Complexity bounds for the rational Newton-Puiseux algorithm over finite fields

We carefully study the number of arithmetic operations required to compute rational Puiseux expansions of a bivariate polynomial F over a finite field. Our approach is based on the rational Newton-Puiseux algorithm introduced by D. Duval. In particular, we prove that coefficients of F may be significantly truncated and that certain complexity upper bounds may be expressed in terms of the output size. These preliminary results lead to a more efficient version of the algorithm with a complexity upper bound that improves previously published results. We also deduce consequences for the complexity of the computation of the genus of an algebraic curve defined over a finite field or an algebraic number field. Our results are practical since they are based on well established subalgorithms, such as fast multiplication of univariate polynomials with coefficients in a finite field.     

Microstructural Characterization of the Shear Bands in Fe-Cr-Ni Single Crystal by EBSD

An investigation has been made into the microstructural characterization of the shear bands generated under high-strain rate （≈10^4 s^-1） deformation in Fe-15%Cr-15%Ni single crystal by EBSD-SEM （electron backscatter diffraction-scanning electron microscopy）, TEM （transmission electron in microscopy） and HREM （high- resolution electron microscopy）. The results reveal that the propagation of the shear band exhibits an asymmetrical behavior arising from inhomogenous distribution in plasticity in the bands because of different resistance to the collapse in different crystallographic directions; The γ-ε-α′phase transformations may take place inside and outside the bands, and these martensitic phases currently nucleate at intersections either between the twins and deformation bands or between the twins and ε-sheet. Investigation by EBSD shows that recrystallization can occur in the bands with a grain size of an average of 0.2μm in diameter. These nano-grains are proposed to attribute to the results of either dynamic or static recrystallization, which can be described by the rotational recrystallization mechanism. Calculation and analysis indicate that the strain rate inside the shear band can reach 2.50×10^6 s^-1, which is higher, by two or three orders of magnitude, than that exerted dynamically on the specimen tested.     

Modelling and Characterisation of the Texture Development in the Fusion Zone of An Austenitic Weld

The relation between texture and microstructure and the macroscopic solidification direction has been investigated for an austenitic 316L stainless steel weld. The fusion zone has been characterised by EBSD. Texture development has been simulated by thermal Finite Element Analysis coupled with a simple model of preferential <100>‐oriented solidification following the solidification direction. The thermal part is validated by means of thermocouple measurements at several locations on the specimen. The predicted texture is in very good agreement with the measured one.     

Improving the Design of Greek Hollow Clay Bricks

The hollow clay brick is the typical building unit that is employed not only over the whole Greece but also in many other Mediterranean countries. Nevertheless, its design is completely empirical. In this study, the design of the hollow clay brick is analyzed by employing a finite element package. To carry out this analysis, the thermal conductivity of the solid clay is measured by the transient hot-wire technique. As a consequence of the analysis, an improvement of 24 % in the design of the hollow clay brick is proposed.     

Pull-through performance of carbon fibre epoxy composites

An investigation of the through-thickness properties of carbon fibre prepreg laminates, Non-Crimp Fabric laminates and non-crimp 3D orthogonal woven composites by pull-through testing was performed. Influence of matrix system and curing temperature on the performance of the 3D woven composites was investigated.     

The structure solution of the F-type i-ZnMgHf from the X-ray diffraction

ABSTRACT

We report a successful growth of the ZnMgHf F-type icosahedral quasicrystal in the form of faceted single grains. By varying the heat treatment parameters we were able to obtain single crystals with a quality suitable for a single crystal X-ray diffraction which was conducted in a synchrotron facility. Ab initio structure solution by a charge flipping algorithm manifests the existence of two types of Bergman clusters. Clusters are differentiated by the preferential occupation of the high-symmetry positions by hafnium in a rhombic triacontahedron, being the outer shell of the atomic cluster.

This paper is part of a Thematic Issue on The Crystallographic Aspects of Metallic Alloys.     

Two-way Bayesian hierarchical phylogenetic models: An application to the co-evolution of gp120 and gp41 during and after enfuvirtide treatment

Enfuvirtide (ENF) is a fusion inhibitor that prevents the entry of HIV virions into target cells. Studying the characteristics of viral evolution during treatment and after a treatment interruption can lend insight into the mechanisms of viral evolution and fitness. Although interruption of anti-HIV therapy often results in rapid emergence of an archived “wild-type” virus population, previous work from our group indicates that when only ENF is interrupted, viral gp41 continues to evolve forward and resistance mutations are lost due to back-mutation and remodeling of the envelope protein. To examine the co-evolution of gp120 and gp41 during ENF interruption we extend the Bayesian Hierarchical Phylogenetic model (HPM). Current HPMs enforce conditional independence across all outcomes while biologically all gene regions within a patient should return the same tree unless recombination confers an evolutionary selective advantage. A two-way-interaction HPM is proposed that provides middle ground between these two extremes and allows us to test for differences in evolutionary pressures across gene regions in multiple patients simultaneously. When the model is applied to a well-characterized cohort of HIV-infected patients interrupting ENF we find that across patients, the virus continued to evolve forward in both gene regions. Overall, the hypothesis of independence over dependence between the gene regions is supported. Models that allow for the examination of co-evolution over time will be increasingly important as more therapeutic classes are developed, each of which may impact other through novel and complex mechanisms.     

Halogen bonding: Recent advances

Halogen bonding (XB), as a directional interaction between covalently bound halogen atoms (XB donor) and Lewis bases (A, XB acceptor), has been recently intensively investigated as a powerful tool in crystal engineering. After a short review on the origin and general features of halogen bonding, current developments towards (i) the elaboration of three-dimensional networks, (ii) the interaction with anionic XB acceptors, (iii) its identification in biological systems and (iv) the formation of liquid crystal phases will be described. Theoretical analyses, statistical studies and experimental electron density determinations converge to describe halogen bonding as a relatively weak structure directing tool, when compared with hydrogen bonding. However, when the halogen atom is strongly activated as in iodoperfluorinated molecules or cationic aromatic systems can halogen bonding act as an efficient and reliable structure directing tool.     

Megasonic agitation for enhanced electrodeposition of copper

In this paper we propose an agitation method based on megasonic acoustic streaming to overcome the limitations in plating rate and uniformity of the metal deposits during the electroplating process. Megasonic agitation at a frequency of 1 MHz allows the reduction of the thickness of the Nernst diffusion layer to less than 600 nm. Two applications that demonstrate the benefits of megasonic acoustic streaming are presented: the formation of uniform ultra-fine pitch flip-chip bumps and the metallisation of high aspect ratio microvias. For the latter application, a multi-physics based numerical simulation is implemented to describe the hydrodynamics introduced by the acoustic waves as they travel inside the deep microvias.