1 citations · 2 across the 21 of their papers we have counts for
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On a Multispecies Electrodiffusion Model in Higher-Dimensional Porous Media
Elie Abdo, Christofer Ghazale
We consider the Nernst--Planck--Darcy system describing the electrodiffusion of ionic species with arbitrary valences and different diffusivities, transported by a Darcy flow d…
Entropy Analysis of some Active Scalar Equations
Elie Abdo
We study a broad family of active scalar equations with fractional dissipation on and prove that their entropy diverges to at a sharp rate of order $\log t…
On the Non-isothermal Nernst-Planck-Navier-Stokes System
Elie Abdo, Quyuan Lin
Electrodiffusion has been extensively studied in the isothermal setting, whereas the mathematical theory of thermally coupled electrodiffusion remains comparatively underdeveloped.…
EML Trees Are Universal Approximators
Joe Germany, Elie Abdo, Joseph Bakarji
The recently introduced EML (Exp-Minus-Log) function acts as continuous analogue of NAND gates, providing a compositional building block capable of representing elementary function…
Long time dynamics of the Nernst-Planck-Darcy System on
Elie Abdo, Joe Germany, Mohammad Khalil Hamdan +1
We study ionic electrodiffusion modeled by the Nernst--Planck equations describing the evolution of ionic species in a three-dimensional incompressible fluid flowing through a…
Convergence Analysis of PINNs for Fractional Diffusion Equations in Bounded Domains
Elie Abdo, Lihui Chai, Ruimeng Hu +1
We establish the convergence of physics-informed neural networks (PINNs) for time-dependent fractional diffusion equations posed on bounded domains. The presence of fractional Lapl…