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Many dense granular systems are non-monodisperse, consisting of particles of different sizes, and will segregate based on size during flow. This phenomenon is an important aspect of many industrial and geophysical processes, necessitating…
In the past two decades, many research groups worldwide have tried to understand and categorize simple regimes in the charge transfer of such biological systems as DNA. Theoretically speaking, the lack of exact theories for electron-nuclear…
There are many processes in cell biology that can be modeled in terms of particles diffusing in a two-dimensional (2D) or three-dimensional (3D) bounded domain $\Omega \subset \R^d$ containing a set of small subdomains or interior…
The charging of insulating samples degrades the quality and complicates the interpretation of images in scanning electron microscopy and is important in other applications, such as particle detectors. In this paper we analyze this…
Regions of stellar and planetary interiors that are unstable according to the Schwarzschild criterion, but stable according to the Ledoux criterion, are subject to a form of oscillatory double-diffusive (ODD) convection often called…
A design tool was formulated for optimizing the efficiency of inorganic, thin-film, photovoltaic solar cells. The solar cell can have multiple semiconductor layers in addition to antireflection coatings, passivation layers, and buffer…
The need for reliable predictions of the solar activity cycle motivates the development of dynamo models incorporating a representation of surface processes sufficiently detailed to allow assimilation of magnetographic data. In this series…
A system of drift-diffusion equations for the electron, hole, and oxygene vacancy densities in a semiconductor, coupled to the Poisson equation for the electric potential, is analyzed in a bounded domain with mixed Dirichlet-Neumann…
Biological cells can release compounds into their direct environment, generally inhomogeneously over their cell membrane, after which the compounds spread by diffusion. In mathematical modelling and simulation of a collective of such cells,…
The global scales of solar convection are studied through three-dimensional simulations of compressible convection carried out in spherical shells of rotating fluid which extend from the base of the convection zone to within 15 Mm of the…
This paper describes a new 2D model for the photospheric evolution of the magnetic carpet. It is the first in a series of papers working towards constructing a realistic 3D non-potential model for the interaction of small-scale solar…
We study the dynamics of a one-dimensional non-linear and non-local drift-di usion equation set in the half-line, with the coupling involving the trace value on the boundary. The initial mass M of the density determines the behaviour of the…
We introduce a model for describing the dynamics of large numbers of interacting cells. The fundamental dynamical variables in the model are sub-cellular elements, which interact with each other through phenomenological intra- and…
We propose a dual scale drift-diffusion model for interfacial growth and etching processes. The two scales are: (i) a depletion layer width surrounding the aggregate and (ii) a drift length.The interplay between these two antithetical…
Motile eukaryotic cells display distinct modes of migration that often occur within the same cell type. It remains unclear, however, whether transitions between the migratory modes require changes in external conditions, or whether the…
In this paper, the initial value problem for the Debye--Hueckel drift-diffusion equation is studied. This equation was introduced as a model describing plasma behavior and is also known as a simulation model of MOSFET, and so its solution…
Organic solar cells are a promising avenue for renewable energy, and our study introduces a comprehensive model to investigate exciton dissociation processes at the donor-acceptor interface. Examining quantum efficiency and emitted phonons…
Here we formulate and solve the 3D radiative transfer problem of the polarization of the solar continuous radiation. Our approach takes into account not only the anisotropy of the continuum radiation, but also the symmetry-breaking effects…
Recent observations and simulations indicate that solar flares undergo extremely complex three-dimensional (3D) evolution, making 3D particle transport models essential for understanding electron acceleration and interpreting flare…
We investigated existence of global weak solutions for a system of chemotaxis type with nonlinear degenerate diffusion, arising in modelling Multiple Sclerosis disease. The model consists of three equations describing the evolution of…