arXiv subjects

Akram Al-Sabbagh

Publications and source records attributed to Akram Al-Sabbagh.

3 recordsLinked to original sources

arXiv2021

The unified version of mixing maps between non-void sets

The nonlinear concepts of mixed summable families and maps for the spaces that only non-void sets are developed. Several characterizations of the corresponding concepts are achieved and the proof for a general Pietsch Domination-type theorem is established. Furthermore, this work has presented plenty of composition and inclusion results between different classes of mappings in the abstract settings. Finally, a generalized notation of mixing maps and their characteristics are extended to a more general setting.

math.FA↗

arXiv2016

Density-Dependence Subdiffusion in Chemotaxis

The purpose of this work is to propose a nonlinear non-Markovian model of subdiffusive transport that involves chemotactic substance affecting the cells at all time, not only during the jump. This leads the random waiting time to be dependent on the chemotactic gradient, making the escape rates also dependent on the gradient as well as the nonlinear density dependence. We systematically derive subdiffusive fractional master equation, then we consider the diffusive limit of the fractional master equation. We finally solve the resulting fractional subdiffusive master equation stationery and analyse the role of the chemotactic gradient in the resulting stationary density with a constant and a quadratic chemotactic gradient.

cond-mat.stat-mech↗

arXiv2016

A non-linear subdiffusion model for a cell-cell adhesion in chemotaxis

The purpose of this work is to propose a non-Markovian and nonlinear model of subdiffusive transport that involves adhesion affects the cells escape rates form position x, with chemotaxis. This leads the escape rates to be dependent on the particles density at the neighbours as well as the chemotactic gradient. We systematically derive subdiffusive fractional master equation, then we consider the diffusive limit of the fractional master equation. We finally solve the resulted fractional subdiffusive master equation stationery and analyse the role of adhesion in the resulted stationary density.

q-bio.CB↗