A thermodynamic theory is formulated to describe the phase transition and critical phenomenon in traffic flow. Based on the two-velocity difference model, the time-dependent Ginzburg-Landau （TDGL） equation under cer...A thermodynamic theory is formulated to describe the phase transition and critical phenomenon in traffic flow. Based on the two-velocity difference model, the time-dependent Ginzburg-Landau （TDGL） equation under certain condition is derived to describe the traffic flow near the critical point through the nonlinear analytical method. The corresponding two solutions, the uniform and the kink solutions, are given. The coexisting curve, spinodal line and critical point are obtained by the first and second derivatives of the thermodynamic potential. The modified Korteweg- de Vries （mKdV） equation around the critical point is derived by using the reductive perturbation method and its kink antikink solution is also obtained. The relation between the TDGL equation and the mKdV equation is shown. The simulation result is consistent with the nonlinear analytical result.展开更多
针对COB-LED(Chip on Board-Light Emitting Diode)散热问题,文中基于二维热传导方程建立了一个可快速计算COB-LED散热器表面热分布的数学模型。为了便于模型求解,采用有限差分法求解该数学模型并选择交替方向隐格式作为其差分格式。根...针对COB-LED(Chip on Board-Light Emitting Diode)散热问题,文中基于二维热传导方程建立了一个可快速计算COB-LED散热器表面热分布的数学模型。为了便于模型求解,采用有限差分法求解该数学模型并选择交替方向隐格式作为其差分格式。根据模型中的边界条件和初始条件设计COB-LED常温点亮实验,并基于ANSYS有限元分析软件进行仿真分析。通过比较求解结果、仿真结果和实验结果验证该数学模型的合理性。结果表明,求解结果与实验结果中最高温度相对误差约23.57%,且两者的温度变化趋势一致。求解结果与仿真结果中最高温度相对误差约34.84%,且温度分布较为接近,证明了该数学模型的合理性与正确性。展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11072117,10802042,and 60904068)the Natural Science Foundation of Zhejiang Province of China (Grant No.Y6100023)+1 种基金the Natural Science Foundation of Ningbo City(Grant No.2009B21003)K.C.Wong Magna Fund in Ningbo University
文摘A thermodynamic theory is formulated to describe the phase transition and critical phenomenon in traffic flow. Based on the two-velocity difference model, the time-dependent Ginzburg-Landau （TDGL） equation under certain condition is derived to describe the traffic flow near the critical point through the nonlinear analytical method. The corresponding two solutions, the uniform and the kink solutions, are given. The coexisting curve, spinodal line and critical point are obtained by the first and second derivatives of the thermodynamic potential. The modified Korteweg- de Vries （mKdV） equation around the critical point is derived by using the reductive perturbation method and its kink antikink solution is also obtained. The relation between the TDGL equation and the mKdV equation is shown. The simulation result is consistent with the nonlinear analytical result.
文摘针对COB-LED(Chip on Board-Light Emitting Diode)散热问题,文中基于二维热传导方程建立了一个可快速计算COB-LED散热器表面热分布的数学模型。为了便于模型求解,采用有限差分法求解该数学模型并选择交替方向隐格式作为其差分格式。根据模型中的边界条件和初始条件设计COB-LED常温点亮实验,并基于ANSYS有限元分析软件进行仿真分析。通过比较求解结果、仿真结果和实验结果验证该数学模型的合理性。结果表明,求解结果与实验结果中最高温度相对误差约23.57%,且两者的温度变化趋势一致。求解结果与仿真结果中最高温度相对误差约34.84%,且温度分布较为接近,证明了该数学模型的合理性与正确性。
