地方高校数学建模教学模式的探索与实践

针对地方高校学生的特点和培养目标,探索了地方高校以数学建模竞赛、数学模型课、数学实验课为中心的数学建模教学模式的步骤、措施和方法;总结了地方高校数学建模竞赛活动的实践经验.     

Direct Numerical Simulation of Subsonic Round Turbulent Jet

Direct numerical simulation(DNS) of spatially developing round turbulent jet flow with Reynolds number 4,700 was carried out. Over 20 million grid points were used in this simulation. Fully compressible three-dimensional Navier–Stokes equations were solved. High order explicit spatial difference schemes and Runge–Kutta time integration scheme were used to calculate derivatives and time marching, respectively. Non-reflecting boundary conditions and exit zone techniques were adopted. Some refined computational grids were used in order to capture the smallest turbulent structures near the centerline of the jet. Low level disturbance were imposed on the jet inflow velocity to trigger the developing of turbulence. Turbulent statistics such as mean velocity, Reynolds stresses, third order velocity moments were obtained and compared with experimental data. One-dimensional velocity autospectra was also calculated. The inertial region where the spectra decays according to the k^− 5/3 was observed. The quantitative profiles of mean velocity and all of the third order velocity moments which were difficult to measure via experimental techniques were presented here in detail. The jet flow was proven to be close to fully self-similar around 19 jet diameters downstream of jet exit. The statistic data and revealed flow feature obtained in this paper can provide valuable reference for round turbulent jet research.     

纯氮气反应溅射AlN薄膜及性质研究

在不同氮气浓度、不同溅射气压和衬底温度为20～370 ℃的条件下,分别在多种衬底上采用反应磁控溅射法沉积AlN薄膜.X射线衍射图谱表明:温度大于180 ℃时可在多种衬底上沉积出具有c轴择优取向的纤锌矿AlN薄膜.衬底温度和溅射时间的增加有利于薄膜结晶性的改善. 1.5 Pa的纯氮气气氛和Si(100)衬底是最佳择优生长条件.由紫外-可见光透射谱计算得到:在石英衬底上沉积的薄膜折射率为1.80～1.85,膜厚约为 1 μm、光学能隙为6.1 eV.原子力显微镜照片表明:在Si(100)衬底上制备的薄膜表面平滑,均方根粗糙度为2.2～13.2 nm.     

La,Pr,Nd掺杂对纳米TiO2光催化性能的影响

采用水解共沉淀法制备了稀土元素(La, Pr, Nd)掺杂量为0.5wt;～1.5wt;的TiO2光催化剂样本,并对其进行了XRD、TG-DTA、TEM、BET和UV-Vis表征.结果表明,所制备的TiO2光催化剂是以锐钛矿晶型为主的纳米颗粒,掺杂抑制了TiO2晶型由锐钛矿向金红石的转变,同时减小了晶粒尺寸、增大了比表面积、提高了吸光度,且使TiO2半导体的吸光范围发生了红移.将制得的TiO2光催化剂应用于溶液中草酸的降解反应,用K2MnO4滴定法分析降解效率,发现经掺杂改性后的TiO2样本光催化效率均有提高.其中,以掺杂量为1.0wt;的La掺杂样本具有最高的降解效率,与纯TiO2样本相比对草酸的降解率提高了近45;.     

磁场对激波冲击R22重气柱作用过程影响的数值模拟

为研究平面入射激波与磁化R22重质圆形气柱的作用过程,首先通过数值方法得到了不同初始条件下激波诱导R22气柱的Kelvin-Helmholtz (KH)及Richtmyer-Meshkov (RM)不稳定性导致的重气柱变形过程,并详细讨论了不同情况下透射激波在气柱内聚焦诱导射流的过程;然后在加入磁场的情况下,采用CTU+CT算法进行数值模拟,以保证数值结果满足任意时刻磁场的散度为零。计算结果表明:磁场对激波诱导R22气柱不稳定性具有抑制作用;法向磁场和流向磁场都可以很好地抑制RM不稳定性;对于KH不稳定性,法向磁场的控制效果更好,不仅可以抑制界面上涡串的卷起,还可以阻止主涡的发展,而流向磁场做不到后者;磁场对射流影响不大,射流处的磁能量可以一定程度上抑制射流的衰减,同时法向磁场可以减小聚焦时压力及速度峰值。     

