linear regime, interference effects of two or four spatially displaced Airy beams lead to accelerated intensity structures that can be used for optical induction of novel light guiding refractive index structures, the nonlinear cross-interaction betw...

How can we get higher angular resolution than the simple full width at half maximum of the Airy function,/D, where D is the largest that we can afford? One answer is indicated in the bottom panel of Figure 8.18. If we mask off all of our telescope mirror except two small apertures of diameter d at the edge, the “central peak” of our image becomes twice as sharp as the Airy function but with h...

In this paper, we study a change in the propagation trajectory of set autofocusing laser beams using fractional Fourier transform. Clusters displaced bounded Airy-Gaussian supplemented by phase function that deflects beam similarly to prism are considered. The shift and deviation (according carrier spatial frequencies) make it possible beams. influence parameters under consideration on properti...

Random tilings of the two-periodic Aztec diamond contain three macroscopic regions: frozen, where are deterministic; rough, correlations between dominoes decay polynomially; smooth, exponentially. In a previous paper, authors found that certain averaging height function differences at rough-smooth interface converged to extended Airy kernel point process. this we augment local geometrical pictu...