Related papers: An analytic interface dynamo over a shear layer of…
We present a detailed study of the growth of the Parker instability in a differentially rotating disk embedded in an azimuthal equilibrium magnetic field, such as the interstellar gas or an accretion disk. Basic properties of the…
Rotational shear layers at the boundary between radiative and convective zones, tachoclines, play a key role in the process of magnetic field generation in solar-like stars. We present two sets of global simulations of rotating turbulent…
Flux-dominated solar dynamo models have demonstrated to reproduce the main features of the large scale solar magnetic cycle, however the use of a solar like differential rotation profile implies in the the formation of strong toroidal…
We consider a diffusion process with coefficients that are periodic outside of an "interface region" of finite thickness. The question investigated in this article is the limiting long time/large scale behavior of such a process under…
We consider a one-dimensional diffusion process with coefficients that are periodic outside of a finite 'interface region'. The question investigated in this article is the limiting long time / large scale behaviour of such a process under…
The use of continuum phase-field models to describe the motion of well-defined interfaces is discussed for a class of phenomena, that includes order/disorder transitions, spinodal decomposition and Ostwald ripening, dendritic growth, and…
Dynamic wetting poses a well-known challenge in classical sharp-interface formulation as the no-slip wall condition leads to a contact line singularity that is typically regularized with a Navier boundary condition, often requiring…
Motivated by biological applications on tumour invasion through thin membranes, we study a porous-medium type equation where the density of the cell population evolves under Darcy's law, assuming continuity of both the density and flux…
We investigate a novel Marangoni-induced instability that arises exclusively in diffuse fluid interfaces, absent in classical sharp-interface models. Using a validated phase-field Navier-Stokes-Allen-Cahn framework, we linearize the…
We have obtained exact analytical expressions in closed form, for the linear modes excited in finite and discrete systems that are driven by a spatially homogeneous alternating field. Those modes are extended for frequencies within the…
We consider the wave equation $\varepsilon^2(-\partial_t^2 + \Delta)u + f(u) = 0$ for $0<\varepsilon\ll 1$, where $f$ is the derivative of a balanced, double-well potential, the model case being $f(u) = u-u^3$. For equations of this form,…
The helioseismically observed solar tachocline is a thin internal boundary layer of shear that separates the rigidly-rotating solar radiative zone from the differentially-rotating convective zone and is believed to play a central role in…
A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is also…
In multi-component soft matter, interface properties often play a key role in determining the properties of the overall system. The identification of the internal dynamic structures in non-equilibrium situations requires the interface…
In 1969 Leighton developed a quasi-1D mathematical model of the solar dynamo, building upon the phenomenological scenario of Babcock(1961). Here we present a modification and extension of Leighton's model. Using the axisymmetric component…
We consider a degenerate partial differential equation arising in population dynamics, namely the porous medium equation with a bistable reaction term. We study its asymptotic behavior as a small parameter, related to the thickness of a…
Four results associated with the diffuse-interface model (DIM) for contact lines are reported in this paper. First, a boundary condition is derived, which states that the fluid near a solid wall must have a certain density $\rho_{0}$…
At the base of the Sun's convective zone, a narrow shear layer called the tachocline separates strong latitudinal differential rotation above from nearly rigid rotation in the radiative zone below. The observed thinness of the tachocline is…
The analysis of complex fibrous systems or materials on the micro- and nanoscale, which have a high practical relevance for many technical or biological systems, requires accurate analytical descriptions of the adhesive and repulsive forces…
We study the influence of various magnetic diffusivity profiles on the evolution of the poloidal and toroidal magnetic fields in a kinematic flux transport dynamo model for the Sun. The diffusivity is a poorly understood ingredient in solar…