含甲基磺化杂萘联苯聚醚砜酮质子交换膜材料的合成与性能

以4-(3,5-二甲基-4-羟基苯基)2,3-二氮杂萘-1-酮,3,3′-二磺酸钠-4,4′-二氟苯甲酮和4,4′-二氯二苯砜为原料,利用亲核缩聚反应,通过改变磺化单体的含量,制备出一系列不同磺化度的杂萘联苯聚醚砜酮(SPPESK-DM).采用FTIR、1H-NMR表征了聚合物的结构,热失重分析仪研究了聚合物的耐热稳定性,以N-甲基-2-吡咯烷酮为溶剂采用溶液浇铸法成膜研究该系列聚合物膜的性能.结果表明,SPPESK-DM磺酸基的热分解温度在260℃以上,主链分解温度在410℃以上;膜的吸水率、溶胀率、离子交换容量和质子传导率均随着磺化度的增大而增大,磺化度为1.0的SPPESK-DM50的质子传导率达到1.08×10-2S/cm(85℃),且甲醇渗透系数为2.06×10-7cm2/s,低于Nafion117膜的甲醇渗透系数(2×10-6cm2/s).此系列膜的耐氧化性比较优异,可望用于质子交换膜燃料电池中.     

含铽配合物的PVP纤维的制备及发光性质

通过静电纺丝法制得了含有稀土铽配合物(Tb(AA)3Phen)的聚乙烯吡咯烷酮(PVP)的荧光纤维丝。通过考察纺丝液的浓度,静电纺丝过程中的电压、溶剂配比以及电导率对PVP纤维丝形貌的影响,制备出表面光滑、直径均一、尺寸大小在80~150 nm之间的纤维。荧光性能测试显示,Tb(AA)3Phen/PVP纤维的荧光强度随着Tb(AA)3Phen含量的增加而增加,稀土配合物含量为15%时,纤维的荧光强度达到最强,之后出现浓度猝灭现象;通过X射线衍射(XRD)、透射电镜(TEM)等测试表明,Tb(AA)3Phen在PVP纤维中以分子簇或极小颗粒(小于10 nm)的状态存在,这种良好的分散效果减小了电子在跃迁过程中的非辐射跃迁几率,从而增强了纤维的荧光强度和荧光寿命。     

Modulation of the morphology of ZnO nanostructures via aminolytic reaction: from nanorods to nanosquamas

Various diversified morphology-modulated ZnO nanostructures including nanorods, nanotetrahedrons, nanofans, nanodumbbells, and nanosquamas have been successfully prepared via an effective aminolytic reaction of zinc carboxylates with oleylamine in noncoordinating and coordinating solvents. Their shape- and structural defect-dependent optical properties have been investigated as well. Highly crystalline defect-free nanotetrahedrons/nanorods have a sharp band-edge emission, and highly defective nanodumbbells/nanosquamas show a very broad deep-trap emission, resulting from the radiative recombination of electrons with holes in singly ionized oxygen vacancies.     

新型酰胺类化合物的合成及其生物活性

选取原儿茶酸和胡椒酸两种羧酸化合物,通过酰胺键与L-酪氨酸甲酯、D-酪氨酸甲酯、章胺、多巴胺4种具有生物活性的胺类的化合物偶联。成功合成了8个新型酰胺类化合物,其结构经¹H NMR和 ¹³C NMR表征。此外,还测试所有目标分子的体外酪氨酸酶抑制活性和DPPH自由基清除能力,对目标分子的酪氨酸酶抑制活性和抗氧化活性进行了初步评价。