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.     

Compound Node–Kayles on paths

In his celebrated book [J.H. Conway, On Numbers and Games, Academic Press, New-York, 1976, Second edition (2001), A.K. Peters, Wellesley, MA], J.H. Conway introduced twelve versions of compound games. We analyze these twelve versions for the Node–Kayles game on paths. For usual disjunctive compound, Node–Kayles has been solved for a long time under normal play, while it is still unsolved under misère play. We thus focus on the ten remaining versions, leaving only one of them unsolved.     

Flow modeling of linear and nonlinear fluids in two scale fibrous fabrics

The fundamental macroscopic material property needed to quantify the flow in a fibrous medium viewed as a porous medium is the permeability. Composite processing models require the permeability as input data to predict flow patterns and pressure fields. As permeability reflects both the magnitude and anisotropy of the fluid/fiber resistance, efficient numerical techniques are needed to solve linear and nonlinear homogenization problems online during the flow simulation. In a previous work the expressions of macroscopic permeability were derived in a double-scale porosity medium for both Newtonian and rheo-thinning resins. In the linear case only a microscopic calculation on a representative volume is required, implying as many microscopic calculations as representative microscopic volumes exist in the whole fibrous structure. In the non-linear case, and even when the porous microstructure can be described by a unique representative volume, microscopic calculation must be carried out many times because the microscale resin viscosity depends on the macroscopic velocity, which in turn depends on the permeability that results from a microscopic calculation. Thus, a nonlinear multi-scale problem results. In this paper an original and efficient offline-online procedure is proposed for the efficient solution of nonlinear flow problems in porous media.     

Terrain Modelling from Feature Primitives

We introduce a compact hierarchical procedural model that combines feature‐based primitives to describe complex terrains with varying level of detail. Our model is inspired by skeletal implicit surfaces and defines the terrain elevation function by using a construction tree. Leaves represent terrain features and they are generic parametrized skeletal primitives, such as mountains, ridges, valleys, rivers, lakes or roads. Inner nodes combine the leaves and subtrees by carving, blending or warping operators. The elevation of the terrain at a given point is evaluated by traversing the tree and by combining the contributions of the primitives. The definition of the tree leaves and operators guarantees that the resulting elevation function is Lipschitz, which speeds up the sphere tracing used to render the terrain. Our model is compact and allows for the creation of large terrains with a high level o detail using a reduced set of primitives. We show the creation of different kinds of landscapes and demonstrate that our model allows to efficiently control the shape and distribution of landform features.     

Lattice-Dynamic Treatment of Vibrational and Elastic Properties of Cotunnite-Type ZrO2 and HfO2: Comparison with Ambient Pressure Polymorphs

The results of the joint lattice-dynamical model treatment of the vibrational and elastic properties of the cotunnite-type zirconia and hafnia are presented. The model is capable of reproducing the frequencies of the Raman-active vibrations, and provides their symmetry assignment. Also it predicts the position of the infrared-active bands. The model successfully describes the elastic properties of the low-pressure polymorphs, but could not reproduce the bulk modulus of OII-ZrO₂ of 332 GPa obtained from a volume-pressure dependence. The current results give an estimate of the bulk modulus of 254 GPa.     

Adaptive Mesh Refinement for One-Dimensional Three-Phase Flows in Heterogeneous Fractured Porous Media

This article presents an analysis of the implementation of the adaptive mesh refinement (AMR) technique to one-dimensional three-phase flows in heterogeneous fractured media. Variations of matrix permeability and matrix–fracture transfer shape factor cause matrix saturation discontinuities. In order to avoid directly performing refining or coarsening operations on these matrix quantities, we suggest using two separated grid systems for the fracture and matrix equations, respectively. The fracture and matrix equations are decoupled by a special decomposition approach during the Newton-Raphson procedure for solving the resulting nonlinear equations. The numerical examples show that the proposed AMR technique is fast with good accuracy.     

Robocast zirconia-toughened alumina scaffolds: Processing,structural characterisation and interaction with human primary osteoblasts

Zirconia-toughened alumina (ZTA) is the gold-standard ceramic in hip arthroplasty, but still lacks direct osseointegration and a metal shell, often coated with a bioactive layer, is currently required. The latter could potentially be replaced by a thinner, architectured ZTA layer, thereby allowing for larger acetabular components, with larger range of motion and lower dislocation risk. Robocasting may be an adequate technique to fabricate the architectured layer. Therefore, as a first step, this study aimed to produce ZTA scaffolds (3D-ZTA) by robocasting and assess their in vitro response. Shape retention was achieved by using a stable, well-dispersed, high solid loading ink injected in acid pH waterbath. 3D-ZTA exhibit regularly spaced microporous, rough struts and fully interconnected macroporosity. Human primary osteoblasts were homogenously distributed inside 3D-ZTA and showed increased osteogenic marker expression compared to 2D-ZTA control. Further work will focus on optimizing scaffold design to improve cell retention and extracellular matrix maturation.     

The mini-conical slump flow test: Analysis and numerical study

This paper provides a general study on cement paste flow. Both mini-slump and Marsh cone tests are used to evaluate the workability of fresh paste mixtures derived from self compacting concretes. A numerical approach is used to reproduce global flow behavior and to check the accuracy of the obtained viscosity as well as the validity of expressions available in the literature giving yield stress from the final diameter of slumped paste. The computational modeling allows access to local information in order to analyze different regions and corresponding flow types, i.e. falling solid and flowing fresh cementing material mixtures.The limitation of some empirical models allowing the prediction of yield stress τ₀ and plastic viscosity μ from mini-slump tests is underlined, conditions of validity are expressed and a new expression is proposed.     

Organocatalyzed Conjugate Addition of Carbonyl Compounds to Nitrodienes/Nitroenynes and Synthetic Applications

The purpose of this study is to point out the synthetic utility of a new class of Michael acceptors (nitrodienes and nitroenynes). The highly enantioselective organocatalytic Michael addition of carbonyl compounds to these functionalized nitroolefins has been carried out in the presence of (S)‐diphenylprolinol silyl ether to achieve some interesting building blocks in high selectivities. The adducts thus obtained can be easily converted by taking advantage of the corresponding unsaturated carbon‐carbon bond. In presence of the double bond, metathesis or electrophilic activation could be carried out whereas in the presence of the triple bond electrophilic activation could be conducted. We thus focused on a gold‐catalyzed cyclization of the bis‐homopropargylic alcohol to afford the corresponding substituted tetrahydrofuran. Then, we also demonstrated that organic and gold catalysts were compatible in a one‐pot process. Indeed, we developed a one‐pot enantioselective organocatalytic Michael addition to a nitroenyne followed by a gold‐catalyzed acetalization/cyclization to achieve tetrahydrofuranyl ethers in high diastereo‐ and enantioselectivities with excellent yields.