Related papers: The Integral Equation Method for a Steady Kinemati…
This paper concerns kinematic helical dynamos in a spherical fluid body surrounded by an insulator. In particular, we examine their behaviour in the regime of large magnetic Reynolds number $\Rm$, for which dynamo action is usually…
In this paper, we present a frequency-domain volume integral method to model the microseismic wavefield in heterogeneous anisotropic-elastic media. The elastic wave equation is written as an integral equation of the Lippmann-Schwinger type,…
A new fully discrete linearized $H^1$-conforming Lagrange finite element method is proposed for solving the two-dimensional magneto-hydrodynamics equations based on a magnetic potential formulation. The proposed method yields numerical…
We consider a dynamo wave in the solar convective shell for the kinematic $\alpha\omega$-dynamo model. The spectrum and eigenfunctions of the corresponding equations are derived analytically with the aid of the WKB method. Our main aim here…
This contribution investigates the connection between isogeometric analysis and integral equation methods for full-wave electromagnetic problems up to the low-frequency limit. The proposed spline-based integral equation method allows for an…
For a simple spherically symmetric mean-field dynamo model we investigate the possibility of determining the radial dependence of the coefficient $\alpha$. Growth rates for different magnetic field modes are assumed to be known by…
This work presents a fast direct solver strategy for electromagnetic integral equations in the high-frequency regime. The new scheme relies on a suitably preconditioned combined field formulation and results in a single skeleton form plus…
Critical analyses of well-known methods of derivation of kinetic and hydrodynamic equations is presented. Another method of derivation of kinetic and hydrodynamic equations from classic mechanics is described. It is shown that equations of…
We analyze the behavior of a quantum system described by a one-dimensional asymmetric potential consisting of a step plus a harmonic barrier. We solve the eigenvalue equation by the integral representation method, which allows us to…
We present direct numerical simulations and alpha-model simulations of four familiar three-dimensional magnetohydrodynamic (MHD) turbulence effects: selective decay, dynamic alignment, inverse cascade of magnetic helicity, and the helical…
Estimates for the nonlinear alpha effect in helical turbulence with an applied magnetic field are presented using two different approaches: the imposed-field method where the electromotive force owing to the applied field is used, and the…
We propose a time-adaptive predictor/multi-corrector method to solve hyperbolic partial differential equations, based on the generalized-$\alpha$ scheme that provides user-control on the numerical dissipation and second-order accuracy in…
In this paper we consider the spatial semi-discretization of conservative PDEs. Such finite dimensional approximations of infinite dimensional dynamical systems can be described as flows in suitable matrix spaces, which in turn leads to the…
Analytic solutions of the mean-field induction equation predict a nonoscillatory dynamo for homogeneous helical turbulence or constant alpha effect in unbounded or periodic domains. Oscillatory dynamos are generally thought impossible for…
We present a computational method to solve the magnetohydrodynamic equations in spherical geometry. The technique is fully nonlinear and wholly spectral, and uses an expansion basis that is adapted to the geometry: Chandrasekhar-Kendall…
The axisymmetric form of the hydrodynamic equations within the smoothed particle hydrodynamics (SPH) formalism is presented and checked using idealized scenarios taken from astrophysics (free fall collapse, implosion and further pulsation…
Mean-field dynamo equations are addressed with the aid of the path-integral method. The evolution of magnetic field is treated as a three-dimensional Wiener random process, and the mean magnetic-field equations are obtained with the Wiener…
In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary differential equations. A general method and…
The Sturm-Liouville eigenvalue equation for eigenmodes of the radial oscillations is determined for spherically symmetric perfect fluid configurations in spacetimes with a nonzero cosmological constant and applied in the cases of…
In the convergence analysis of numerical methods for solving partial differential equations (such as finite element methods) one arrives at certain generalized eigenvalue problems, whose maximal eigenvalues need to be estimated as…