等离子体Euler-Poisson系统的渐近极限

研究了等离子物理中在环面T^3上可压的Euler-Poisson系统的渐近极限问题．对于好的初值,运用能量方法和梯度的div—curl分解不等式严格证明了了可压的Euler—Poisson系统到不可压的Euler方程的收敛性,并建立了关于德拜长度λ的一致先验估计．     

Heisenberg方程与Euler—Lagrange方程的一致性

本文一般性地证明了经典力学体系中Hamilton正则方程和经典Poisson括号关系式与Euler—Lagrange方程的一致性以及量子力学体系中Heisenberg方程和对易关系与量子Euler—Lagrange方程的一致性。     

高维Euler方程组的强松弛极限

利用能量积分, 讨论在初值充分小的情形下, 高维带有阻尼项的Euler方程组光滑解的整体存在性和强松弛极限, 得到了解的一致先验估计, 并证明当松弛时间趋于0时, 整体解的渐近行为由多孔渗流方程控制.     

高维Euler方程组的强松驰极限

利用能量积分, 讨论在初值充分小的情形下, 高维带有阻尼项的Euler方程组光滑解的整体存在性和强松弛极限, 得到了解的一致先验估计, 并证明当松弛时间趋于0时, 整体解的渐近行为由多孔渗流方程控制.     

高维Euler方程组的强松驰极限

利用能量积分,讨论在初值充分小的情形下,高维带有阻尼项的Euler方程组光滑解的整体存在性和强松弛极限,得到了解的一致先验估计,并证明当松弛时间趋于0时,整体解的渐近行为由多孔渗流方程控制.     

一类带小扰动的Raman散射的数学模型研究

研究一类带小扰动的Raman散射的数学模型的相关问题，使用积分方程和Banach不动点定理证明初值问题的解的存在唯一，并利用多重尺度法求解渐近解，再借助积分方程和Gronwall不等式得到渐近解的余项估计，从而证明了渐近解的一致有效性。     

一类非线性反应扩散方程整体解的渐近性态

本文考虑了一类非线性反应扩散方程初值问题解的整体存在性及渐近性态，并给出了当ｔ→∞时解的衰减速度。     

粗糙面及其上方任意形状截面导体目标的瞬态散射

利用时域积分方程研究了一维导体粗糙面及其上方任意形状截面二维导体目标的复合脉冲散射．在给出时域电场积分方程的基础上推导了显式及隐式MOT步进方程,计算了Gauss脉冲波照射下粗糙面加目标时中心点的电流及电场远场随时间的响应,并将计算结果与频域矩量法结合离散Fourier逆变换（MOM-IDFT）进行了对比,验证了所得方法的有效性．最后详细讨论了电流及电场远场时间响应随目标尺寸大小、距离粗糙面高度及入射角的变化情形．     

一类非线性扰动波方程的渐近理论及应用

对二阶半线性波动方程的初值问题，本文将给出一个渐近方法。初值问题的适定性及形式近似解的合理性都在时间变量无穷大时成立。作为渐近理论的应用。本文对带初值问题的Ｒａｙｌｅｉｇｈ波方程进行了详细的讨论。     

格点能量变化时离散晶格中荷电粒子在任意含时电场作用下的运动

本文研究了当格点能量变化时一维键上的带电粒子在任意含时电场作用下的运动,给出了动量空间的普遍的形式解,并就静电场的情形讨论了粒子在动量空间的局域性问题.     

关于等热双极半导体模型松弛极限的一个注记

在这个注记里,考虑了一维等热双极半导体模型.这个系统实际上是在动量方程有电场项和磨擦阻力项(阻力系数是τ-1)的欧拉一泊松方程组.当τ→O+,使用熵不等式和L1里的弱紧性原理,证明了一维等热双极半导体模型的弱熵解收敛到相应的双极漂移-扩散方程的解.也即是:当τ充分小时,等热双极半导体模型和相应的双极漂移-扩散方程是相似的.     

Weak solutions of the isothermal bipolar hydrodynamic model for semiconductors with large data

This paper is devoted to weak solutions of Cauchy problem to the isothermal bipolar hydrodynamic model with large data. The model takes the bipolar Euler-Poisson form, with electric field and relaxation terms added to the momentum equations. Using Glimm scheme to the hyperbolic part and the standard theory to the ordinary differential equations, we first construct the approximation solutions, then from the facts that the total charge is quasi-conservation, we can obtain a uniform estimate of the total variation of the electric field, which allows to prove the L∞ estimate of densities and velocities, and the convergence of the scheme. Then we can prove the global existence of weal solution to Cauchy problem with large data.     

