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In this article, we continue our mathematical study of organic solar cells (OSCs) and propose a two-scale (micro- and macro-scale) model of heterojunction OSCs with interface geometries characterized by an arbitrarily complex morphology.…
We describe a mathematical model for heterojunctions in semiconductors which can be used, e.g., for modeling higher efficiency solar cells. The continuum model involves well-known drift-diffusion equations posed away from the interface.…
We present and discuss a mathematical model for the operation of bilayer organic photovoltaic devices. Our model couples drift-diffusion-recombination equations for the charge carriers (specifically, electrons and holes) with a…
This paper presents a one-dimensional transient drift--diffusion simulator for advanced solar cells, integrating a structure-preserving finite-volume spatial discretization with Scharfetter--Gummel--type fluxes and a high-order, L-stable…
Drift-diffusion models that account for the motion of both electronic and ionic charges are important tools for explaining the hysteretic behaviour and guiding the development of metal halide perovskite solar cells. Furnishing numerical…
We consider a nonlinear drift-diffusion system for multiple charged species in a porous medium in 2D and 3D with periodic microstructure. The system consists of a transport equation for the concentration of the species and Poisson's…
Drift-diffusion model is an indispensable modeling tool to understand the carrier dynamics (transport, recombination, and collection) and simulate practical-efficiency of solar cells (SCs) through taking into account various carrier…
This article is an attempt to provide a self consistent picture, including existence analysis and numerical solution algorithms, of the mathematical problems arising from modeling photocurrent transients in Organic-polymer Solar Cells…
A one-dimensional many-body model is established to mimic the charge distribution and dynamics in nonfullerene organic solar cells. Two essential issues are taken into account in the model: The alternating donor and acceptor structure and…
Various biological cells secrete diffusing chemical compounds into their environment for communication purposes. Secretion usually takes place over the cell membrane in a spatially heterogeneous manner. Mathematical models of these…
The recent emergence of lead-halide perovskites as active layer materials for thin film semiconductor devices including solar cells, light emitting diodes, and memristors has motivated the development of several new drift-diffusion models…
Diffusion models are a special type of generative model, capable of synthesising new data from a learnt distribution. We introduce DISPR, a diffusion-based model for solving the inverse problem of three-dimensional (3D) cell shape…
We investigate multicellular sender receiver systems embedded in hydrogel beads, where diffusible signals mediate interactions among heterogeneous cells. Such systems are modeled by PDE ODE couplings that combine three dimensional diffusion…
In this paper, we study one-dimensional linear Schr\"odinger equations with multiple moving potentials, known as transfer charge models. Focusing on the non-self-adjoint setting that arises in the study of solitons, we systematically…
Recent advancements in the ability to construct three-dimensional (3D) tissues and organoids from stem cells and biomaterials have not only opened abundant new research avenues in disease modeling and regenerative medicine but also have…
An efficient descriptor model for fast screening of potential materials for solar cell applications is presented. It works for both excitonic and non-excitonic solar cells materials, and in addition to the energy gap it includes the…
Based on the drift-kinetic theory, we develop a model for particle acceleration and transport in solar flares. The model describes the evolution of the particle distribution function by means of a numerical simulation of the drift-kinetic…
In this work, we introduce a novel generative denoising diffusion model for synthesizing the Sun's three-dimensional coronal magnetic field, a complex and dynamic region characterized by evolving magnetic structures. Despite daily…
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 present and analyse a model for cell signalling processes in biological tissues. The model includes diffusion and nonlinear reactions on the cell surfaces, and both inter- and intracellular signalling. Using techniques from the theory of…