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

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

Torsion-Adding and Asymptotic Winding Number for Periodic Window Sequences

In parameter space of nonlinear dynamical systems, windows of periodic states are aligned following routes of period-adding configuring periodic window sequences. In state space of driven nonlinear oscillators, we determine the torsion associated with the periodic states and identify regions of uniform torsion in the window sequences. Moreover, we find that the measured of torsion differs by a constant between successive windows in periodic window sequences. We call this phenomenon as torsion-adding. Finally, combining the torsion and the period adding rules, we deduce a general rule to obtain the asymptotic winding number in the accumulation limit of such periodic window sequences

Four-dimensional topological Einstein-Maxwell gravity

The complete on-shell action of topological Einstein-Maxwell gravity in four-dimensions is presented. It is shown explicitly how this theory for SU(2) holonomy manifolds arises from four-dimensional Euclidean N=2 supergravity. The twisted local BRST symmetries and twisted local Lorentz symmetries are given and the action and stress tensor are shown to be BRST-exact. A set of BRST-invariant topological operators is given. The vector and antisymmetric tensor twisted supersymmetries and their algebra are also found.Comment: Published version. Expanded discussion of new results in the introduction and some clarifying remarks added in later sections. 22 pages, uses phyzz

Abundant cyanopolyynes as a probe of infall in the Serpens South cluster-forming region

We have detected bright HC7N J = 21-20 emission toward multiple locations in the Serpens South cluster-forming region using the K-Band Focal Plane Array at the Robert C. Byrd Green Bank Telescope. HC7N is seen primarily toward cold filamentary structures that have yet to form stars, largely avoiding the dense gas associated with small protostellar groups and the main central cluster of Serpens South. Where detected, the HC7N abundances are similar to those found in other nearby star forming regions. Toward some HC7N `clumps', we find consistent variations in the line centroids relative to NH3 (1,1) emission, as well as systematic increases in the HC7N non-thermal line widths, which we argue reveal infall motions onto dense filaments within Serpens South with minimum mass accretion rates of M ~ 2-5 M_sun Myr^-1. The relative abundance of NH3 to HC7N suggests that the HC7N is tracing gas that has been at densities n ~ 10^4 cm^-3, for timescales t < 1-2 x 10^5 yr. Since HC7N emission peaks are rarely co-located with those of either NH3 or continuum, it is likely that Serpens South is not particularly remarkable in its abundance of HC7N, but instead the serendipitous mapping of HC7N simultaneously with NH3 has allowed us to detect HC7N at low abundances in regions where it otherwise may not have been looked for. This result extends the known star-forming regions containing significant HC7N emission from typically quiescent regions, like the Taurus molecular cloud, to more complex, active environments.Comment: 19 pages, 13 figures, accepted to MNRAS. Version with full resolution figures available at http://www.dunlap.utoronto.ca/~friesen/Friesen_HC7N.pd

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

One-loop unitarity of scalar field theories on Poincare invariant commutative nonassociative spacetimes

We study scalar field theories on Poincare invariant commutative nonassociative spacetimes. We compute the one-loop self-energy diagrams in the ordinary path integral quantization scheme with Feynman's prescription, and find that the Cutkosky rule is satisfied. This property is in contrast with that of noncommutative field theory, since it is known that noncommutative field theory with space/time noncommutativity violates unitarity in the above standard scheme, and the quantization procedure will necessarily become complicated to obtain a sensible Poincare invariant noncommutative field theory. We point out a peculiar feature of the non-locality in our nonassociative field theories, which may explain the property of the unitarity distinct from noncommutative field theories. Thus commutative nonassociative field theories seem to contain physically interesting field theories on deformed spacetimes.Comment: 25 pages, 9 figures ; appendix and references adde