稳态双极黏滞量子流体力学模型的正解的存在性

研究一类带有特殊黏滞项的稳态双极流体力学模型正解的存在性。这个模型含有三阶量子修正项和二阶黏滞项。先将原方程组变形为常见的形式。得到原问题的等价问题利用先验估计和Leray-Schauder不动点定理。证明了无论是等熵还是等温条件下,对于所有的电流密度,此模型存在正解。     

稳态双极粘滞量子流体力学模型的正解的存在性

文章研究一类带有特殊粘滞项的稳态双极流体力学模型正解的存在性.这个模型含有三阶量子修正项和二阶黏滞项。文章先将原方程组变形为常见的形式,得到原问题的等价问题利用先验估计和Leray-Schauder不动点定理证明了无论是等熵还是等温条件下,对于所有的电流密度,此模型存在正解.     

Tunnelling between the edges of two lateral quantum Hall systems

The edge of a two-dimensional electron system in a magnetic field consists of one-dimensional channels that arise from the confining electric field at the edge of the system. The crossed electric and magnetic fields cause electrons to drift parallel to the sample boundary, creating a chiral current that travels along the edge in only one direction. In an ideal two-dimensional electron system in the quantum Hall regime, all the current flows along the edge. Quantization of the Hall resistance arises from occupation of N one-dimensional edge channels, each contributing a conductance of e2/h. Here we report differential conductance measurements, in the integer quantum Hall regime, of tunnelling between the edges of a pair of two-dimensional electron systems that are separated by an atomically precise, high-quality, tunnel barrier. The resultant interaction between the edge states leads to the formation of new energy gaps and an intriguing dispersion relation for electrons travelling along the barrier: for example, we see a persistent conductance peak at zero bias voltage and an absence of tunnelling features due to electron spin. These features are unexpected and are not consistent with a model of weakly interacting edge states. Remnant disorder along the barrier and charge screening may each play a role, although detailed numerical studies will be required to elucidate these effects.     

一维光子晶体中的几率密度和拓扑相

用光量子理论给出一维光子晶体(AB)^N中光子的几率密度、几率流密度和Zak相, 当介质B的折射率n_b=1.12时, 用量子方法计算出三条带的Zak相. 结果表明:  当入射角θ和周期数N改变时, 光子晶体的几率密度和几率流密度近似为周期变化, 且其振幅随入射角θ和周期数N的增加而增大; 当入射光的频率与透射率T=100%相对应时, 几率密度的振幅最大, 当入射光的频率与透射率T=0相对应时, 几率密度不为零, 但几率密度的振幅迅速衰减到零, 即光子晶体中存在光子的量子隧道效应.     

Euler-Poisson方程组到不可压Euler型方程的收敛性(英文)

研究了在环Τ3上带松弛项的无压力的Euler-Poisson系统的拟中性极限问题.对于好的初值,运用梯度的div-curl分解技术和能量估计方法,严格证明了可压的Euler-Poisson方程组到不可压Euler型方程的收敛性;并建立了关于德拜长度λ的一个先验估计.     

Asymptotic behavior of the solutions to the one-dimensional nonisentropic hydrodynamic model for semiconductors

In this paper, the asymptotic behavior of the global smooth solutions to the Cauchy problem for the one-dimensional nonisentropic Euler-Poisson (or full hydrodynamic) model for semiconductors, where the energy equation with non-zero thermal conductivity coefficient are contained, is discussed. The global existence of smooth solutions for the Cauchy problem with small perturbed initial data is proved. In particular, that the solutions converge to the corresponding stationary solutions exponentially fast as t → ∞ is showed. Biography: LI Yeping(1972–), male, Associate professor, Ph.D., research direction: nonlinear partial differential equations.     

Dirichlet-Neumann Problem for Unipolar Isentropic Quantum Drift-Diffusion Model

This paper studies the existence, semiclassical limit, and long-time behavior of weak solutions to the unipolar isentropic quantum drift-diffusion model, a fourth order parabolic system. Semi-discretization in time and entropy estimates give the global existence and semiclassical limit of nonnegative weak solutions to the one-dimensional model with a nonnegative large initial value and a Dirichlet-Neumann boundary condition. Furthermore, the weak solutions are proven to exponentially approach constant steady state as time increases to infinity.