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We present the plane-symmetric solitonlike solutions of magnetostatic equilibria by solving the nonlinear Grad-Shafranov (GS) equation numerically. The solutions have solitonlike and periodic structures in the $x$ and $y$ directions,…
We present a novel extension of multi-output Gaussian processes for handling heterogeneous outputs. We assume that each output has its own likelihood function and use a vector-valued Gaussian process prior to jointly model the parameters in…
We consider fluid flows for which the linearized Navier-Stokes operator is strongly non-normal. The responses of such flows to external perturbations are spanned by a generically very large number of non-orthogonal eigenmodes. They are…
With the help of the generalized characteristics(GC) of the first order partial differential equations(PDE) we calculate the differential equation system of characteristics of the homogenous magneto hydrodynamical equations(MHD).
In the article the authors present a numerical method for modelling a laminar-turbulent transition in magnetohydrodynamic flows. The equations in the small magnetic Reynolds numbers approach is considered. Speed, pressure and electrical…
In this tutorial, a derivation of magnetohydrodynamics (MHD) valid beyond the usual ideal gas approximation is presented. Non-equilibrium thermodynamics is used to obtain conservation equations and linear constitutive relations. When…
A new class of integro-partial differential equation models is derived for the prediction of granular flow dynamics. These models are obtained using a novel limiting averaging method (inspired by techniques employed in the derivation of…
An algebraic technique adapted to the problems of the fundamental theoretical physics is presented. The exposition is an elaboration and an extension of the methods proposed in previous works by the aut
We deal with a class of abstract nonlinear stochastic models with multiplicative noise, which covers many 2D hydrodynamical models including the 2D Navier-Stokes equations, 2D MHD models and 2D magnetic B\'enard problems as well as some…
In this paper we present applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. According to variational approach in the general case we have the solution as a…
Magnetohydrodynamics (MHD) is a continuum level model for conducting fluids subject to external magnetic fields, e.g. plasmas and liquid metals. The efficient and robust solution of the MHD system poses many challenges due to it's…
This letter describes a method for estimating regions of attraction and bounds on permissible perturbation amplitudes in nonlinear fluids systems. The proposed approach exploits quadratic constraints between the inputs and outputs of the…
A new probabilistic representation is presented for solutions of the incompressible Navier-Stokes equations in 3 dimensions with given forcing and initial velocity. This representation expresses solutions as scaled conditional expectations…
We introduce matrix coupled (local and nonlocal) dispersionless equations, construct wide classes of explicit multipole solutions, give explicit expressions for the corresponding Darboux and wave matrix valued functions and consider their…
We present a novel high-order nodal artificial viscosity approach designed for solving Magnetohydrodynamics (MHD) equations. Unlike conventional methods, our approach eliminates the need for ad hoc parameters. The viscosity is…
We derive the approximate pressure profiles, density profiles, and temperature profiles of an atmosphere, also called barometric formulas. Our variant of a derivation goes beyond the common standard exercise of a thermodynamics lecture,…
We investigate the large-time behavior of solutions toward the combination of the boundary layer and 3-rarefaction waves to the outflow problem for the compressible non-isentropic Navier-Stokes equations coupling with the Maxwell equations…
We propose a new finite element method for linearized Magnetohydrodynamics. The main novelty is that the proposed scheme is able to handle also non-convex domains and less regular solutions. The method is proved to be pressure robust and…
This paper is concerned with the large-time behavior of solutions to the outflow problem of full compressible Navier-Stokes equations in the half line. This is one of the series of papers by the authors on the stability of nonlinear waves…
In this paper, we investigate the similarity solutions for a steady laminar incompressible boundary layer equations governing the Magnetohydrodynamic (MHD) flow near the forward stagnation point of two-dimensional and axisymmetric bodies.…