Related papers: The Singular Behaviour of Ambipolar Diffusion Reve…
A new solution to the mono-dimensional diffusion equation for time-variable first kind boundary condition is presented where the time-variable function at the surface is derived proposing a surface saturation model. This solution may be…
In this work we investigate the unique identifiability and stable recovery of a spatially dependent variable-order in the subdiffusion model from the boundary flux measurement. We establish several new unique identifiability results from…
We present a robust and accurate numerical method for the anisotropic diffusion equation in curvilinear coordinates. This study extends the recent work [Muir et al., Computer Physics Communications, 2025] for solving the anisotropic…
This paper investigates the existence of localised axisymmetric (radial) patterns on the surface of a ferrofluid in the presence of a uniform vertical magnetic field. We formally investigate all possible small-amplitude solutions which…
An evolutionary process of the fast magnetic reconnection in ``free space'' which is free from any influence of outer circumstance has been studied semi-analytically, and a self-similarly expanding solution has been obtained. The…
We implement a new semi-analytical approach to investigate radially self-similar solutions for the steady-state advection-dominated accretion flows (ADAFs). We employ the usual $\alpha$-prescription for the viscosity and all the components…
Magnetohydrodynamic (MHD) simulations of the solar atmosphere are often performed under the assumption that the plasma is fully ionized. However, in the lower solar atmosphere a reduced temperature often results in only the partial…
We find for the first time the asymptotic representation of the solution to the space dependent variable order fractional diffusion and Fokker-Planck equations. We identify a new advection term that causes ultra-slow spatial aggregation of…
We present analytical and numerical solutions which describe a hot, viscous, two-temperature accretion flow onto a neutron star or any other compact star with a surface. We assume Coulomb coupling between the protons and electrons, and…
Solute dispersion due to an instantaneously released source in steady, laminar, axisymmetric flows with an axial inflow and radial outflow is investigated analytically. Attention is given to large-time characteristics of dispersion, where…
We analyze the properties of steady and time-dependent C shocks under conditions prevailing in giant molecular clouds. For steady C shocks, we show that ionization equilibrium holds and use numerical integrations to obtain the shock…
The scientific community employs complicated multiphysics simulations to understand the physics in Solar, Stellar, and Interstellar media. These must be tested against known solutions to ensure their validity. Several well-known tests…
The complete eleven-dimensional supergravity solutions with 16 supersymmetries on manifolds of the form $AdS_3 \times S^3 \times S^3 \times \Sigma$, with isometry $SO(2,2) \times SO(4) \times SO(4)$, and with either $AdS_4 \times S^7$ or…
In theory, diffusion curves promise complex color gradations for infinite-resolution vector graphics. In practice, existing realizations suffer from poor scaling, discretization artifacts, or insufficient support for rich boundary…
We present a novel numerical method for solving the anisotropic diffusion equation in magnetic fields confined to a periodic box which is accurate and provably stable. We derive energy estimates of the solution of the continuous initial…
This paper establishes a theory of nonlinear spectral decompositions by considering the eigenvalue problem related to an absolutely one-homogeneous functional in an infinite-dimensional Hilbert space. This approach is both motivated by…
For a model convection-diffusion problem, we address the presence of oscillatory discrete solutions, and study difficulties in recovering standard approximation results for its solution. We justify the presence of non-physical oscillations…
We follow the ambipolar-diffusion--driven formation and evolution of a fragment in a magnetically supported molecular cloud, until a hydrostatic protostellar core forms at its center. This problem was formulated in Paper I. We determine the…
We study dipole-mode and scissors-mode oscillations of a harmonically-trapped dipolar supersolid, composed of dipolar droplets arranged on a one-dimensional (1D) or a two-dimensional (2D) lattice, to establish the robustness of its…
In this work exact solutions for the equation that describes anomalous heat propagation in 1D harmonic lattices are obtained. Rectangular, triangular, and sawtooth initial perturbations of the temperature field are considered. The solution…