An adaptive pruning algorithm for the discrete L-curve criterion

We describe a robust and adaptive implementation of the L-curve criterion. The algorithm locates the corner of a discrete L-curve which is a log–log plot of corresponding residual norms and solution norms of regularized solutions from a method with a discrete regularization parameter (such as truncated SVD or regularizing CG iterations). Our algorithm needs no predefined parameters, and in order to capture the global features of the curve in an adaptive fashion, we use a sequence of pruned L-curves that correspond to considering the curves at different scales. We compare our new algorithm to existing algorithms and demonstrate its robustness by numerical examples.     

The emergence of a giant component in random subgraphs of pseudo‐random graphs

Let G be a d‐regular graph G on n vertices. Suppose that the adjacency matrix of G is such that the eigenvalue λ which is second largest in absolute value satisfies λ = o(d). Let G_p with p = α/d be obtained from G by including each edge of G independently with probability p. We show that if α < 1, then whp the maximum component size of G_p is O(log n) and if α > 1, then G_p contains a unique giant component of size Ω(n), with all other components of size O(log n). © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 2004     

Magnetic order in RCr\mathsf{_{2}}Si\mathsf{_{2}} intermetallics

The magnetic structure and ordering temperatures of three intermetallic compounds which crystallize in the tetragonal ThCr₂Si₂ structure, TbCr₂Si₂, HoCr₂Si₂ and ErCr₂Si₂, have been determined by neutron diffraction, differential scanning calorimetry and magnetization measurements. The Cr-sublattice orders anti-ferromagnetically with Néel temperatures of 758 K for TbCr₂Si₂, 718 K for HoCr₂Si₂ and 692 K for ErCr₂Si₂. Chromium atoms located at 4d crystallographic sites are aligned anti-parallel along the c-axis, with G_ZCr magnetic modes. In contrast with metallic bcc Cr, the refined room temperature value of the ordered Cr moment is anomalously large for all three compounds. No long range magnetic order of the R sublattice in TbCr₂Si₂ and HoCr₂Si₂ is observed, whilst the Er sublattice in ErCr₂Si₂ orders independently of the Cr sublattice below 2.4 K with moments ferromagnetically aligned in the basal plane.Received: 4 November 2003, Published online: 30 January 2004PACS: 75.25. + z Spin arrangements in magnetically ordered materials (including neutron and spin-polarized electron studies, synchrotron-source X-ray scattering, etc.) - 75.30.Cr Saturation moments and magnetic susceptibilities - 75.50.Ee Antiferromagnetics     

Excited-state dynamics in Yb3+-Ho3+-doped fluoroindate glasses

This work has been partially supported by Gobierno Autonomo de Canarias under contact number 226–265/93.     

A novel approach to thermal Analysis of Thin films

A novel instrument is described called the Thin film Analyser (TFA) which quantitatively measures changes in mechanical and rheological properties of drying films in-situ on a test panel. It is based around a simple force-sensing device, capable of carrying various probes, which can be positioned in anX-Y plane over the panel. Temperature control is achieved by means of a heating block under the sample. By imposing a thermal gradient along the block, measurements can be obtained at a series of temperatures in a single experiment. Several applications of the TFA to the drying of curable and latex-based coatings are discussed, as well as some more specialized uses. The TFA concept represents a novel approach to the thermal analysis of thin films.The authors gratefully acknowledge the design, engineering and software development work of the Instrument Group at ICI Paints, in particular John Hayton, Neil Burrows, Tony Evans and Ian Francis, who have now built three versions of the TFA.     

Moisture sorption, transport, and hydrolytic degradation in polylactide

Management of moisture penetration and hydrolytic degradation of polylactide (PLA) is extremely important during the manufacturing, shipping, storage, and end-use of PLA products. Moisture transport, crystallization, and degradation, in PLA have been measured through a variety of experimental techniques including size-exclusion chromatography, differential scanning calorimetry, and X-ray diffraction. Quartz crystal microbalance and dynamic vapor sorption experiments have also been used to measure moisture sorption isotherms in PLA films with varying crystallinity. A surprising result is that, within the accuracy of the experiments, crystalline and amorphous PLA films exhibit identical sorption isotherms.     

Characterization of graded-index planar waveguides and analysis of modal coupling for the design of integrated optical components produced by ion-exchange in glass and induced by Kerr effect

An experimental analysis of graded-index (GRIN) planar waveguides produced by ion exchange in soda-lime glass is presented. This study is based on a recent model describing nonlinear diffusion. Likewise the modal coupling between planar waveguides, produced in the same substrate, is analyzed in order to design efficient integrated optical components. Finally, waveguiding structures induced by Kerr effect in glass are proposed and analyzed.     

Decontamination treatment of uranium in tricarbonated solutions

It has been established that the coexistence of chemical species structurally different from cerium, is a direct consequence of the time taken for its preparation. Its practical applications, within the scope of purifying uranium, may constitute the most important technological aspect in the process of ionic exchange, to separate¹⁴¹Ce from uranium.