Scroll codes over curves of higher genus

We construct linear codes from scrolls over curves of high genus and study the higher support weights d _i of these codes. We embed the scroll into projective space ${\mathbb{P}^{k-1}}$ and calculate bounds for the d _i by considering the maximal number of ${\mathbb{F}_q}$ -rational points that are contained in a codimension h subspace of ${\mathbb{P}^{k-1}}$ . We find lower bounds of the d _i and for the cases of large i calculate the exact values of the d _i . This work follows the natural generalisation of Goppa codes to higher-dimensional varieties as studied by S.H. Hansen, C. Lomont and T. Nakashima.     

Trisection for genus 2 curves in odd characteristic

We provide trisection (division by 3) algorithms for Jacobians of genus 2 curves over finite fields \(\mathbb {F}_q\) of odd characteristic which rely on the factorization of a polynomial whose roots correspond (bijectively) to the set of trisections of the given divisor. We also construct a polynomial whose roots allow us to calculate the 3-torsion divisors. We show the relation between the rank of the 3-torsion subgroup and the factorization of this 3-torsion polynomial, and describe the factorization of the trisection polynomials in terms of the Galois structure of the 3-torsion subgroup. We also generalize these ideas for \(\ell \in \{5,7\}\).     

Effective electroelastic moduli of 3-3(0-3) piezocomposites

In a high volume fraction particle-loaded piezocomposite, some ferroelectric particles appear to be in contact, as in a 3-3 connectivity material; others are isolated in the polymer matrix, as in a pure 0-3 connectivity material. Such a material can be considered as a composite of composites characterized by a 3-3(0-3) connectivity. This paper follows two others that have described a matrix method to calculate all of the effective parameters of pure 0-3 and 3-3 connectivity piezocomposites. These previous models are used to obtain the effective properties of a 3-3(0-3) composite. A proportion of 0-3 connectivity in the composite is introduced, and the effective properties are studied as a function of this proportion. Experimental results compared with these predictions show that the model allows an evaluation of the proportion of 0-3 connectivity through the analysis of the electromechanical performance of the composite samples.     

Computing a hyperelliptic integral using arithmetic in the Jacobian of the curve

In this paper, we describe an efficient algorithm for computing an elementary antiderivative of an algebraic function defined on a hyperelliptic curve. Our algorithm combines B. M. Trager's integration algorithm and a technique for computing in the Jacobian of a hyperelliptic curve introduced by D. G. Cantor. Our method has been implemented and successfully compared to Trager's general algorithm.Work partially made at Departement Informatik ETH ZurichUnité de Recherche Associée au CNRS 1586     

Temperature dependence of the elastic moduli of multiferroic PbFe2/3W1/3O3 ceramics

Elastic properties of multiferroic PbFe_2/3W_1/3O₃ (PFW) ceramics have been studied in a temperature range of 4.2–400 K, which contains the regions of existence of the ferroelectric relaxor and antiferromagnetic phases. The longitudinal, shear, and bulk elasticity moduli, Young’s modulus, and Poisson’s ratio of PFW ceramics have been determined for the first time. Regions of temperature stability of the elastic properties extending over several dozen degrees have been found.     

Nonlinear dynamic moduli in asphalt

Conventional and polymer modified asphalts (PMA) are routinely tested in small amplitude oscillations. It is probable that asphalt as a part of paving mixture is exposed to large deformations. Hence a better understanding of asphalt behavior in large amplitude oscillations (LAOS) is needed. LAOS experimental results for a base asphalt and its blend with radial SBS polymer are discussed in terms of nonlinear dynamic moduli.

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Résumé Les bitumes conventionnels ou modifiés par polymères (BMP) sont couramment mis à l'épreuve par des oscillations de petite amplitude. Il est probable que le bitume en tant que partie d'un mélange de chaussée soit exposé à de grandes déformations. Donc une meilleure compréhension du comportement du bitume dans les oscillations à grande amplitude (OGAM) est nécessaire. Les résultats OGAM expérimentaux pour une base de bitume et son mélange avec un polymère radial SBS sont examinés sur la base du module dynamique non linéaire.

