Sensitive Dependence on Parameters of Continuous-time Nonlinear Dynamical Systems

We would like to thank the partial support of this work by the Brazilian agencies FAPESP (processes: 2011/19296-1 and 2013/26598-0, CNPq and CAPES. MSB acknowledges EPSRC Ref. EP/I032606/1.Peer reviewedPostprin

Non-Chern-Simons Topological Mass Generation in (2+1) Dimensions

By dimensional reduction of a massive BF theory, a new topological field theory is constructed in (2+1) dimensions. Two different topological terms, one involving a scalar and a Kalb-Ramond fields and another one equivalent to the four-dimensional BF term, are present. We constructed two actions with these topological terms and show that a topological mass generation mechanism can be implemented. Using the non-Chern-Simons topological term, an action is proposed leading to a classical duality relation between Klein-Gordon and Maxwell actions. We also have shown that an action in (2+1) dimensions with the Kalb-Ramond field is related by Buscher's duality transformation to a massive gauge-invariant Stuckelberg-type theory.Comment: 8 pages, no figures, RevTE

Trapping Phenomenon Attenuates the Consequences of Tipping Points for Limit Cycles

We would like to thank the partial support of this work by the Brazilian agencies FAPESP (processes: 2011/19296-1, 2013/26598-0, and 2015/20407-3), CNPq and CAPES. MSB acknowledges EPSRC Ref. EP/I032606/1.Peer reviewedPublisher PD

Uniqueness of canonical tensor model with local time

Canonical formalism of the rank-three tensor model has recently been proposed, in which "local" time is consistently incorporated by a set of first class constraints. By brute-force analysis, this paper shows that there exist only two forms of a Hamiltonian constraint which satisfies the following assumptions: (i) A Hamiltonian constraint has one index. (ii) The kinematical symmetry is given by an orthogonal group. (iii) A consistent first class constraint algebra is formed by a Hamiltonian constraint and the generators of the kinematical symmetry. (iv) A Hamiltonian constraint is invariant under time reversal transformation. (v) A Hamiltonian constraint is an at most cubic polynomial function of canonical variables. (vi) There are no disconnected terms in a constraint algebra. The two forms are the same except for a slight difference in index contractions. The Hamiltonian constraint which was obtained in the previous paper and behaved oddly under time reversal symmetry can actually be transformed to one of them by a canonical change of variables. The two-fold uniqueness is shown up to the potential ambiguity of adding terms which vanish in the limit of pure gravitational physics.Comment: 21 pages, 12 figures. The final result unchanged. Section 5 rewritten for clearer discussions. The range of uniqueness commented in the final section. Some other minor correction

How good are MatLab, Octave and Scilab for Computational Modelling?

In this article we test the accuracy of three platforms used in computational modelling: MatLab, Octave and Scilab, running on i386 architecture and three operating systems (Windows, Ubuntu and Mac OS). We submitted them to numerical tests using standard data sets and using the functions provided by each platform. A Monte Carlo study was conducted in some of the datasets in order to verify the stability of the results with respect to small departures from the original input. We propose a set of operations which include the computation of matrix determinants and eigenvalues, whose results are known. We also used data provided by NIST (National Institute of Standards and Technology), a protocol which includes the computation of basic univariate statistics (mean, standard deviation and first-lag correlation), linear regression and extremes of probability distributions. The assessment was made comparing the results computed by the platforms with certified values, that is, known results, computing the number of correct significant digits.Comment: Accepted for publication in the Computational and Applied Mathematics journa

Quasi-degenerate neutrinos and tri-bi-maximal mixing

We consider how, for quasi-degenerate neutrinos with tri-bi-maximal mixing at a high-energy scale, the mixing angles are affected by radiative running from high to low-energy scales in a supersymmetric theory. The limits on the high-energy scale that follow from consistency with the observed mixing are determined. We construct a model in which a non-Abelian discrete family symmetry leads both to a quasi-degenerate neutrino mass spectrum and to near tri-bi-maximal mixing.Comment: 8 pages, 3 figure

Mass generation for non-Abelian antisymmetric tensor fields in a three-dimensional space-time

Starting from a recently proposed Abelian topological model in (2+1) dimensions, which involve the Kalb-Ramond two form field, we study a non-Abelian generalization of the model. An obstruction for generalization is detected. However we show that the goal is achieved if we introduce a vectorial auxiliary field. Consequently, a model is proposed, exhibiting a non-Abelian topological mass generation mechanism in D=3, that provides mass for the Kalb-Ramond field. The covariant quantization of this model requires ghosts for ghosts. Therefore in order to quantize the theory we construct a complete set of BRST and anti-BRST equations using the horizontality condition.Comment: 8 pages. To appear in Physical Review