Related papers: Modeling battery cells under discharge using kinet…
This paper proposes a new equivalent circuit model for rechargeable batteries by modifying a double-capacitor model proposed in [1]. It is known that the original model can address the rate capacity effect and energy recovery effect…
We analyze a class of cell-bulk coupled PDE-ODE models, motivated by quorum and diffusion sensing phenomena in microbial systems, that characterize communication between localized spatially segregated dynamically active signaling…
As a concrete setting where stochastic partial differential equations (SPDEs) are able to model real phenomena, we propose a stochastic Meinhardt model for cell repolarisation and study how parameter estimation techniques developed for…
In order to achieve a better understanding of degradation processes in lithium-ion batteries, the modelling of cell dynamics at the mircometer scale is an important focus of current mathematical research. These models lead to…
The Cahn-Hilliard reaction model, a nonlinear, evolutionary PDE, was introduced to model phase separation in lithium-ion batteries. Using Butler-Volmer kinetics for electrochemical consistency, this model allows lithium-ions to enter the…
Modelling the Calvin cycle of photosynthesis leads to various systems of ordinary differential equations and reaction-diffusion equations. They differ by the choice of chemical substances included in the model, the choices of stoichiometric…
The analytically tractable model employing Quantum Markovian Master Equations, derived by weak coupling procedure and satisfying complete positivity, is proposed to describe a model of molecular battery charged by a non-equilibrium…
In this contribution we present a new modeling and simulation framework for parametrized Lithium-ion battery cells. We first derive a new continuum model for a rather general intercalation battery cell on the basis of non-equilibrium…
In this work, we derive analytical expressions governing state-of-charge and current imbalance dynamics for two parallel-connected batteries. The model, based on equivalent circuits and an affine open circuit voltage relation, describes the…
A significant problem associated with batteries is the rapid reduction of charge-storage capacity with increasing charge/discharge rate. For example, improving this rate-performance is required for fast-charging of car batteries.…
A class of coupled cell-bulk ODE-PDE models is formulated and analyzed in a two-dimensional domain, which is relevant to studying quorum sensing behavior on thin substrates. In this model, spatially segregated dynamically active signaling…
In this paper we study a system of partial differential equations which models lithium-ion batteries. The system describes the conservation of Lithium and conservation of charges in the solid and electrolyte phases, together with the…
This manuscript presents an algorithm for individual Lithium-ion (Li-ion) battery cell state of charge (SOC) estimation in a large-scale battery pack under minimal sensing, where only pack-level voltage and current are measured. For battery…
A simple stochastic model of solute drag by moving grain boundaries (GBs) is presented. Using a small number of parameters, the model describes solute interactions with GBs and captures nonlinear GB dynamics, solute saturation in the…
Mathematical modeling with Ordinary Differential Equations (ODEs) has proven to be extremely successful in a variety of fields, including biology. However, these models are completely deterministic given a certain set of initial conditions.…
Batteries are playing an increasingly central role as distributed energy resources in the shift toward power systems dominated by renewable energy sources. However, existing battery models must invariably rely on complementarity constraints…
We consider a model for the dynamics of active cells interacting with their quiescent counterparts under the influence of acidity characterized by proton concentration. The active cells perform nonlinear diffusion and infer proliferation or…
Accurate estimation of a battery's state of charge and state of health is essential for safe and reliable battery management. Existing approaches often decouple these two states, lack stability guarantees, and exhibit limited generalization…
We introduce a discrete time microscopic single particle model for kinetic transport. The kinetics is modeled by a two-state Markov chain, the transport by deterministic advection plus a random space step. The position of the particle after…
Analyzing rate-performance data in battery electrodes is greatly facilitated by access to simple analytical models. Here we describe a number of simple equations for fitting capacity-rate data. These equations output fit parameters, such as…