MIMS EPrints
Not a member yet
2151 research outputs found
Sort by
Local limit theorems for free groups
No full textIn this paper we obtain a local limit theorem for elements of a free group G under the abelianization map [·] :G ® G/[G,G]. This is obtained via an analysis involving subshifts of finite type, where we obtain a result of independent interest. The case of fundamental groups of compact surfaces of genus ³ 2 is also discussed
Livsic theorems for connected Lie groups
No full textLet be a hyperbolic diffeomorphism on a basic set and let be a connected Lie group. Let be Hölder. Assuming that satisfies a natural partial hyperbolicity assumption, we show that if is a measurable solution to a.e., then must in fact be Hölder. Under an additional centre bunching condition on , we show that if assigns `weight' equal to the identity to each periodic orbit of , then for some Hölder . These results extend well-known theorems due to Livsic when is compact or abelian
Flame propagation in Poiseuille flow under adiabatic conditions
No full textWe describe flame propagation in a channel subject to a Poiseuille flow, within the thermo-diffusive approximation and an adiabatic context. The two-dimensional flame fronts addressed may be either assisted or opposed by the flow. The problem is characterized by two parameters, the intensity of the flow u0 and the spatial scale small epsilon, Greek. The total burning rate and the propagation speed are determined in terms of u0 and small epsilon, Greek and different distinguished regimes are described. From the results, simple criteria for flame flashback in channels are identified. Conclusions concerning the long-term evolution of an ignition kernel in the present flow are also drawn. The results may also be useful in interpreting similar features encountered in more complicated flow situations. For example, the quadratic dependence of the burning rate on u0 for weak flow intensities, and linear dependence for larger u0, is similar to that of the turbulent flame speed when the latter is considered as a function of the velocity fluctuations or turbulence intensity
Three-dimensional free convection in molten gallium
Get PDFConvective flow of molten gallium is studied in a small-aspect-ratio rectangular, differentially heated enclosure. The three-dimensional nature of the steady flow is clearly demonstrated by quantitative comparison between experimental temperature measurements, which give an indication of the strength of the convective flow, and the results of numerical simulations. The three-dimensional flow structure is characterized by cross-flows which are an order of magnitude smaller than the main circulation, and spread from the endwall regions to the entire enclosure when the Grashof number is increased beyond Gr = 104. The mergence of these effects in the centre of the enclosure leads to a complex central divergent flow structure which underpins the observed transition to oscillatory convection
Relative equilibria of point vortices on the sphere
Get PDFWe prove the existence of many different symmetry types of relative equilibria for systems of identical point vortices on a non-rotating sphere. The proofs use the rotational symmetry group SO(3) and the resulting conservation laws, the time-reversing reflectional symmetries in O(3), and the finite symmetry group of permutations of identical vortices. Results include both global existence theorems and local results on bifurcations from equilibria. A more detailed study is made of relative equilibria which consist of two parallel rings with n vortices in each rotating about a common axis. The paper ends with discussions of the bifurcation diagrams for systems of 3–6 identical vortices
Lines tagent to four unit spheres with coplanar centres
No full textWe prove that there are at most eight lines tangent to four unit spheres in \R3 if the centres of the spheres are coplanar, but not collinear. This bound is sharp
The Hooley-Huxley contour method for problems in number fields III: Frobenian functions
Get PDFIn this paper we study finite valued multiplicative functions defined on ideals of a number field and whose values on the prime ideals depend only on the Frobenius class of the primes in some Galois extension. In particular we give asymptotic results when the ideals are restricted to "small regions". Special cases concern Ramanujan's tau function in small intervals and relative norms in "small regions" of elements from a full module of the Galois extension
Ill and well-posed models of granular flow
No full textA unified method of generating models for the flow of granular materials is used to confirm and extend the results of Schaeffer and co-workers [15], [17]–[19], namely that many existing models exhibit linear ill-posedness with regard to initial conditions. A model proposed in Harris [6], [7] is analyzed by the same method and it is established that, firstly, the model exhibits well-posedness under certain well-defined conditions, secondly, that when these conditions fail to hold, the model exhibits ill-posedness and thirdly, the mathematical ill-posedness corresponds to a real physical instability
Multistability in the quasiperiodically forced circle map
Get PDFIt is well-known that the dynamics of the Arnol′d circle map is phase-locked in regions of the parameter space called Arnol′d tongues. If the map is invertible, the only possible dynamics is either quasiperiodic motion, or phase-locked behavior with a unique attracting periodic orbit. Under the influence of quasiperiodic forcing the dynamics of the map changes dramatically. Inside the Arnol′d tongues open regions of multistability exist, and the parameter dependency of the dynamics becomes rather complex. This paper discusses the bifurcation structure inside the Arnol′d tongue with zero rotation number and includes a study of nonsmooth bifurcations that happen for large nonlinearity in the region with strange nonchaotic attractors
Newton's Method in Floating Point Arithmetic and Iterative Refinement of Generalized Eigenvalue Problems
Get PDFWe examine the behavior of Newton's method in floating point arithmetic, allowing for extended precision in computation of the residual, inaccurate evaluation of the Jacobian and unstable solution of the linear systems. We bound the limiting accuracy and the smallest norm of the residual. The application that motivates this work is iterative refinement for the generalized eigenvalue problem. We show that iterative refinement by Newton's method can be used to improve the forward and backward errors of computed eigenpairs