Quasi-genericity of bifurcations to high dimensional invariant tori for maps

We consider a family of maps in a Banach spaceE near the situation when the derivative at the fixed point has two pairs of complex eigenvalues lying on the unit circle, the other part of the spectrum being strictly inside the unit disc. We focus our attention on the region of the parameter space where the truncated normal form of the maps shows a bifurcation of a family of invariantT ¹-circles into a family of invariantT ²-tori. We show that this problem needs a 3 dimensional parameter unfolding and that, for the complete maps, bifurcation occurs at points _,, where is the rotation number on the non-normally hyperbolicT ¹-circle, ande ^±2i are the eigenvalues of the constant matrix conjugated to the non-contracting part of the linearization on the normal fiber bundle overT ¹. Making some non-resonance and diophantine assumptions on (, ) leading to a positive measure Cantor set inT ², we show that in paraboloïdal regions of the 3 dim. parameter space we have clean bifurcations as for the truncated normal form. The complement of these regions forms a set of bubbles such as the ones obtained by Chenciner in [Chen] for a codimension 2 problem for maps in ². The main tool here is a generalization for a matrix function onT ¹, close to a constant, of the quasi-conjugacy to a constant, modulo a minimum of additional parameters (moved quasi-conjugacy). For the infinite dimensional case we use aC decoupling result on the angular dependent linear parts into a contraction, still angular dependent, and another part quasi-conjugated to a constant matrix. This type of analysis applies for a wide range of problems, where truncated normal forms of the maps give bifurcations fromT ⁿ toT ⁿ⁺¹ tori, and this needs a (n+1)-dimensional parameter unfolding.We gratefully acknowledge the DRET (contrat 86/1445) who supported one of the authors (J.L.) during this work. This research has been also supported by the E.E.C. contract No. ST 2J-0316-C (EDB) on Mathematical problems in nonlinear Mechanics     

Computer-simulated diffraction patterns for metastable austenitic steels

The paper deals with the computer simulation of composite theoretical electron-diffraction patterns for metastable austenitic steels, containing deformation and martensite transformation structures. In many cases generated data can be used for interpretation of experimentally determined diffraction patterns. A few examples are presented which demonstrate that the application of the composite theoretical diffraction patterns may be complicated due to various diffraction effects which can modify the geometry of experimentally obtained diffraction patterns.     

Kinetics of the photodissociation iodine laser with slow pumping

Systematic calculations of maximum inversion were performed for iodine photodissociation laser in dependence on the mixture composition. The flash-lamp radiation was modelled as emanating from an optically thin Xe plasma. Duration of the pumping pulse is about 300 s. The sensitivity of the model to the values of kinetic constants was also tested.     

Spectroscopic factors of9Be,10B and13C from (d,t) reactions

The differential cross sections of tritons from the (d, t) reaction on⁹Be,¹⁰B and¹³C targets have been measured in the angular range of 5° _LAB110° with relatively small errors, 5%. The experimental data were analysed in terms of the standard DWBA using both zero-range and exact finite-range approaches.     

Time dependence of the luminescence excited by rectangular pulses

The theory of the time dependence of luminescence, during and after excitation by rectangular pulse, is discussed. Some phenomena, which cannot be described as direct excited luminescence, will be mentioned. In order to explain these phenomena, the model for energy transfer between two monomolecular centres has been used. On the basis of this model, the theoretical time dependence of the luminescence is obtained. The theoretical formula describe qualitatively very well the experimental observations in ZnSMn and other compounds.     

Off-shell behaviour of theN-N interaction in a six-quark resonating group model of the deuteron

Two different 6-quark resonating group models of the deuteron are investigated to study the off-shell property of theN-N interaction. In the first model the quarks interact by a central one-gluon-exchange potential plus confinement potential. The meson-exchange contribution to then-p potential is simulated by a central GaussianN-N potential. In the second model the quarks interact by one-gluon-and one-pion-exchange potentials (central and noncentral) plus confinement potential. A small additional -exchange potential between neutron and proton binds the deuteron at the correct energy.Several off-shell variants of the two resonating group models are compared with each other by analyzing their elastic electron scattering cross sections. It is found that the standard renormalized version of the resonating group model yields potentials and wave functions that may be considered physical within the limitations of the model. Unitary off-shell transformations, which modify potentials and wave functions in any sizeable way, lead to a disagreement between the charge distribution predicted by the model via analysis of electron scattering and the charge distribution following from the microscopic quark distribution.Both of the 6-quark models support a soft repulsive core of the tripletn-p potential with a core height of around 900 MeV.     

The search for organically bonded iron in New Zealand brown coals

Brown coal from two areas in New Zealand was treated with acids (HF and HCl) to remove the clays. Iron was then introduced into the “cleaned” coal by ion exchange. Mössbauer spectra of the untreated coal, the low temperature ash of the coal, “cleaned” coal and ion-exchanged coal were analysed. From these spectra we conclude that a pair of lines with QS～1 mm s^?1 and IS～0.45 mm s^?1 is probably due to organically bonded iron.     

Calculation of transverse and longitudinal space charge effects within the framework of the fully six-dimensional formalism

In the following report we describe a method for calculating the envelope of a particle bunch in linear coupled storage rings and transport systems in the presence of transverse and longitudinal space charge forces using the (canonical) variablesx, p _x ,z, p _z , σ=s?v ₀·t,p _σ=ΔE/E ₀ of the fully six-dimensional formalism. This work is an extension of earlier calculations on transverse space charge forces [1] to include the synchrotron oscillations. The extension is achieved by defining a 6-dimensional ellipsoid in thex?p _x ?z?p _z ?σ?p _σ space. The motion of this ellipsoid under the influence of the external fields and the instantaneous space charge forces can be described by six generating orbit vectors which can be combined into a 6-dimensional matrixB(s). This “bunch-shape matrix”,B(s), contains complete information about the configuration of the bunch. The solution of the equations of motion is carried through in the thin lens approximation. The formalism can also encompass acceleration by cavity fields.     

Positive muons in bismuth: determination of their sites,detection of a large local lattice contraction and giant associated electric field gradients,evidence for short and long range diffusion

Using a high purity Bi single crystal the temperature and orientation dependence of the zero and transverse field muon spin relaxation rate has been studied in detail. The results imply that the ⁺ occupies one of the two possible interstitial sites in the distorted rhombohedral crystal structure of Bi below 10 K and the other site above 80 K. At both sites the nearest neighbor Bi atoms are found to be shifted towards the ⁺ by 10% of their nominal distance, implying a large local lattice contraction. In concomitance extremely strong electric field gradients are manifest at the nn Bi nuclei. An almost temperature independent reduced relaxation rate in the temperature range from 20 K to 60 K is interpreted in terms of short range diffusion along a limited chain of alternating types of sites. Above 100 K both long range and short range diffusion are indicated.     

Resonant coupling of optical phonons to J-multiplet excitations in intermediate valent Sm0.75Y0.25S

An anomalous splitting of theJ=0J=1 multiplet transition has been observed by magnetic neutron scattering from intermediate valent Sm_0.75Y_0.25S. The splitting is discussed in terms of a resonant coupling of optical phonons to the magnetic exciton built from the localizedJ=0J=1 multiplet transition by magnetic intersite coupling.