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Linear instability of planar shear banded flow
No full textWe study the linear stability of planar shear banded flow with respect to perturbations with wave vector in the plane of the banding interface, within the nonlocal Johnson-Segalman model. We find that perturbations grow in time, over a range of wave vectors, rendering the interface linearly unstable. Results for the unstable eigenfunction are used to discuss the nature of the instability. We also comment on the stability of phase separated domains to shear flow in model H
A monster graph
No full textThe structure of the point-line collinearity graph of the maximal 2-local geometry for the Monster simple group is investigated. The main results describe the first two discs around an arbitrary vertex
On mass conservation in least squares methods
No full textWe compare three least-squares finite element reformulations of the Stokes equations, paying particular attention to mass conservation. The first problem we approximate has a simple analytical solution over a convex region. Even for this simple problem, without special treatment of the conservation of mass term, very poor numerical solutions may result. Sufficiently weighting this term leads to a dramatic improvement in the results over a range of test problems
Lie powers in prime degree
No full textLet Lp(V) denote the pth Lie power of a finite-dimensional module V for a group G over a field of prime characteristic p, where Lp(V) is regarded as a submodule of the tensor power Tp(V). There is a natural homomorphism from Lp(V) onto the pth metabelian Lie power Mp(V). We show that the kernel of this homomorphism is a direct summand of Tp(V) and apply this result to the generic case where G is the general linear group on V and the field is infinite. In this case we find the indecomposable direct summands of Lp(V) and their multiplicities
Nonaxisymmetric magnetic field generation in rapidly rotating late-type stars
Get PDFRecently the discovery of the “flip-flop” phenomenon, by which a predominant “active” longitude jumps by about 180 °, on several rapidly rotating late-type stars has directed attention to the issues surrounding the presence of large-scale nonaxisymmetric magnetic fields in these objects. Here we study nonlinear mean field dynamo models with quasi-cylindrical rotation laws, acting in spherical shells. Stable nonaxisymmetric magnetic fields are found to be generated for a range of parameters and, for certain of these models, jumps in a measure plausibly related to the position of active longitudes are found to occur. In general, nonaxisymmetric fields appear to be easier to generate in thinner dynamo-active regions. However, flip-flops appear to be stronger for intermediate thicknesses of the dynamo-active shells
An inverse boundary value problem for harmonic differential forms
No full textWe show that the full symbol of the Dirichlet to Neumann map of the k-form Laplace's equation on a Riemannian manifold (of dimension greater than 2) with boundary determines the full Taylor series, at the boundary, of the metric. This extends the result of Lee and Uhlmann for the case k = 0. The proof avoids the computation of the full symbol by using the calculus of pseudo-differential operators parametrized by a boundary normal coordinate and recursively calculating the principal symbol of the difference of boundary operators
The scattering of Rossby waves from finite abrupt topography
No full textThe scattering of first mode linear baroclinic Rossby waves by a top-hat ridge in a continuously stratified ocean, with Brunt-Väisälä frequency that decays exponentially with depth below a surface mixed layer, is the subject of this study. A numerical mode matching technique is used to calculate the transmission coefficients for the propagating modes over the ridge. It is found that the scattered field depends crucially upon the stratification. For example, when the majority of the density variation is confined to a thin thermocline, corresponding to a small e-folding scale, gamma -1, for the Brunt-Väisälä frequency, a large amount of the incident wave energy is reflected by a small amplitude ridge. Appreciable energy conversion between the propagating barotropic and baroclinic modes takes place in this case. An asymptotic analysis for a small amplitude ridge is presented that confirms these numerical results. In the limit gamma -1? 0, it is demonstrated that the scattered field in the continuously stratified ocean model differs markedly from the two-layer solution. The latter does not exhibit appreciable reflection of the incident wave energy for a small amplitude ridge. In conclusion, the application of a two-layer ocean model to describe Rossby wave scattering by ridges in place of a continuously stratified model cannot be recommended
Invariants de classes: le cas semi-stable
No full textWe define here an analogue, for a semi-stable group scheme whose generic fiber is an abelian variety, of M. J. Taylor's class-invariant homomorphism (defined for abelian schemes), and we give a geometric description of it. Then we extend a result of Taylor, Srivastav, Agboola and Pappas concerning the kernel of this homomorphism in the case of an elliptic curve
Theoretical study of receptivity of a thin weakly non-parallel shock layer to acoustic disturbances (in Russian)
Get PDFTheoretical study of receptivity of a thin weakly non-parallel shock layer to acoustic disturbances is performed. We apply the general theory of boundary layer receptivity to the case of shock layer eigen modes excited by the impinging acoustic wave. The spectrum of eigen modes is obtained in analytical form in the thin shock layer approximation, assuming the flow inside the shock layer is uniform. This allows to predict the effective directions of an impinging acoustic wave that cause resonance with the eigen modes, as well as locate the regions of the shock layer where the resonance is taking place
Symmetric Hamiltonian Bifurcations
No full textThe purpose of these notes is to give a brief survey of bifurcation theory of Hamiltonian systems with symmetry; they are a slightly extended version of the 5 lectures given by JM on Hamiltonian Systems with Symmetry at the Peyresq Summer School. Attention is focussed on bifurcations near equilibrium solutions and relative equilibria. [Taken from introduction