ROOT PROBLEM FOR CONVENIENT MAPS

In this paper we study when the minimal number of roots of the so-called convenient maps horn two-dimensional CW complexes into closed surfaces is zero We present several necessary and sufficient conditions for such a map to be root free Among these conditions we have the existence of specific fittings for the homomorphism induced by the map on the fundamental groups, existence of the so-called mutation of a specific homomorphism also induced by the map, and existence of particular solutions of specific systems of equations on free groups over specific subgroups

Strong surjectivity of maps from 2-complexes into the 2-sphere

Given a model 2-complex K(P) of a group presentation P, we associate to it an integer matrix Delta(P) and we prove that a cellular map f : K(P) -> S(2) is root free (is not strongly surjective) if and only if the diophantine linear system Delta(P) Y = (deg) over right arrow (f) has an integer solution, here (deg) over right arrow (f) is the so-called vector-degree of f

Integrable maps with non-trivial topology: application to divertor configurations

We explore a method for constructing two-dimensional area-preserving, integrable maps associated with Hamiltonian systems, with a given set of fixed points and given invariant curves. The method is used to find an integrable Poincare map for the field lines in a large aspect ratio tokamak with a poloidal single-null divertor. The divertor field is a superposition of a magnetohydrodynamic equilibrium with an arbitrarily chosen safety factor profile, with a wire carrying an electric current to create an X-point. This integrable map is perturbed by an impulsive perturbation that describes non-axisymmetric magnetic resonances at the plasma edge. The non-integrable perturbed map is applied to study the structure of the open field lines in the scrape-off layer, reproducing the main transport features obtained by integrating numerically the magnetic field line equations, such as the connection lengths and magnetic footprints on the divertor plate.

Tokamak magnetic field lines described by simple maps

The magnetic field line structure in a tokamak can be obtained by direct numerical integration of the field line equations. However, this is a lengthy procedure and the analysis of the solution may be very time-consuming. Otherwise we can use simple two-dimensional, area-preserving maps, obtained either by approximations of the magnetic field line equations, or from dynamical considerations. These maps can be quickly iterated, furnishing solutions that mirror the ones obtained from direct numerical integration, and which are useful when long-term studies of field line behavior are necessary (e.g. in diffusion calculations). In this work we focus on a set of simple tokamak maps for which these advantages are specially pronounced.

FUSION ENHANCEMENT/SUPPRESSION AND IRREVERSIBILITY IN REACTIONS INDUCED BY WEAKLY BOUND NUCLEI

We show that halo effects enhance fusion cross sections of weakly bound systems, comparing with the situation when there is no-halo. We introduce dimensionless fusion functions and energy variable quantity to investigate systematical trends in the fusion cross sections of weakly bound nuclei at near-barrier energies. We observe very clearly complete fusion suppression at energies above the barrier due to dynamic effects of the breakup on fusion. We explain this suppression in terms of the repulsive polarization potential produced by the breakup.

CLUSTER MODEL FOR REACTIONS INDUCED BY WEAKLY BOUND AND/OR EXOTIC HALO NUCLEI WITH MEDIUM-MASS TARGETS

An experimental overview of reactions induced by the stable, but weakly-bound nuclei (6)Li, (7)Li and (9)Be, and by the exotic, halo nuclei (6)He, (8)B, (11)Be and (17)F On medium-mass targets, such as (58)Ni, (59)Co or (64)Zn, is presented. Existing data on elastic scattering, total reaction cross sections, fusion, breakup and transfer channels are discussed in the framework of a CDCC approach taking into account the breakup degree of freedom.

Reaction mechanisms for weakly-bound, stable nuclei and unstable, halo nuclei on medium-mass targets

An experimental overview of reactions induced by the stable, but weakly-bound nuclei (6)Li, (7)Li and (9)Be, and by the exotic, halo nuclei (6)He, (8)B, (11)Be and (17)F on medium-mass targets, such as (58)Ni, (59)Co or (64)Zn, is presented. Existing data on elastic scattering, total reaction cross sections, fusion processes, breakup and transfer channels are discussed in the framework of a CDCC approach taking into account the breakup degree of freedom.