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Editorial Note Prof. Ludo Zanzotto is a RILEM Senior Member and a member of RILEM TC 182-PEB (Perfonnance testing and evaluation of bituminous materials).     

A matrix method for modeling electroelastic moduli of 0-3 piezo-composites

A model is proposed to predict the electroelastic moduli of 0-3 connectivity piezo-composites from which parameters such as longitudinal wave velocity and thickness mode coupling factor can be deduced. The composite, a polymer loaded with ceramic particles, is represented by a unit cell, and a matrix manipulation is shown to be a practical way to perform a generalization of the series and parallel analysis used for 2-2 connectivity composites. The anisotropy of the ceramic phase is taken into account, and its effect on the properties of the composite is shown. The model is then used to optimize composite performance and to choose the two constituents through comparison of results obtained using several commercial polymers and ceramics.     

钛酸钡陶瓷烧结动力学曲线的研究

以超重力反应沉淀法(HGRP)制备的纳米钛酸钡粉体为原料,以热膨胀仪为测试手段,对钛酸钡陶瓷的烧结动力学曲线特征进行了研究.结果表明,烧结温度和成型坯片密度都会对钛酸钡陶瓷的烧结过程产生影响,所表现出的烧结动力学曲线特征也不相同,而升温速率几乎不对坯片的烧结动力学曲线特征产生影响.随着烧结温度的升高,坯片收缩率增大,当烧结温度由1150℃升到1300℃时,收缩率由6.7%增大到23.2%;坯片的密度增大,收缩率减小,当成型坯片相对密度由61.08%增大到64.42%时,收缩率由17.5%减少到14.4%;升温速率增大,坯片开始收缩的温度及收缩率几乎不变.     

Effective moduli of multi-scale composites

The effective moduli of a multi-scale composite are evaluated by a bottom-up (hierarchical) modeling approach. We focus on a two-scale structure in which the small scale includes a platelet array inside a matrix, and the large scale contains fibers inside a composite matrix. We demonstrate that the principal moduli of the multi-scale composite can be fine-tuned by the platelet arrangement and orientation. As a case study, we consider the phenomenon of fiber micro-buckling within the multi-scale composite. It is found that the compressive micro-buckling strength can be considerably increased for specific platelet orientations. The multi-scale design approach presented here can be used to generate novel families of composite materials with tunable mechanical properties.     

Dynamic moduli of CaCO3- and Mg(OH)2-filled polypropylene

Fillers suppressed the temperature dependence of storage modulus and caused the flattening of the temperature dependence of the loss modulus in the glass transition region of polypropylene (PP). The glass transition temperature (T _β) of PP did not change with filler content (v _f). This indicates that none of the fillers affect the mobility of PP in the bulk. A new loss maximum appeared at 50 °C forv _f>0.2. This maximum became more prominent when increasing either the filler content or filler specific surface area. Interparticle interactions, leading to the space network of weakly bonded particles, affected PP mobility indirectly. The enhanced interfacial adhesion led to a further decrease of PP mobility nearT _β and to the increase of the new loss maximum at 50 °C.     

Determination of dynamic elastic moduli and shear moduli of aged wood by means of ultrasonic devices

Due to ecological and environmental factors, re-using aged wood is becoming more and more important, also in applications where mechanical strength plays a central role. The aim of this study was to examine specific mechanical parameters of naturally aged and dried wood and to better understand the influence of aging on the elastic behaviour of wood. To this aim, measurements on boards and on small, clear wood specimens were carried out. Ultrasound velocities of longitudinal and, in some cases, of transversal waves were measured to determine dynamic elastic moduli and shear moduli. The measurements were performed on structural timber of aged Norway spruce (aged wood) and compared with specimens of recently cut and kiln dried timber of the same species (recent wood) as a reference with comparable density properties and average annual ring width. The measurements revealed higher values of dynamic elastic modulus for aged wood in the longitudinal and radial directions, but no significant difference was found in the tangential direction or in the shear moduli. It is supposed that the difference is more likely a consequence of variability in densities and the structure parameters (annual ring structure, microfibril angle, growth conditions) rather than a consequence of the wood age. The relation between the dynamic elastic modulus in the longitudinal direction and wood density was nearly the same for aged and recent wood specimens, so with increased prudence, grading methods developed for recent wood can also be applied for aged wood.     

