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991.
YANG Wei-Hong 《理论物理通讯》2001,35(2):219-222
The simplified forms of generalized
magnetohydrodynamic equations have been derived. The K. Appert theory and Hain-Lüst equation are two special cases of our results when p→0 and
ω/ωci→0. It is shown
that the process of taking any limits (p→0 or ω/ωci→0) will result in a singularity at the Alfvén resonant layer. 相似文献
992.
A one-dimensional stability transport code has been developed to simulate the evolution of tokamak plasma discharges. Explicit
finite-difference methods have been used to follow the temporal evolution of the electron temperature equation. The poloidal
field diffusion equation has been solved at every time step. The effects of MHD instabilities have been incorporated by solving
equations for MHD mixing and tearing modes as and when required. The code has been applied to follow the evolution of tokamak
plasma discharges obtained in the Saha Institute of Nuclear Physics (SINP) tokamak. From these simulations, we have been able
to identify the possible models of thermal conductivity, diffusion and impurity contents in these discharges. Effects of different
MHD modes have been estimated. It has been found that in low q
0 discharge m=1, n=1 and m=2, n=1 modes play major role in discharge evolution. These modes are found to result in the positive jump in the loop voltage
which was also observed in the experiments. Hollow current density profile j
φ
and negative shear in the q profile have also been found in the rising phase of a discharge. 相似文献
993.
François Y. Génin 《Interface Science》2001,9(1-2):83-92
Holes and hillocks can commonly be observed on the surface of thin films after thermal processing. For films deposited on a substrate with a different coefficient of thermal expansion, strains due to thermal expansion mismatch can produce very large stresses. While capillary forces tend to produce a thermal groove at a grain boundary (GB), compressive and tensile stresses can form, respectively, a ridge or a canal at the GB. These phenomena can strongly influence mobility of a GB. The formation of a canal enhances the potential for pinning the GB, whereas the formation of a ridge tends to repel the GB.After a short overview of the theory, analytical and numerical solutions for surface profiles of static and travelling GBs under stress are presented. The results of the computed profiles are compared to experimental surface morphologies in aluminum thin film. 相似文献
994.
本文对三维有界及无界区域上描述地球物理流动的磁流体型发展方程解的 全局L2稳定性进行了讨论.在解满足适当的条件下,证明了此解为稳定的,并得到 非强迫二维磁流体流动在三维扰动下的稳定性. 相似文献
995.
A system of ordinary differential equations of mixed order on an interval (0, r0) is considered, where some coefficients are singular at 0. Special cases have been dealt with by Kako , where the essential spectrum of an operator associated with a linearized MHD model was calculated, and more recently by Hardt , Mennicken and Naboko . In both papers this operator is a selfadjoint extension of an operator on sufficiently smooth functions. The approach in the present paper is different in that a suitable operator associated with the given system of ordinary differential equations is explicitly defined as the closure of an operator defined on sufficiently smooth functions. This closed operator can be written as a sum of a selfadjoint operator and a bounded operator. It is shown that its essential spectrum is a nonempty compact subset of ℂ, and formulas for the calculation of the essential spectrum in terms of the coefficients are given. 相似文献
996.
997.
Large-scale horizontal vortices associated with deformations of the aluminum-electrolyte interface have been observed in operating
aluminum reduction cells as well as in physical and numerical models. To expose their importance, we analyze a particular
class of magnetohydrodynamic (MHD) interfacial instabilities which are induced by rotation. As we focus on a single vortex,
a cylindrical geometry is preferred. Two analytical models are proposed. In a first model based on the MHD shallow-water approximation,
we consider a vortex that has a solid rotation profile to obtain a wave equation and a dispersion relation. A more realistic
second model includes a viscous rotation profile and the treatment of the base-state interface deformation. Energetics of
the flow gives further insight on how an initial perturbation evolves as an oscillatory or a non-oscillatory instability,
depending on the direction of rotation. We find that the mechanism at the very origin of these instabilities is neither due
to a shear between the two layers—and are therefore not Kelvin–Helmholtz instabilities—nor simply due to magnetic force alone,
but rather to the indirect action of the centripetal pressure due to the rotation induced by magnetic force.
