A twist localizes three-dimensional patterns

A mechanism for the localization of spatially periodic, self-organized patterns in anisotropic media which requires systems extended in all three spatial dimensions is presented: When the anisotropy axis is twisted the pattern becomes localized in planes parallel to the anisotropy axis. An analytic description of the effect is developed and used to interpret recent experiments in the high-frequency regime of electroconvection by Bohatsch and Stannarius [Phys. Rev. E {\bf 60}, 5591 (1999)]. The localization width is found to be of the order of magnitude of the geometrical average of pattern wavelength and the inverse twist.Comment: 7 pages, 2 figures, submitted to PRE; minor changes in resubmissio

On the limits of spectral methods for frequency estimation

An algorithm is presented which generates pairs of oscillatory random time series which have identical periodograms but differ in the number of oscillations. This result indicate the intrinsic limitations of spectral methods when it comes to the task of measuring frequencies. Other examples, one from medicine and one from bifurcation theory, are given, which also exhibit these limitations of spectral methods. For two methods of spectral estimation it is verified that the particular way end points are treated, which is specific to each method, is, for long enough time series, not relevant for the main result.Comment: 18 pages, 6 figures (Referee did not like the previous title. Many other changes

A frequency measure robust to linear filtering

A definition of frequency (cycles per unit-time) based on an approximate reconstruction of the phase-space trajectory of an oscillator from a signal is introduced. It is shown to be invariant under linear filtering, and therefore inaccessible by spectral methods. The effect of filtering on frequency in cases where this definition does not perfectly apply is quantified.Comment: 10 pages, 2 figure

Pattern Formation from Defect Chaos --- A Theory of Chevrons

For over 25 years it is known that the roll structure of electroconvection (EC) in the dielectric regime in planarly aligned nematic liquid crystals has, after a transition to defect chaos, the tendency to form chevron structures. We show, with the help of a coarse-grained model, that this effect can generally be expected for systems with spontaneously broken isotropy, that is lifted by a small external perturbation. The linearized model as well as a nonlinear extension are compared to simulations of a system of coupled amplitude equations which generate chevrons out of defect chaos. The mechanism of chevron formation is similar to the development of Turing patterns in reaction diffusion systems.Comment: 17 pages, Latex, 11 PS-figures, submitted to Physica

Dynamic opacity for abstract types

Existential types are the standard formalisation of abstract types. While this formulation is sufficient in entirely statically typed languages, it proves to be too weak for languages enriched with forms of dynamic typing: in the presence of operations performing type analysis, the abstraction barrier erected by the static typing rules for existential types is no longer impassable, because parametricity is violated. We present a light-weight calculus for polymorphic languages with abstract types that addresses this shortcoming. It features a variation of existential types that retains most of the simplicity of standard existentials. It relies on modified scoping rules and explicit coercions between the quantified variable and its witness type