Breakup effects in fusion and total reaction cross sections of weakly bound systems

We use a new technique to investigate the systematic behavior of near barrier complete fusion, total fusion and total reaction cross sections of weakly bound systems. A dimensionless fusion excitation function is used as a benchmark to which renormalized fusion data are compared and dynamic breakup effects can be disentangled from static effects. The same reduction procedure is used to study the effect of the direct reaction mechanisms on the total reaction cross section.

Reaction functions for weakly bound systems

We propose a new technique to analyze total reaction cross sections. In this technique, which has been previously applied to fusion reactions, the experimental data are used to build a dimensionless reaction function, which does not depend oil the system size or details of the optical potential. In this way, total reaction cross sections for different systems can be directly compared. We employ this technique to perform a systematic study of reaction cross sections of weakly bound systems in different mass ranges, and compare their reaction functions with the ones of tightly bound systems with similar masses. We show that breakup reactions and neutron transfers in halo systems lead to large reaction functions, well above the ones of typical tightly or weakly bound stable systems. (C) 2009 Elsevier B.V. All rights reserved.

Dynamic effects of breakup on fusion reactions of weakly bound nuclei

The traditional reduction methods to represent the fusion cross sections of different systems are flawed when attempting to completely eliminate the geometrical aspects, such as the heights and radii of the barriers, and the static effects associated with the excess neutrons or protons in weakly bound nuclei. We remedy this by introducing a new dimensionless universal function, which allows the separation and disentanglement of the static and dynamic aspects of the breakup coupling effects connected with the excess nucleons. Applying this new reduction procedure to fusion data of several weakly bound systems, we find a systematic suppression of complete fusion above the Coulomb barrier and enhancement below it. Different behaviors are found for the total fusion cross sections. They are appreciably suppressed in collisions of neutron-halo nuclei, while they are practically not affected by the breakup coupling in cases of stable weakly bound nuclei. (C) 2009 Elsevier B.V. All rights reserved.

X-ray spectrometry: a powerful tool for the measurement of complete fusion of weakly bound nuclei

We describe how the method of detection of delayed K x-rays produced by the electron capture decay of the residual nuclei can be a powerful tool in the investigation of the effect of the breakup process on the complete fusion (CF) cross-section of weakly bound nuclei at energies close to the Coulomb barrier. This is presently one of the most interesting subjects under investigation in the field of low-energy nuclear reactions, and the difficult experimental task of separating CF from the incomplete fusion (ICF) of one of the breakup fragments can be achieved by the x-ray spectrometry method. We present results for the fusion of the (9)Be + (144)Sm system. Copyright (c) 2008 John Wiley & Sons, Ltd.

Total reaction cross-sections for light weakly bound systems

We have measured the elastic scattering cross-section for (8)Li + (9)Be and (8)Li + (51)V systems at 19.6 MeV and 18.5 MeV, respectively. We have also extracted total reaction cross sections from the elastic scattering analysis for several light weakly bound systems using the optical model with Woods-Saxon and double-folding-type potentials. Different reduction methods for the total reaction cross-sections have been applied to analyze and compare simultaneously all the systems.

Spectroscopic evidence of extended states in quantized Hall phase of weakly coupled GaAs/AlGaAs multi-layers

The influence of the interlayer coupling on formation of the quantized Hall conductor phase at the filling factor v = 2 was studied in the multi-layer GaAs/AlGaAs heterostructures. The disorder broadened Gaussian photoluminescence line due to the localized electrons was found in the quantized Hall phase of the isolated multi-quantum well structure. On the other hand, the quantized Hall phase of the weakly coupled multi-layers emitted an unexpected asymmetrical line similar to that one observed in the metallic electron systems. We demonstrated that the observed asymmetry is caused by a partial population of the extended electron states formed in the quantized Hall conductor phase due to the interlayer percolation. A sharp decrease of the single-particle scattering time associated with these extended states was observed at the filling factor v = 2. (c) 2007 Elsevier B.V. All rights reserved.

Decay of geometry for Fibonacci critical covering maps of the circle

We study the growth of Df `` (f(c)) when f is a Fibonacci critical covering map of the circle with negative Schwarzian derivative, degree d >= 2 and critical point c of order l > 1. As an application we prove that f exhibits exponential decay of geometry if and only if l <= 2, and in this case it has an absolutely continuous invariant probability measure, although not satisfying the so-called Collet-Eckmann condition. (C) 2009 Elsevier Masson SAS. All rights reserved.