Stabilizing the intensity of a wave amplified by a beam of particles

The intensity of an electromagnetic wave interacting self-consistently with a beam of charged particles as in a free electron laser, displays large oscillations due to an aggregate of particles, called the macro-particle. In this article, we propose a strategy to stabilize the intensity by re-shaping the macro-particle. This strategy involves the study of the linear stability (using the residue method) of selected periodic orbits of a mean-field model. As parameters of an additional perturbation are varied, bifurcations occur in the system which have drastic effect on the modification of the self-consistent dynamics, and in particular, of the macro-particle. We show how to obtain an appropriate tuning of the parameters which is able to strongly decrease the oscillations of the intensity without reducing its mean-value.     

On the Robustness of Gaussian Elimination with Partial Pivoting

It has been recently shown that large growth factors might occur in Gaussian Elimination with Partial Pivoting (GEPP) also when solving some plausibly natural systems. In this note we argue that this potential problem could be easily solved, with much smaller risk of failure, by very small (and low cost) modifications of the basic algorithm, thus confirming its inherent robustness. To this end, we first propose an informal model with the goal of providing further support to the comprehension of the stability properties of GEPP. We then report the results of numerical experiments that confirm the viewpoint embedded in the model. Basing on the previous observations, we finally propose a simple scheme that could be turned into (even more) accurate software for the solution of linear systems.     

High-performance liquid chromatography of thiazolidinic compounds obtained by condensation of pyridoxal 5'-phosphate or pyridoxal with aminothiols (L- or D-cysteine, cysteamine, L-cysteine ethyl ester).

We investigated six thiazolidine 4-carboxylic acids of biological interest, obtained by condensation of pyridoxal 5'-phosphate or pyridoxal with L- or D-cysteine, cysteamine or L-cysteine ethyl ester. A reversed-phase high-performance liquid chromatographic method, using a C18 column for their separation, was developed by sequential optimization of the pH and the gradient of the mobile phase. Resolution of the compounds was obtained with an analysis time of less than 20 min.     

Stable solution of tridiagonal systems

In this paper we present three different pivoting strategies for solving general tridiagonal systems of linear equations. The first strategy resembles the classical method of Gaussian elimination with no pivoting and is stable provided a simple and easily checkable condition is met. In the second strategy, the growth of the elements is monitored so as to ensure backward stability in most cases. Finally, the third strategy also uses the right‐hand side vector to make pivoting decisions and is proved to be unconditionally backward stable. This revised version was published online in August 2006 with corrections to the Cover Date.     

Parallel algebraic reductions among numerical problems

In this note we consider, for a number of linear algebra problems, an environment allowing approximate computations. Within this framework we show that the relative complexity of these problems should be studied according to a strict notion of reducibility, which corresponds to the well-known many-one reducibility of combinatorial complexity.     

Nonlinear evolution of q=1 triple tearing modes in a tokamak plasma

In magnetic configurations with two or three q=1 (with q being the safety factor) resonant surfaces in a tokamak plasma, resistive magnetohydrodynamic modes with poloidal mode numbers m much larger than 1 are found to be linearly unstable. It is found that these high-m double or triple tearing modes significantly enhance through nonlinear interactions the growth of the m=1 mode. This may account for the sudden onset of the internal resistive kink, i.e., the fast sawtooth trigger. Based on the subsequent reconnection dynamics that can proceed without formation of the m=1 islands, it is proposed that high-m triple tearing modes are a possible mechanism for precursor-free partial collapses during sawtooth oscillations.     

Unprecedented Inversion of Selectivity and Extraordinary Difference in the Complexation of Trivalent f Elements by Diastereomers of a Methylated Diglycolamide

When considering f elements, solvent extraction is primarily used for the removal of lanthanides from ore and their recycling, as well as for the separation of actinides from used nuclear fuel. Understanding the complexation mechanism of metal ions with organic extractants, particularly the influence of their molecular structure on complex formation is of fundamental importance. Herein, we report an extraordinary (up to two orders of magnitude) change in the extraction efficiency of f elements with two diastereomers of dimethyl tetraoctyl diglycolamide (Me₂-TODGA), which only differ in the orientation of a single methyl group. Solvent extraction techniques, extended X-ray absorption fine structure (EXAFS) measurements, and density functional theory (DFT) based ab initio calculations were used to understand their complex structures and to explain their complexation mechanism. We show that the huge differences observed in extraction selectivity results from a small change in the complexation of nitrate counter-ions caused by the different orientation of one methyl group in the backbone of the extractant. The obtained results give a significant new insight into metal–ligand complexation mechanisms, which will promote the development of more efficient separation techniques.     

From chaos of lines to Lagrangian structures in flux conservative fields

A numerical method is proposed in order to track field lines of three-dimensional divergence free fields. Field lines are computed by a locally valid Hamiltonian mapping, which is computed using a symplectic scheme. The method is theoretically valid everywhere but at points where the field is null or infinite. For any three dimensional flux conservative field for which problematic points are sufficiently sparse, a systematic procedure is proposed and implemented. Construction of field lines is achieved by means of tracers and the introduction of various Hamiltonians adapted to the “geometrical state” each line or tracer is. The states are artificially defined by an a priori given frame of reference and Cartesian coordinates, and refer to a Hamiltonian which is locally valid at the time step to be computed. This procedure ensures the preservation of the volume (flux condition) during the iteration. This method is first tested with an ABC-type flow. Its benefits when compared to typical Runge-Kutta scheme are demonstrated. Potential use of the method to exhibit “coherent” Lagrangian structures in a chaotic setting is shown. An illustration to the computation of magnetic field lines resulting from a three-dimensional MHD simulation is also provided.