Augmented Lagrangian Algorithms Based on the Spectral Projected Gradient Method for Solving Nonlinear Programming Problems

The spectral projected gradient method SPG is an algorithm for large-scale bound-constrained optimization introduced recently by Birgin, Martínez, and Raydan. It is based on the Raydan unconstrained generalization of the Barzilai-Borwein method for quadratics. The SPG algorithm turned out to be surprisingly effective for solving many large-scale minimization problems with box constraints. Therefore, it is natural to test its perfomance for solving the sub-problems that appear in nonlinear programming methods based on augmented Lagrangians. In this work, augmented Lagrangian methods which use SPG as the underlying convex-constraint solver are introduced (ALSPG) and the methods are tested in two sets of problems. First, a meaningful subset of large-scale nonlinearly constrained problems of the CUTE collection is solved and compared with the perfomance of LANCELOT. Second, a family of location problems in the minimax formulation is solved against the package FFSQP.     

Critical Behavior of Two Interacting Linear Polymer Chains in a Good Solvent

A model of two interacting (chemically different) linear polymer chains is solved exactly using the real-space renormalization group transformation on a family of Sierpinski gasket type fractals and on a truncated 4-simplex lattice. The members of the family of the Sierpinski gasket-type fractals are characterized by an integer scale factorb which runs from 2 to ∞. The Hausdorff dimensiond _F of these fractals tends to 2 from below asb → ∞. We calculate the contact exponenty for the transition from the State of segregation to a State in which the two chains are entangled forb = 2-5. Using arguments based on the finite-size scaling theory, we show that forb→∞, y = 2 - v(b) d _F, wherev is the end-toend distance exponent of a chain. For a truncated 4-simplex lattice it is shown that the system of two chains either remains in a State in which these chains are intermingled in such a way that they cannot be told apart, in the sense that the chemical difference between the polymer chains completely drop out of the thermodynamics of the system, or in a State in which they are either zipped or entangled. We show the region of existence of these different phases separated by tricritical lines. The value of the contact exponenty is calculated at the tricritical points.     

New Imperfect Conjugate Gradient Algorithm

We present a method which generates conjugate search directions and maintains the quadratic convergence property, when applied to a quadratic function, even when the line searches are not exact. The method is similar to that given by Dixon, but needs one less vector store. When the method is applied to a number of general functions of different dimensionality, results show the efficiency of the method.     

线状锗等离子体X射线线谱的时间分辨测量

用自行研制的X射线条纹晶体谱仪首次测量了线状锗等离子体的X射线时间分辨谱。给出了类Ne-锗L线共振线的时间演化过程,并用类Ne-锗L线共振线与其双电子俘获伴线的相对强度比粗估了锗等离子体的电子温度及其随时间的变化,实验给出了X光激光增益区介质的电子温度为400～760eV,同时给出了电子温度保持相对恒定的时间不小于90ps(电子温度变化小于2％)。     

Application of Novel Focusing Mirrors in Gyrotron Transmission Lines

A novel focusing mirror based on the shifting of the beam phase according to the Gaussian beam optics enabled us to realize a focusing elements with different focal lengths in different directions and to convert the gyrotron output into a Gaussian-like beam. In this paper, we compare the quality of beams produced by the new system (which includes novel mirrors) and a conventional system consisting of a quasi-optical antenna, an ellipsoidal mirror and two parabolic cylinder mirrors.     

Investigations of He implantation and subsequent annealing effects in InP

The influence of 70 keV He⁺ ion implantation and subsequent annealing of Cz-indium phosphide (InP) samples has been investigated using a slow positron beam-based Doppler broadening spectrometer. Three samples with ion fluences of 1 × 10¹⁶, 5 × 10¹⁶ and 1 × 10¹⁷ cm⁻² were studied in the as-implanted condition as well as after annealing at 640 °C for times between 5 and 40 min. It was found that the line-shape parameter of the positron-electron annihilation peak in the implanted layer increases after 5 min annealing, then after longer annealing times it starts to decline gradually until it reaches a value close to the value of the as-grown sample. This implies that vacancy-like defects can be created in InP by He implantation followed by short-thermal annealing at T > 600 °C. Comparison of the results with a study where cavities were observed in He-implanted InP has been carried out.     

Measurement of storage time, estimation of ion number and study of absorption line profile in a Paul trap

Europium (Eu⁺) ions were confined in a Paul trap and detected by non-destructive method. Storage time of Eu⁺ ions achieved in vacuum was improved by orders of magnitude employing buffer gas cooling. The experimentally detected signal was fitted to the ion response signal and the total number of ions trapped was estimated. It is found that the peak signal amplitude as well as the product of FWHM and the peak signal amplitude is proportional to the total number of trapped ions. The trapped ion secular frequency was swept at different rates and its effect on the absorption line profile was studied both experimentally and theoretically.     

Ray-Singer type theorem for the refined analytic torsion

We show that the refined analytic torsion is a holomorphic section of the determinant line bundle over the space of complex representations of the fundamental group of a closed oriented odd-dimensional manifold. Further, we calculate the ratio of the refined analytic torsion and the Farber-Turaev combinatorial torsion. As an application, we establish a formula relating the eta-invariant and the phase of the Farber-Turaev torsion, which extends a theorem of Farber and earlier results of ours. This formula allows to study the spectral flow using methods of combinatorial topology.     

Champ de vitesse dans un échangeur à vortex en régime turbulentHeat exchanger velocity field with turbulent inlet condition

We consider the isothermal flow through a cylindrical flat chamber, a model of some particular heat exchanger, for which LDV measurements and a numerical simulation have been performed. Experimental results show the establishment of an important vortex zone, the secondary flow extending all along the chamber radius. This observation leads to an expected significant increase of the fluid mixing. Results issued from the numerical simulation appear to be in close agreement with experimental data. Nevertheless, the k–ε model used here must be improved to obtain a better approach near the vortex centre. To cite this article: S. Petitot et al., C. R. Mecanique 330 (2002) 593–599.     

On the excitation of a closely spaced array by a line source

An infinite row of periodically spaced, identical rigid circularcylinders is excited by an acoustic line source which is parallelto the generators of the cylinders. A method for calculatingthe scattered field accurately and efficiently is presented.When the cylinders are sufficiently close together, Rayleigh–Blochsurface waves that propagate energy to infinity along the arrayare excited. An expression is derived which enables the amplitudesof these surface waves to be computed without requiring thesolution to the full scattering problem.