MIMS EPrints
Not a member yet
2151 research outputs found
Sort by
Viscous linear stability analysis of rectangular duct and cavity flows
Get PDFThe viscous linear stability of four classes of incompressible flows inside rectangular containers is studied numerically. In the first class the instability of flow through a rectangular duct, driven by a constant pressure gradient along the axis of the duct (essentially a two-dimensional counterpart to plane Poiseuille flow – PPF), is addressed. The other classes of flow examined are generated by tangential motion of one wall, in one case in the axial direction of the duct, in another perpendicular to this direction, corresponding respectively to the two-dimensional counterpart to plane Couette flow (PCF) and the classic lid-driven cavity (LDC) flow, and in the fourth case a combination of both the previous tangential wall motions. The partial-derivative eigenvalue problem which in each case governs the temporal development of global three-dimensional small-amplitude disturbances is solved numerically. The results of Tatsumi & Yoshimura (1990) for pressure-gradient-driven flow in a rectangular duct have been confirmed; the relationship between the eigenvalue spectrum of PPF and that of the rectangular duct has been investigated. Despite extensive numerical experimentation no unstable modes have been found in the wall-bounded Couette flow, this configuration found here to be more stable than its one-dimensional limit. In the square LDC flow results obtained are in line with the predictions of Ding & Kawahara (1998b), Theofilis (2000) and Albensoeder et al. (2001b) as far as one travelling unstable mode is concerned. However, in line with the predictions of the latter two works and contrary to all previously published results it is found that this mode is the third in significance from an instability analysis point of view. In a parameter range unexplored by Ding & Kawahara (1998b) and all prior investigations two additional eigenmodes exist, which are both more unstable than the mode that these authors discovered. The first of the new modes is stationary (and would consequently be impossible to detect using power-series analysis of experimental data), whilst the second is travelling, and has a critical Reynolds number and frequency well inside the experimentally observed bracket. The effect of variable aspect ratio of the cavity on the most unstable eigenmodes is also considered, and it is found that an increase in aspect ratio results in general destabilization of the flow. Finally, a combination of wall-bounded Couette and LDC flow, generated in a square duct by lid motion at an angle with the homogeneous duct direction, is shown to be linearly unstable above a Reynolds number \Rey\,{=}\,800 (based on the lid velocity and the duct length/height) at all parameter values examined. The excellent agreement with experiment in LDC flow and the alleviation of the erroneous prediction of stability of wall-bounded Couette flow is thus attributed to the presence of in-plane basic flow velocity components
The equivalence of some conjectures of Dade and Robinson
No full textWe demonstrate that Conjecture 4.1 of [G.R. Robinson, Proc. London Math. Soc. (3) 72 (1996) 312–330] and Dade's projective conjecture are equivalent in a way which is compatible with the p-local rank. Further we consider refinements of these conjectures similar to those of Isaacs, Navarro and Uno, show their equivalence and demonstrate that in order to verify them it suffices to consider only those groups with no non-central normal p-subgroup
Part 1: the reconstruction problem
Get PDFThis book section provides a comprehensive introduction to reconstruction algorithms in Electrical Impedance Tomography (EIT) aimed at graduate students starting their research in this area
A signalizer functor theorem for groups of finite Morley rank
No full textThere is a longstanding conjecture, due to Gregory Cherlin and Boris Zilber, that all
simple groups of finite Morley rank are simple algebraic groups. Towards this end, the
development of the theory of groups of finite Morley rank has achieved a good theory of
Sylow 2-subgroups. It is now common practice to divide the Cherlin–Zilber conjecture
into different cases depending on the nature of the connected component of the Sylow
2-subgroup, known as the Sylow◦ 2-subgroup.
We shall be working with groups whose Sylow◦ 2-subgroup is divisible, or odd type
groups. To date, the main theorem in the area of odd type groups is Borovik’s trichotomy
theorem. The “trichotomy” here is a case division of the minimal counterexamples within
odd type.
More technically, Borovik’s result represents a major success at transferring signalizer
functors and their applications from finite group theory to the finite Morley rank setting.
The major difference between the two settings is the absence of a solvable signalizer
functor theorem. This forced Borovik to work only with nilpotent signalizer functors, and
the trichotomy theorem ends up depending on the assumption of tameness to assure that
the necessary signalizer functors are nilpotent.
The present paper shows that one may obtain a connected nilpotent signalizer functor
from any sufficiently non-trivial solvable signalizer functor. This result plugs seamlessly
into Borovik’s work to eliminate the assumption of tameness from his trichotomy theorem.