相似文献
998.
Banavara N. Shashikanth Artan Sheshmani Scott David Kelly Jerrold E. Marsden 《Theoretical and Computational Fluid Dynamics》2008,22(1):37-64
We present a (noncanonical) Hamiltonian model for the interaction of a neutrally buoyant, arbitrarily shaped smooth rigid
body with N thin closed vortex filaments of arbitrary shape in an infinite ideal fluid in Euclidean three-space. The rings are modeled
without cores and, as geometrical objects, viewed as N smooth closed curves in space. The velocity field associated with each ring in the absence of the body is given by the Biot–Savart
law with the infinite self-induced velocity assumed to be regularized in some appropriate way. In the presence of the moving
rigid body, the velocity field of each ring is modified by the addition of potential fields associated with the image vorticity
and with the irrotational flow induced by the motion of the body. The equations of motion for this dynamically coupled body-rings
model are obtained using conservation of linear and angular momenta. These equations are shown to possess a Hamiltonian structure
when written on an appropriately defined Poisson product manifold equipped with a Poisson bracket which is the sum of the
Lie–Poisson bracket from rigid body mechanics and the canonical bracket on the phase space of the vortex filaments. The Hamiltonian
function is the total kinetic energy of the system with the self-induced kinetic energy regularized. The Hamiltonian structure
is independent of the shape of the body, (and hence) the explicit form of the image field, and the method of regularization,
provided the self-induced velocity and kinetic energy are regularized in way that satisfies certain reasonable consistency
conditions.
相似文献
999.
This work presents a finite element solution of the 3D magneto‐hydrodynamics equations. The formulation takes explicitly into account the local conservation of the magnetic field, giving rise to a conservative formulation and introducing a new scalar variable. A stabilization technique is used in order to allow equal linear interpolation on tetrahedral elements of all the variables. Numerical tests are performed in order to assess the stability and the accuracy of the resulting methods. The convergence rates are calculated for different stabilization parameters. Well‐known MHD benchmark tests are calculated. Results show good agreement with analytical solutions. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
1000.
M.E. Kavousanakis L. Russo C.I. Siettos A.G. Boudouvis G.C. Georgiou 《ournal of non Newtonian Fluid Mechanics》2008,151(1-3):59
We discuss how matrix-free/timestepper algorithms can efficiently be used with dynamic non-Newtonian fluid mechanics simulators in performing systematic stability/bifurcation analysis. The timestepper approach to bifurcation analysis of large-scale systems is applied to the plane Poiseuille flow of an Oldroyd-B fluid with non-monotonic slip at the wall, in order to further investigate a mechanism of extrusion instability based on the combination of viscoelasticity and non-monotonic slip. Due to the non-monotonicity of the slip equation the resulting steady-state flow curve is non-monotonic and unstable steady states appear in the negative-slope regime. It has been known that self-sustained oscillations of the pressure gradient are obtained when an unstable steady state is perturbed [M.M. Fyrillas, G.C. Georgiou, D. Vlassopoulos, S.G. Hatzikiriakos, A mechanism for extrusion instabilities in polymer melts, Polymer Eng. Sci. 39 (1999) 2498–2504].Treating the simulator of a distributed parameter model describing the dynamics of the above flow as an input–output “black-box” timestepper of the state variables, stable and unstable branches of both equilibrium and periodic oscillating solutions are computed and their stability is examined. It is shown for the first time how equilibrium solutions lose stability to oscillating ones through a subcritical Hopf bifurcation point which generates a branch of unstable limit cycles and how the stable periodic solutions lose their stability through a critical point which marks the onset of the unstable limit cycles. This implicates the coexistence of stable equilibria with stable and unstable periodic solutions in a narrow range of volumetric flow rates. 相似文献