探索课程教学与科学研究的融合,促进教研相长

结合理工科"大学物理实验"课程的教学和实践平台,以培养创新人才为目标,实现了科学探究与课程学习的有机融合.通过开展课程内外的实践创新活动,本科生与教师一起自主研发系列创新实验并在国际教学研究期刊上发表高水平的论文,使学生获得融课程学习和科学研究于一体的高峰体验,同时在基础实践课程中推动了教研相长.     

Dynamics of the Kuramoto Model with Bimodal Frequency Distribution on Complex Networks

We introduce a piecewise uniform frequency distribution to model a symmetrical bimodal natural frequency distribution and investigate the dynamics in the Kuramoto model on complex networks. We find that the scenario of the synchronization transition depends on the network topology. For an ER network, the incoherent state, standing wave states and stationary synchronous states are encountered successively with the increase of the coupling strength. However, for an SF network, there exists another type of synchronous states, traveling wave states, between the standing wave states and the stationary synchronous states.     

用甲基叔丁基甲醚对苯酚叔丁基化的反应研究

目前我国生产对叔丁基苯酚的方法通常以酚类为原料，烯烃或醚类为烷基化试 剂，其中异丁烯是主要烷基化试剂，但异丁烯在储存、运输等方面存在着一定的弊 端．采用直接以甲基叔丁基甲醚为烷基化试剂，研究了苯酚与甲基叔丁基甲醚的烷 基化反应．并对各影响因素进行了讨论，其中催化剂用量和原料比对反应影响最大 ，温度次之，反应时间影响最小．实验中得出了制备反应的最佳条件；苯酚转化率 大于85％，对叔丁基苯酚产率为78％，得到较理想产率．并与以异丁烯为烷基化试 剂进行了比较，具有成本低、流程短、操作简便、安全等特点，应用前景非常好．     

Evolutionary Prisoners' Dilemma Game on Scale-Free Networks with Degree-Degree Correlation

Degree-degree correlation and heterogeneity in degree are important topological properties characterizing scale-free networks. We consider an evolutionary prisoners＇ dilemma game on scale-free networks and investigate how degree-degree correlation influences cooperation. It is found that the cooperator frequency displays resonance-like behavior with the variation of Pearson correlation coefficient. A measure on local heterogeneity in a network is proposed and it is realized that cooperation is proportional to the local heterogeneity.     

Intermittencies in complex Ginzburg-Landau equation by varying system size

Dynamical behaviour of the one-dimensional complex Ginzburg--Landau equation (CGLE) with finite system size $L$ is investigated, based on numerical simulations. By varying the system size and keeping other system parameters in the defect turbulence region (defect turbulence in large $L$ limit), a number of intermittencies new for the CGLE system are observed in the processes of pattern formations and transitions while the system dynamics varies from a homogeneous periodic oscillation to strong defect turbulence.     

非线性动力系统在分岔点处的临界慢化行为

Lyapunov指数是定量描述非线性动力系统轨道稳定性的主要方法之一,同时也是分析系统分岔行为的常用手段.实际应用中,人们通常只关心Lyapunov指数的正负,并以此来判断系统轨道是否稳定,而对于Lyapunov指数为零,即动力学分岔点处系统的行为特征讨论甚少.本文以几类经典的非线性动力系统为例,针对系统在分岔点处的轨道稳定性进行理论和数值分析.研究发现,不同系统在分岔点处其微扰后的轨道均以幂律,而非指数的形式收敛,呈现出经典物理系统在相变临界点处的慢化行为.通过理论分析,我们解析得到分岔点处计算临界指数的一般公式,并通过数值模拟对理论公式的准确性进行了验证.临界慢化是物理系统在相变点处的普遍现象,文中关于非线性系统在分岔点处临界慢化行为的发现将加深人们对于动力学分岔本质的认识,同时也是对现有教材中关于Lyapunov指数相关知识的有益补充.     

Evolutionary Prisoner＇s Dilemma on a Weighted Scale-Free Network

We investigate the evolutionary prisoner＇s dilemma on a weighted scale-free network where the diversity of teaching ability is introduced to the network in the form of weight. Though the diversity of teaching ability is not a sufficient condition for the enhancement of cooperation, we find that the degree-dependent teaching ability plays an active role in the evolution of cooperation. A new phenomenon is found when the degree-dependent teaching ability is used： the distribution of the cooperator frequency displays a two-peak structure for a certain parameter range. We also investigate the effects of the degree-degree correlation of the network on the evolution of cooperation in the presence of the diversity of the teaching ability.     

Effects of Degree on Cooperation in Evolutionary Prisoner's Dilemma Games on Structured Populations

We focus on the effects of individuals＇ degrees on spontaneous cooperation. By investigating evolutionary PDGs on random networks with two distinct degrees, we find some resonance-type behaviors of the cooperator frequency with the variation of degree. We also find that increasing hums degree actually disfavors the cooperation though the heterogeneity in degree can enhance cooperation in the population.     

Paths to Synchronization on Complex Networks with External Drive

We investigate the dynamics of the Kuramoto model on complex networks with part of the oscillators subjected to an external drive. It is found that the mutual synchronization is attracted to the drive when the frequency of the drive is close to the mean frequency of oscillators and, otherwise, mutual synchronization coexists with the driven synchronization. We also find that the synchronization between the mutual synchronization and the driven synchronization is dependent on the network topology when the coupling strength among oscillators is far away from the global synchronization in the absence of the drive. The transition is continuous on Erdoes-Renyi networks while it is discontinuous on scale free networks.