In the meantime, a new approach to the trichotomy theorem has been developed by
Borovik [7], based on the “generic identification theorem” of Berkman and Borovik [5].
Borovik uses his original signalizer functor arguments, and incorporates the result of the
present paper.
The paper is organized as follows. The first section will develop a limited characteristic
zero notion of unipotence to complement the usual p-unipotence theory. The section on
centralizers and generation which follows will establish some background needed in the
rest of the paper. In Section 4 we prove our main result on signalizer functors, and in
Section 5 we discuss some applications. With Borovik’s kind permission, we include a
proof of the nilpotent signalizer functor theorem as an appendix. The results of Section 3
are based in part on a section of an unpublished version of [3]
Computing the Polar Decomposition and the Matrix Sign Decomposition in Matrix Groups
No full textFor any matrix automorphism group \G associated with a
bilinear or sesquilinear form,
Mackey, Mackey, and Tisseur have recently shown that the
matrix sign decomposition factors of A\in\G also lie in \G;
moreover, the polar factors of lie in \G if the matrix of the underlying
form is unitary.
Groups satisfying the latter condition
include the complex orthogonal,
real and complex symplectic, and pseudo-orthogonal groups.
This work is concerned with exploiting the structure of \G when computing the
polar and matrix sign decompositions of matrices in \G.
We give sufficient conditions for a matrix iteration to preserve the
group structure and show that a family of globally convergent
rational Pad\'e-based iterations of Kenney and Laub satisfy these conditions.
The well-known scaled Newton iteration for computing the unitary polar
factor does not preserve group structure,
but we show that the approach of the iterates to the group
is precisely tethered to the approach to unitarity,
and that this forces a different and exploitable structure in the iterates.
A similar relation holds for the Newton iteration for the matrix sign function.
We also prove that the number of iterations needed for convergence of the
structure-preserving methods
can be precisely predicted by running an associated scalar iteration.
Numerical experiments are given to compare the cubically and quintically
converging iterations with Newton's method and to test stopping criteria.
The overall conclusion is that the structure-preserving iterations
and the scaled Newton iteration are all of practical interest,
and which iteration is to be preferred is problem-dependent
Superdecomposable pure injective modules exist over some string algebras
No full textWe prove that over every non-domestic string algebra over a countable field there exists a superdecomposable pure-injective module
A local limit theorem for closed geodesics and homology
No full textIn this paper, we study the distribution of closed geodesics on a compact negatively curved manifold. We concentrate on geodesics lying in a prescribed homology class and, under certain conditions, obtain a local limit theorem to describe the asymptotic behaviour of the associated counting function as the homology class varies
Mackey functors and control of fusion
No full textThis paper presents an algebraic approach to Mislin's theorem that control of -fusion is equivalent to inducing a mod- cohomology isomorphism. There are consequences for the cohomology of -permutation modules
On the onset of oscillatory convection in molten gallium
Get PDFThe results of experimental and numerical investigations of the onset of oscillatory convection in a sidewall heated rectangular cavity of molten gallium are reported. Detailed comparisons are made between experimental observations and calculations from numerical simulations of a three-dimensional Boussinesq model. The onset of time-dependence takes place through supercritical Hopf bifurcations and the loci of critical points in the ()-plane are qualitatively similar with excellent agreement between the frequencies of the oscillatory motion. This provides a severe test of the control of the experiment since the mode of oscillation is extremely sensitive to imperfections.
Detailed numerical investigations reveal that there are a pair of Hopf bifurcations which exist on two asymmetric states which themselves arise at a subcritical pitchfork from the symmetric state. There is no evidence for this in the experiment and this qualitative difference is attributed to non-Boussinesq perturbations which increase with .
However, the antisymmetric spatial structure of the oscillatory state is robust and is present in both the experiment and the numerical model. Moreover, the detailed analysis of the numerical results reveals the origins of the oscillatory instability
A Black-Box Multigrid Preconditioner for the Biharmonic Equation
Get PDFWe examine the convergence characteristics of a preconditioned Krylov subspace solver applied to the linear systems arising from low-order mixed finite element approximation of the biharmonic problem. The key feature of our approach is that the preconditioning can be realized using any “black-box” multigrid solver designed for the discrete Dirichlet Laplacian operator. This leads to preconditioned systems having an eigenvalue distribution consisting of a tightly clustered set together with a small number of outliers. Numerical results show that the performance of the methodology is competitive with that of specialized fast iteration methods that have been developed in the context of biharmonic problems