An Infinite Dimensional Approach to the Third Fundamental Theorem of Lie

We revisit the third fundamental theorem of Lie (Lie III) for finite dimensional Lie algebras in the context of infinite dimensional matrices.Comment: This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007, Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

On-line control of tension in web winding systems based on wound roll internal stress computation

One of the key challenges in the processing of flexible media such as plastic films is to obtain rolls without any aspect defect: if one considers that a "defect" (i.e. wrinkling or buckling) is due to the fact that the stress generated within the roll is greater than some "plasticity threshold", then it is crucial to predict the internal stress. Several process parameters must be carefully mastered, among which the winding tension is very important. Offline optimization of the tension can a priori guarantee the production of perfect rolls, with respect to the internal stress. Nevertheless, the industrial control systems never generate perfect follow-up of the tension reference value, because the tension which is actually imposed (i.e. measured) exhibits oscillations due to the imperfections of the winding system, including geometrical irregularities of the rolls. The fluctuations about the tension nominal value induce variations in the stress within the roll as compared to the value which would result from an ideal control. As a consequence, it is judicious to change the tension reference value during the winding process, according to some criterion defined from the stress computed within the roll, and then to apply this new "up-dated" reference to the forthcoming web layers. This new way of online tension control requires new concepts such as "robust multivariable control", because distributed control may not work as well.The first step consists in computing the internal stress generated within a roll of a wound web (for instance plastic film). For that purpose, a modified non-linear model is developed in the spirit of Hakiel's. The web's winding process can be considered as a continuous accretion process, in the sense that the stress components at a given point are continuously modified by the upper superimposed layers. In addition, the residual air films which separate the web layers are taken into account in an indirect way through the radial Young's modulus of the roll which is a non-linear (polynomial) function of the compressive stress component. Several illustrative examples are presented and commented. Then, having prescribed an optimization criterion for the winding tension, an optimization algorithm based on the simplex principle is described. Finally, a new concept of online tension control, based on prediction-correction is proposed. Dividing the roll radius into several segments, the tension reference is computed and corrected for each range of roll radius values, by using the predictive model for the stress within the roll. The adjusted tension is reactualized step by step, following the optimization principle as described above and it will be considered as the new tension reference value for the coming layers. A comparison between offline and online tension controls clearly shows the improvement given by the new optimization technique (online)

Control and online tension reference optimization in winding systems: Application to an identified three-motors simulator

It is well known that the tension reference value, which a priori guarantees a good quality roll, is based on the stress generated within the roll. However, due to the imperfections of the winding systems and to the limited performances of the disturbances rejection controllers, a control with fixed reference never generates perfect follow-up of the tension. A solution would consist in adjusting the tension reference online, according to real measurements.In a previous paper, the criterion for tension adjustment was the tangential stress. A method for online control based on prediction-correction using the simplex algorithm was presented. This method was tested numerically.In the present paper, we propose to generalize the criterion of tension reference optimization by considering both the tangential and the radial stress within the roll during winding. The same optimization algorithm is used, taking into account the dynamic tension model. Moreover, a dynamic gauge is now introduced, so that it can vary during the winding process. It generally represents the limits of elastic deformations of the web.The new optimization algorithm for the on-line reference tension calculation has been validated on a dynamic non-linear winding model. This complete model used for simulations was validated on a three-motor setup using brushless motors. The setup is with PI controllers, where the web velocity is imposed by master traction motor and the tension is controlled by unwinding and winding motors.In this approach, a new tension-prediction algorithm using a linear parameter varying (LPV) model is used. The influence of the tension prediction algorithm is also analyzed.Several illustrative examples will be presented and the improvement as compared to an offline control will be commented

Gauge optimization of the reference tension in winding systems using wound internal stresses calculation

In winding process, the quality of the roll is directly connected to its stress state. The winding tension is the most significant parameter which plays an important role in the stresses generated within a roll, during winding. If the stresses exceed a critical value, defects can appear in the roll and make the web non usable.This work concerns the estimation and optimization of the maximal dispersion of the reference tension, so that the tangential and radial stresses values remain in a gauge. It aims to find automatically the maximum and minimum limits for the reference tension, so that all curves ranging between these two limits or thresholds, generate radial and tangential stresses, theirs selves included in a gauge fixed in advance. The results lead to a practical gauge optimization of the reference tension for industrial applications

Coupled-channels description of the 40Ca + 58,64Ni transfer and fusion reactions

Preliminary experimental data for nucleon transfer reactions of the 40Ca + 58Ni and 40Ca + 64Ni systems are analyzed with the coupled-channels approach. It is shown that a simple treatment for the transfer in the coupled-channels method cannot reproduce simultaneously the transfer probabilities and the subbarrier enhancement of fusion cross sections

Fusion Hindrance and Quadrupole Collectivity in Collisions of A≃50 Nuclei: The Case of 48Ti + 58Fe

International audience; The fusion excitation function of Ti-48 + Fe-58 has been measured in a wide energy range around the Coulomb barrier, covering 6 orders of magnitude of the cross sections. We present here the preliminary results of this experiment, and a full comparison with the near-by system Ni-58 + Fe-54 where evidence of fusion hindrance shows up at relatively high cross sections. The sub-barrier cross sections of Ti-48 + Fe-58 are much larger than those of Ni-58 + Fe-54. Significant differences are also observed in the logarithmic derivatives, astrophysical S-factors and fusion barrier distributions. The influence of low-energy nuclear structure on all these trends is pointed out and commented. Coupled-channels calculations using a Woods-Saxon potential are able to reproduce the experimental results for Ti-48 + Fe-58. The logarithmic derivative of the excitation function is very nicely fit, and no evidence of hindrance is observed down to around 1 mu b. The fusion barrier distribution is rather wide, flat and structureless. It is only in qualitative agreement with the calculated distribution

Experimental investigations of the sub-Coulomb 12C+12C and 12C+16O reactions

Cluster resonances in light heavy-ion systems like 12C+12C and 12C+16O may have a major impact on astrophysics stellar scenarios. Resonant radiative capture reactions have been studied for these systems at energies at and slightly below their Coulomb barriers to investigate the possible 12C-12C and 12C-16O molecular origin of the resonances. Spins have been attributed to the resonances and specificities of their γ-decay have been identified. At deep sub-barrier energies, a fusion cross section measurement using the particle-γ coincidence technique is discussed for the 12C+12C system. A new project is presented to possibly extend the 12C+12C S low-energy S factor study

Fusion reactions of 58,64Ni+124Sn

International audience; In order to better understand the influence of transfer in sub-barrier nuclear reactions, cross sections for the system ^58,64Ni+^124Sn have been measured down to 0.5-1 mub and compared to detailed coupledchannel calculations. In agreement with a phenomenological Q-value systematics, calculations show the importance of including the coupling to the transfer channel for these heavy systems. No clear evidence of fusion hindrance is observed, probably due to the fact that the cross sections measured in this experiment are not low enough for the appearance of that phenomenon