Solid–liquid equilibria based on an equation of state for chain fluids

Solid–liquid equilibria were studied using an equation of state previously developed for fluids containing chain-like molecules. The method was used to correlate solubilities of normal alkanes and aromatic compounds with high molecular mass in hydrocarbon solvents. With one temperature independent parameter for the interaction energy, good agreement can be obtained between calculated results and experimental data for selected systems.     

Banach space properties sufficient for normal structure

In this paper we establish lower bounds for the weakly convergent sequence coefficient WCS(X) of a Banach space X, in terms of some well known moduli and coefficients. By mean of these bounds we identify several properties, of geometrical nature, which imply normal structure. We show that these properties are strictly more general than other previously known sufficient conditions for normal structure.     

Gevrey normal forms of vector fields with one zero eigenvalue

We study normal forms of isolated singularities of vector fields in Rn or Cn. When all eigenvalues of the linear part of the vector field are nonzero, one can eliminate all so-called nonresonant terms from the equation provided some spectral condition (like Siegel) is satisfied. In this paper, we discuss the case where there is one zero eigenvalue (in that case Siegel's condition is not satisfied), and show that the formal normalizing transformations are either convergent or divergent of at most Gevrey type. In some cases, we show the summability of the normalizing transformations, which leads to the existence of analytic normal forms in complex sectors around the singularity.     

楚雄盆地恐龙化石和围岩的XRF全元素分析

采用X射线荧光光谱分析方法(XRF),对楚雄盆地不同地区的恐龙化石和围岩的元素成分进行对比研究。实验结果表明,恐龙化石中的主元素含量的排序均是Ca、C、Si,而围岩中则均为Si、C、Ca;在恐龙化石中有元素F和As,在围岩中不含F和As;在化石和围岩中Pb元素的含量均较低。其次,通过对禄丰恐龙山的两组化石和围岩元素含量的对比分析,推知恐龙山所处地层可能发生过断裂和错位的地壳变动。实验还发现,武定、牟定和元谋的化石中的微量元素含量具有共同的特点,即元素砷(As)含量略高,钡(Ba)的含量高异常和锌(Zn)含量低异常,有可能是导致这三个地方恐龙动物群的死亡原因之一。     

Matching inductive search bias and problem structure in continuous Estimation-of-Distribution Algorithms

Research into the dynamics of Genetic Algorithms (GAs) has led to the field of Estimation-of-Distribution Algorithms (EDAs). For discrete search spaces, EDAs have been developed that have obtained very promising results on a wide variety of problems. In this paper we investigate the conditions under which the adaptation of this technique to continuous search spaces fails to perform optimization efficiently. We show that without careful interpretation and adaptation of lessons learned from discrete EDAs, continuous EDAs will fail to perform efficient optimization on even some of the simplest problems. We reconsider the most important lessons to be learned in the design of EDAs and subsequently show how we can use this knowledge to extend continuous EDAs that were obtained by straightforward adaptation from the discrete domain so as to obtain an improvement in performance. Experimental results are presented to illustrate this improvement and to additionally confirm experimentally that a proper adaptation of discrete EDAs to the continuous case indeed requires careful consideration.     

Normal mode calculation and IR band assignments of A-type zeolite

Normal mode calculation of A-type zeolite was carried out with the potential energy functions obtained from the constraint method. Mass-weighted cartesian coordinates and the pseudo-lattice method were used. The assignments of IR absorption bands were made with the calculated normal modes, by using the calculated absorption intensities of the modes and the degrees of contribution of the internal coordinates to the modes. The force constants of internal coordinate motions within the framework were also calculated and are compared with the empirical values.     

Numerical analysis of two frictionless elastic-piezoelectric contact problems

In this work, we consider two frictionless contact problems between an elastic-piezoelectric body and an obstacle. The linear elastic-piezoelectric constitutive law is employed to model the piezoelectric material and either the Signorini condition (if the obstacle is rigid) or the normal compliance condition (if the obstacle is deformable) are used to model the contact. The variational formulations are derived in a form of a coupled system for the displacement and electric potential fields. An existence and uniqueness result is recalled. Then, a discrete scheme is introduced based on the finite element method to approximate the spatial variable. Error estimates are derived on the approximate solutions and, as a consequence, the linear convergence of the algorithm is deduced under suitable regularity conditions. Finally, some two-dimensional examples are presented to demonstrate the performance of the algorithm.     

A convergence result in the study of bone remodeling contact problems

We consider the approximation of a bone remodeling model with the Signorini contact conditions by a contact problem with normal compliant obstacle, when the obstacle's deformability coefficient converges to zero (that is, the obstacle's stiffness tends to infinity). The variational problem is a coupled system composed of a nonlinear variational equation (in the case of normal compliance contact conditions) or a variational inequality (for the case of Signorini's contact conditions), for the mechanical displacement field, and a first-order ordinary differential equation for the bone remodeling function. A theoretical result, which states the convergence of the contact problem with normal compliance contact law to the Signorini problem, is then proved. Finally, some numerical simulations, involving examples in one and two dimensions, are reported to show this convergence behaviour.     

On the theory of the shear-induced isotropic-to-nematic phase transition of side chain liquid-crystalline polymers

The shear-induced isotropic-to-nematic phase transition of side chain liquid-crystalline polymers is studied theoretically. A modification of the previous models of main-chain liquid crystals to the case of side chain liquid-crystalline polymers is proposed. Orientational and rheological properties of the model are studied in plane-shear flow. Predictions of the present model agree qualitatively with experimental results (Pujolle-Robic, Noirez in Nature 409:167, 2001).