New global periodic orbit collision/separatrix reconnection scenarios in the standard nontwist map in different regions of parameter space are described in detail, including exact methods for determining reconnection thresholds that are implemented numerically. The results are compared to a break-up diagram of shearless invariant curves. The existence of meanders (invariant tori that are not graphs) is demonstrated numerically for both odd and even period reconnection for certain regions in parameter space, and some of the implications on transport are discussed.In recent years, area-preserving maps that violate the twist condition locally in phase space have been the object of interest in several studies in physics and mathematics. These nontwist maps show up in a variety of physical models, e.g., in magnetic field line models for reversed magnetic shear tokamaks. An important problem is the determination and understanding of the transition to global chaos (global transport) in these models. Nontwist maps exhibit several different mechanisms: the break-up of invariant tori and separatrix reconnections. The latter may or may not lead to global transport depending on the region of parameter space. In this paper we conduct a detailed study of newly discovered reconnection scenarios in the standard nontwist map, investigating their location in parameter space and their impact on global transport.

The breakup of shearless invariant tori with winding number omega=(11+gamma)(12+gamma) (in continued fraction representation) of the standard nontwist map is studied numerically using Greene's residue criterion. Tori of this winding number can assume the shape of meanders [folded-over invariant tori which are not graphs over the x axis in (x,y) phase space], whose breakup is the first point of focus here. Secondly, multiple shearless orbits of this winding number can exist, leading to a new type of breakup scenario. Results are discussed within the framework of the renormalization group for area-preserving maps. Regularity of the critical tori is also investigated.

We examine a two-dimensional electron waveguide with a cut-circle cavity and conical leads. By considering Wigner delay times and the Landauer-Büttiker conductance for this system, we probe the effects of the closed billiard energy spectrum on scattering properties in the limit of weakly coupled leads. We investigate how lead placement and cavity shape affect these conductance and time delay spectra of the waveguide.

The breakup of the shearless invariant torus with winding number ω = √ 2 − 1 is studied numerically using Greene's residue criterion in the standard nontwist map. The residue behavior and parameter scaling at the breakup suggests the existence of a new fixed point of the renormalization group operator (RGO) for area-preserving maps. The unstable eigenvalues of the RGO at this fixed point and the critical scaling exponents of the torus at breakup are computed.