Molecular dynamics simulation of entropy and surface tension for grain boundary of α-Fe

The grain boundary is an interface and the surface tension is one of its important thermodynamic properties. In this paper, the surface tension of the ∑9 grain boundary for α-Fe at various temperatures and pressures is calculated by means of Computer Molecular Dynamics (CMD). The results agree satisfactorily with the experimental data. It is shown that the contribution of entropy to surface tension of grain boundary can be ignored. The project supported by the National Natural Science Foundation of China and the Science Foundation of Chinese Academy of Sciences.     

Avoider-Enforcer games

Let p and q be positive integers and let H be any hypergraph. In a (p,q,H) Avoider-Enforcer game two players, called Avoider and Enforcer, take turns selecting previously unclaimed vertices of H. Avoider selects p vertices per move and Enforcer selects q vertices per move. Avoider loses if he claims all the vertices of some hyperedge of H; otherwise Enforcer loses. We prove a sufficient condition for Avoider to win the (p,q,H) game. We then use this condition to show that Enforcer can win the (1,q) perfect matching game on K2n for every q?cn/logn for an appropriate constant c, and the (1,q) Hamilton cycle game on Kn for every q?cnloglogloglogn/lognlogloglogn for an appropriate constant c. We also determine exactly those values of q for which Enforcer can win the (1,q) connectivity game on Kn. This result is quite surprising as it substantially differs from its Maker-Breaker analog. Our method extends easily to improve a result of Lu [X. Lu, A note on biased and non-biased games, Discrete Appl. Math. 60 (1995) 285-291], regarding forcing an opponent to pack many pairwise edge disjoint spanning trees in his graph.     

Characterization of ceramic PVD thin films on AZ31 magnesium alloys

Ceramic thin films have been widely used to protect the metal substrate as coatings in the past years. In order to improve the poor corrosion resistance of AZ31 magnesium alloy, the study in this paper used the electron beam evaporation method to prepare ceramic PVD films on its surface with TiO₂ and Al₂O₃ as donors, respectively. Atomic force microscopy (AFM), scanning electron microscope (SEM), energy dispersive X-ray spectrometer (EDS), Auger electron spectroscopy (AES) and X-ray diffraction (XRD) were used to investigate the surface morphology, composition and microstructure of the thin films. Both films deposited on AZ31 took on compact top surface morphologies and grew as amorphous structures on substrate. AES test not only showed that films compositions deviated the standard stoichiometric ratios, but also found that element Mg diffused into films and existed as magnesium oxide in the TiO_x film as well as the AlO_x film. In the electrochemical corrosion test, the AlO_x coating on AZ31 exhibited the largest electrochemical impedance in a 3.5% NaCl solution. But it did not show better corrosion resistance than others for the poorer adhesion. Even if its thickness was small, the TiO_x coating on AZ31 exhibited the best corrosion resistance in this study. According to the observation and analysis, the damage of these films on AZ31 in aggressive solutions was mainly due to the existence of pores, microcracks, vacancies and poor adhesion between coating and substrate.     

LD端抽运平直腔Nd:YVO4固态激光器的输出功率特性研究

对LD端抽运平直腔Nd:YVO₄固态激光器输出功率特性受激光器内在诸因素(热透镜效应、腔长、激活孔径等)的制约关系进行了研究.并用传播圆-变换圆图解分析方法给出了合理的解释，同时，对进一步提高其输出功率特性指出了方向. 关键词： 固体激光器 热透镜 变换圆 平直腔     

Generalized KKM Type Theorems in FC-Spaces with Applications (I)

The class KKM(X,Y) (resp., s-KKM(X,Y,Z)) of set-valued mappings with KKM (resp., s-KKM) property is introduced in FC-spaces without any convexity structure. Some generalized KKM (resp., s-KKM) type theorems are proved in FC-spaces under much weak assumptions. As applications, some new section theorems and coincidence theorems are established in FC-spaces. These theorems generalize many known results in literature. The further applications of these results will be given in a follow-up paper.     

Calculation of number and free energy of the conformers of linear alkanes with medium and long chains. Implications for catalysis

A method for calculating the number of rotamers of a linear alkane and of the number of rotamers with a given number of gauche conformations along the chain as a function of the total number of atoms in the chain, using general equations, is presented. A graphical method for generating individual rotamers was applied to the homologs up to decane, which has 1134 rotamers. The steric energies calculated by molecular mechanics (MM2 force field) were used as measures of the heat of formation for the coiled conformations relative to the anti conformer for each molecule, whereas the statistical entropy differences were calculated for classes of coiled rotamers grouped by the number of gauche bonds and steric energy. The free energy values calculated from these components show that already at 400 K hexane exists preferentially in conformations containing gauche bonds. For larger chains the free energy advantage for the coiled chains increases very steeply. The implications for the question of reactions of linear alkanes occurring on the surface or inside the channels of small- and medium-pore zeolites are briefly examined.     

Effect of Incident Intensity on Films Growth in Pulsed Laser Deposition

Incident intensity, defined by the amount of particles deposited per pulse, is an important parameter in the film growth process of pulsed laser deposition （PLD）. Different from previous models, we investigate the irreversible and reversible growth processes by using a kinetic Monte Carlo method and find that island density and film morphology strongly depend on pulse intensity. At higher pulse intensities, lots of adatoms instantaneously diffuse on the substrate surface, and then nucleation easily occurs between the moving adatoms resulting in more smaller-size islands. In contrast, at the lower pulse intensities, nucleation event occurs preferentially between the single adatom and existing islands rather than forming new islands, and therefore the average island size becomes larger in this case. Additionally, our results show that substrate temperature plays an important role in film growth. In particular, it can determine the films shape and weaken the effect of pulse intensity on film growth at the lower temperatures by controlling the mobility rate of atoms. Our results can match the related theoretical and experimental results.     

A family of skew Hadamard difference sets

In 1933 a family of skew Hadamard difference sets was described by Paley using matrix language and was called the Paley-Hadamard difference sets in the literature. During the last 70 years, no new skew Hadamard difference sets were found. It was conjectured that there are no further examples of skew Hadamard difference sets. This conjecture was proved to be true for the cyclic case in 1954, and further progress in favor of this conjecture was made in the past 50 years. However, the conjecture remains open until today. In this paper, we present a family of new perfect nonlinear (also called planar) functions, and construct a family of skew Hadamard difference sets using these perfect nonlinear functions. We show that some of the skew Hadamard difference sets presented in this paper are inequivalent to the Paley-Hadamard difference sets. These new examples of skew Hadamard difference sets discovered 70 years after the Paley construction disprove the longstanding conjecture on skew Hadamard difference sets. The class of new perfect nonlinear functions has applications in cryptography, coding theory, and combinatorics.