Construction of sequences with high Nonlinear Complexity from the Hermitian Function Field

We provide a sequence with high nonlinear complexity from the Hermitian function field $\mathcal{H}$ over $\mathbb{F}_{q^2}$. This sequence was obtained using a rational function with pole divisor in certain $\ell$ collinear rational places on $\mathcal{H}$, where $2 \leq \ell \leq q$. In particular we improve the lower bounds on the $k$th-order nonlinear complexity obtained by H. Niederreiter and C. Xing; and O. Geil, F. \"Ozbudak and D. Ruano

Benchmarking in a rotating annulus: a comparative experimental and numerical study of baroclinic wave dynamics

The differentially heated rotating annulus is a widely studied tabletop-size laboratory model of the general mid-latitude atmospheric circulation. The two most relevant factors of cyclogenesis, namely rotation and meridional temperature gradient are quite well captured in this simple arrangement. The radial temperature difference in the cylindrical tank and its rotation rate can be set so that the isothermal surfaces in the bulk tilt, leading to the formation of baroclinic waves. The signatures of these waves at the free water surface have been analyzed via infrared thermography in a wide range of rotation rates (keeping the radial temperature difference constant) and under different initial conditions. In parallel to the laboratory experiments, five groups of the MetStr\"om collaboration have conducted numerical simulations in the same parameter regime using different approaches and solvers, and applying different initial conditions and perturbations. The experimentally and numerically obtained baroclinic wave patterns have been evaluated and compared in terms of their dominant wave modes, spatio-temporal variance properties and drift rates. Thus certain ``benchmarks'' have been created that can later be used as test cases for atmospheric numerical model validation

On the critical nature of plastic flow: one and two dimensional models

Steady state plastic flows have been compared to developed turbulence because the two phenomena share the inherent complexity of particle trajectories, the scale free spatial patterns and the power law statistics of fluctuations. The origin of the apparently chaotic and at the same time highly correlated microscopic response in plasticity remains hidden behind conventional engineering models which are based on smooth fitting functions. To regain access to fluctuations, we study in this paper a minimal mesoscopic model whose goal is to elucidate the origin of scale free behavior in plasticity. We limit our description to fcc type crystals and leave out both temperature and rate effects. We provide simple illustrations of the fact that complexity in rate independent athermal plastic flows is due to marginal stability of the underlying elastic system. Our conclusions are based on a reduction of an over-damped visco-elasticity problem for a system with a rugged elastic energy landscape to an integer valued automaton. We start with an overdamped one dimensional model and show that it reproduces the main macroscopic phenomenology of rate independent plastic behavior but falls short of generating self similar structure of fluctuations. We then provide evidence that a two dimensional model is already adequate for describing power law statistics of avalanches and fractal character of dislocation patterning. In addition to capturing experimentally measured critical exponents, the proposed minimal model shows finite size scaling collapse and generates realistic shape functions in the scaling laws.Comment: 72 pages, 40 Figures, International Journal of Engineering Science for the special issue in honor of Victor Berdichevsky, 201

Finite Fields: Theory and Applications

Finite fields are the focal point of many interesting geometric, algorithmic and combinatorial problems. The workshop was devoted to progress on these questions, with an eye also on the important applications of finite field techniques in cryptography, error correcting codes, and random number generation

Non-linear axisymmetric pulsations of rotating relativistic stars in the conformal flatness approximation

We study non-linear axisymmetric pulsations of rotating relativistic stars using a general relativistic hydrodynamics code under the assumption of a conformal flatness. We compare our results to previous simulations where the spacetime dynamics was neglected. The pulsations are studied along various sequences of both uniformly and differentially rotating relativistic polytropes with index N = 1. We identify several modes, including the lowest-order l = 0, 2, and 4 axisymmetric modes, as well as several axisymmetric inertial modes. Differential rotation significantly lowers mode frequencies, increasing prospects for detection by current gravitational wave interferometers. We observe an extended avoided crossing between the l = 0 and l = 4 first overtones, which is important for correctly identifying mode frequencies in case of detection. For uniformly rotating stars near the mass-shedding limit, we confirm the existence of the mass-shedding-induced damping of pulsations, though the effect is not as strong as in the Cowling approximation. We also investigate non-linear harmonics of the linear modes and notice that rotation changes the pulsation frequencies in a way that would allow for various parametric instabilities between two or three modes to take place. We assess the detectability of each obtained mode by current gravitational wave detectors and outline how the empirical relations that have been constructed for gravitational wave asteroseismology could be extended to include the effects of rotation.Comment: 24 pages, 20 figures; minor corrections, added extended discussion and one figure in one subsectio

Trees and after: The concept of text topology: Some applications to verb-form distributions in language corpora

International audienceThe model described here relies on the key concepts of topology, i.e. neighbourhood and equivalence of shape. A linguistic object L is studied in text T by means of one or several local questions Q. The set of successive local answers is processed so as to provide a global function characterizing the textual space under scrutiny. We begin with short sequences of tenses to illustrate the way in which to explore originally Emile Benveniste's concepts of history and discourse . We then supply life-size examples of other objects selected for their heuristic value. We go on to demonstrate the model at work on the distribution of strings of finite (F) and non-finite (n) verbal forms in the LOB Corpus of English. A topological chart is produced as the synthetic image mirroring the locations of the relevant linguistic entities throughout the text. All the individual strings concatenating any number of F and n are classified in a table. Alternatively, individual full-text strings can be extracted. We then proceed to refine the notion of lexical distribution in "rafales" in a lemmatized corpus of Latin texts, the purpose being to test the stability of the distributions in individual texts of selected verbs and assess whether a verb's behaviour is related to its semantic status. The final section is devoted to other Latin texts. The use of segments of equal length makes it possible to draw up the narrative profile of each author as revealed by his handling of tenses in main clauses