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A non-equilibrium thermodynamics model able to analyze the combined effect of diffusion and adsorption in porous materials is proposed. The model considers the coupled dynamics of the diffusive phase, described by a diffusion type equation,…
We consider a family of linear viscoelastic shells with thickness $2\varepsilon$ ( $\varepsilon$ , small parameter), clamped along a portion of their lateral face, all having the same middle surface $S$. We formulate the three-dimensional…
We develop and analyse a discrete, one-dimensional model of cell motility which incorporates the effects of volume filling, cell-to-cell adhesion and chemotaxis. The formal continuum limit of the model is a nonlinear generalisation of the…
A 2D nonlinear model for the electrical potential in the edge plasma in a tokamak generates a stiff problem due to the low resistivity in the direction parallel to the magnetic field lines. An asymptotic-preserving method based on a…
Theoretical calculations of the electrical conductivity and electroosmotic transfer as functions of the disperse phase volume fraction and non-dissolving boundary layer thickness were provided on the basis of the cell theory of…
Asymmetric behaviors of capacitance and charging dynamics in the cathode and anode are general for nanoporous supercapacitors. Understanding this behavior is essential for the optimal design of supercapacitors. Herein, we perform…
Lithium-ion batteries exhibit complex nonlinear dynamics, resulting from diffusion and phase transformations coupled to ion intercalation reactions. Using the recently developed Cahn-Hilliard reaction (CHR) theory, we investigate a simple…
This study examines the discharge behaviour of a cylindrical LiFeS2 cell to evaluate the parameters that can be used to predict and estimate the nonlinear dynamic response of a battery. A linear model is developed to simulate the discharge…
In Li-ion batteries the electrochemical potential drives the redox reactions occurring at the interface between electrolyte and storage material, typically active particles for porous electrodes, allowing Li ions intercalation/extraction…
We formulate the continuum field equations and constitutive equations that govern deformation, stress, and electric current flow in a Li-ion half-cell. The model considers mass transport through the system, deformation and stress in the…
This computational research study will analyze the multi-physics of lithium ion insertion into a silicon nanowire in an attempt to explain the electrochemical kinetics at the nanoscale and quantum level. The electron coherent states and a…
Cell polarity refers to the spatial asymmetry of molecules on the cell membrane. Altschuler, Angenent, Wang and Wu have proposed a stochastic model for studying the emergence of polarity in the presence of feedback between molecules. We…
It can be seen by Dynamic Electrical Analysis that the electrical properties of polyetherimide at temperatures above the glass transition are strongly influenced by space charge. We have studied space charge relaxation in two commercial…
Ionic liquids are widely used as electrolytes in electrochemical devices. In this context, many experimental and theoretical approaches have been recently developed for characterizing their interface with electrodes. In this perspective…
We examine a reduced membrane model of liquid crystal polymer networks (LCNs) via asymptotics and computation. This model requires solving a minimization problem for a non-convex stretching energy. We show a formal asymptotic derivation of…
We investigate the outflux of ions through the channels in a cell membrane. The channels undergo an open/close cycle according to a periodic schedule. Our study is based both on theoretical considerations relying on homogenization theory,…
A kinetic model of the electron transfer at the electrode / electrolyte solution interface is developed, implemented in a Monte Carlo framework, and applied to simulate this process in idealised systems consisting of the primitive model of…
Motivated by contact resistance on the front side of a crystalline silicon solar cell, we formulate and analyse a two-dimensional mathematical model for electron flow across a poorly conducting (glass) layer situated between silver…
We study the dynamics of ionic liquids in a thin slit pore geometry. Beginning with the classical and dynamic density functional theories for systems of charged hard spheres, an asymptotic procedure leads to a simplified model which…
This work explores controllability and the control effort required for lithium-ion batteries. Battery packs have become a critical technology in both personal and professional applications as a means to store large amounts of energy.…