Distributions of elastic moduli in mechanically percolating composites

Power-law percolation models contain very little mechanics other than the theoretical or simulated value of a percolation threshold, the volume fraction where a connected microstructure forms. For mechanical percolation these theoretical values do not correspond well to experimental results and so the models are commonly used empirically; results are correlative rather than predictive. In recent work, the effective elastic properties of a model polymer nanocomposite were approximated using a computational micromechanics model within a Monte Carlo framework. Significantly, the statistical averages resulting from these simulations displayed distinct percolation-like behavior. Of equal interest is the distribution of properties that resulted from the randomly simulated microstructures. This strongly suggests that mechanical percolation in nanocomposites is the result of a combination of microstructural mechanisms. Analysis aimed at determining which microstructure produces what response is a challenging task if microstructure is the random variable. In this work, the effective composite properties are considered as the random variable; probability distribution functions (PDFs) of the properties at discrete volume fractions are developed using the Principle of Maximum Informational Entropy. The evolution of these PDFs with increasing volume fraction helps visualize and track the significant property changes that result from microstructural randomness.     

Temperature dependence of the elastic and inelastic moduli of YBa2Cu3O7−δ ceramics

Elastic and inelastic moduli of the superconducting yttrium-barium oxide ceramics YBa₂Cu₃O_7−δ (YBCO) were studied using the ultrasonic resonance technique. In the range from room temperature up to the temperature of the ortho-tetra phase transition, the elastic and inelastic moduli of YBCO samples exhibit a number of anomalies. It is shown that these features are related to the behavior of active oxygen in the ceramics, the phase inhomogeneity of the material, and the phase transitions.     

Storage and loss moduli in discontinuous composites

The paper deals with viscoelastic, rubber-like material unidirectionally reinforced with discontinuous fibres. The longitudinal storage modulus is calculated not only from an equation based on an existing force balance treatment but also from the elastic strain energy stored in matrix and fibres, using two different models to derive the stress and strain distributions from which the stored energy is calculated. There is very good agreement between all the calculations. The energy calculations reveal that loss modulus is also greatly increased by discontinuous reinforcement and enable its value to be estimated. Experiments on storage and loss modulus are reported and show that the calculations underestimate storage modulus and overestimate loss modulus. In both cases the factor of error ～ 2, and arises because the amplified matrix strain is underestimated and is partly hydrostatic; the hydrostatic strain is non-dissipative and therefore does not contribute to the loss modulus. Discontinuous reinforcement can increase loss modulus as well as storage modulus by more than 100 times, and this should help sound and vibration deadening. An estimate is made of the wide ratio of compliance ÷ breaking strength available with discontinuous but not with continuous reinforcement, which opens up new design latitude for components hitherto reinforced with continuous fibres.     

Deciphering the potentiodynamic polarization curves of iron aluminides Fe3Al and Fe3Al + Cr

The potentiodynamic polarization curves of Fe₃Al and Fe₃Al + Cr intermetallics obtained in aerated pH 4 H₂SO₄ acidic solution have been theoretically analyzed. The role of chromium in minimizing the hydrogen embrittlement (HE) of the intermetallic Fe₃Al (resulting in its poor ductility) has been addressed based on the analysis. In the case of the chromium-alloyed iron aluminide, calculations indicate that hydrogen liberation does not occur on the surface due to the shift of the corrosion mixed potential to a value nobler than the electrode potential for the hydrogen evolution reaction. This shift occurs due to the induction of passivity on alloying with Cr resulting in the formation of a passive film. The minimization of HE of iron aluminides on alloying with Cr can thus be understood.