Related papers: Ambipolar diffusion: Self-similar solutions and MH…
We develop analytic approximations to the density evolution of prestellar cores, based on the results of hydrodynamical simulations. We use these approximations as input for a time-dependent gas-grain chemical code to investigate the…
The advection-diffusion and wave equations are the fundamental equations governing any physical law and therefore arise in many areas of physics and astrophysics. For complex problems and geometries, only numerical simulations can give…
We introduce the multivariate decomposition finite element method (MDFEM) for solving elliptic PDEs with uniform random diffusion coefficients. We show that the MDFEM can be used to reduce the computational complexity of estimating the…
We give a sufficient condition for blow up of positive mild solutions to an initial value problem for a nonautonomous weakly coupled system with distinct fractional diffusions. The proof is based on the study of blow up of a particular…
In this paper, we consider the 2D incompressible MHD equations with horizontal dissipation and horizontal magnetic diffusion. We establish local existence and uniqueness of solutions for initial data in $H^s$($s\geq 1$). The proof relays…
The gravitational instability of a filamentary molecular cloud in non-ideal magnetohydrodynamics is investigated. The filament is assumed to be in hydrostatic equilibrium. We add the effect of ambipolar diffusion to the filament which is…
In this paper, we obtain the global well-posedness and the asymptotic behavior of solution of non-resistive 2D MHD problem on the half space. We overcome the difficulty of zero spectrum gap by building the relationship between half space…
We solve the magnetohydrodynamic (MHD) equations governing axisymmetric flows around neutron stars and black holes and found all possible solution topologies for adiabatic accretion. We divide the parameter space spanned by the conserved…
We present a radiation-magnetohydrodynamics (RMHD) simulation of a magnetic cancellation event. The model is calculated with the Bifrost code and spans from the uppermost convection zone to the corona. The cancellation occurs between the…
In this paper we study nonlinear Helmholtz equations with sign-changing diffusion coefficients on bounded domains. The existence of an orthonormal basis of eigenfunctions is established making use of weak T-coercivity theory. All…
We examine by extensive computer simulations the self-diffusion of anisotropic star like particles in crowded two-dimensional solutions. We investigate the implications of the area coverage fraction $\phi$ of the crowders and the…
This is the first paper about the fragmentation and mass outflow in the molecular cloud by using three-dimensional MHD nested-grid simulations. The binary star formation process is studied paying particular attention to the fragmentation of…
Observations of the upper chromosphere shows an enormous amount of intricate fine structure. Much of this comes in the form of linear features which are most often assumed to be well aligned with the direction of the magnetic field in the…
The periodic solutions of a type of nonlinear hyperbolic partial differential equations with a localized nonlinearity are investigated. For instance, these equations are known to describe several acoustical systems with fluid-structure…
Analysing two-dimensional shallow water equations with idealised bottom topographies have many applications in the atmospheric and oceanic sciences; however, restrictive flow pattern assumptions have been made to achieve explicit solutions.…
Recent experiments with degenerate molecular gases dressed by elliptically polarized microwave fields have enabled new control of dipolar interactions via engineered anisotropy. We reveal a symmetry structure of the dipolar interaction that…
A number of physical phenomena are described by nonlinear hyperbolic equations. Presence of discontinuous solutions motivates the necessity of development of reliable numerical methods based on the fundamental mathematical properties of…
Recently, diffusion models have been used to solve various inverse problems in an unsupervised manner with appropriate modifications to the sampling process. However, the current solvers, which recursively apply a reverse diffusion step…
Acoustic wave propagation in a one-dimensional waveguide connected with Helmholtz resonators is studied numerically. Finite amplitude waves and viscous boundary layers are considered. The model consists of two coupled evolution equations: a…
We propose a locally one dimensional (LOD) finite difference method for multidimensional Riesz fractional diffusion equation with variable coefficients on a finite domain. The numerical method is second-order convergent in both space and…