Renormalized solutions of elliptic equations with Robin boundary conditions

In the present paper, we consider elliptic equations with nonlinear and nonhomogeneous Robin boundary conditions of the type{-div(B(x, u)▽u) = f in ?,u = 0 on Γ_0,B(x, u)▽u·n→+γ(x)h(u) =g on Γ_1,where f and g are the element of L~1(?) and L~1(Γ_1), respectively. We define a notion of renormalized solution and we prove the existence of a solution. Under additional assumptions on the matrix field B we show that the renormalized solution is unique.     

Some results for non-linear elliptic problems with mixed boundary conditions

We prove existence and uniqueness results for non-linear elliptic equations with lower order terms, L¹ data, and mixed boundary conditions that include as particular cases the Dirichlet and the Neumann problems. Mathematics Subject Classification (2000) 35J25, 35D05, 35J70, 35J60     

精确计算在π~0重整化链图传播下p→p′微分截面

本文采用中性介子π0与核子N-反核子U-强相互作用的Lorentz不变耦合模型,对质子反质子在中性介子π0重整化链图传播下的散射微分截面,作了严格解析计算后获得了"精确"理论结果;进而,又对该计算结果与π0树图传播下的微分截面作了对比分析,获得了相关辐射修正的重要结果.这对于深入研究质子摊贩质子在高、中、低能区中的弹性碰撞及其描述强相互作用的Lorentz不变耦合模型理论,都将提供某些值得借鉴与参考的理论研究价值.     

磷化物三元混晶中电子-声子相互作用的维度和体积效应

考虑电子-声子耦合强度因维度而异,导出了描述三维、二维和一维混晶中电子-声子相互作用的哈密顿量。考虑构成三元混晶的两种二元晶体的晶格失配会使混晶体积随元素组分比改变,在推导三维、二维和一维三元混晶中极化子自陷能量和重整化有效质量时计入了离子相对位移与二元晶体原胞体积的关系。结果表明:磷化物三元混晶中极化子自陷能量和重整化有效质量随元素组分的变化关系呈明显的非线性特征,对晶格适配明显、电子-声子耦合较强的材料,体积效应不可忽略。维度越低,非线性特征和体积效应越明显。     

Implementation of renormalized excitonic method at ab initio level

The renormalized excitonic method [Hajj et al., Phys Rev B 2005, 72, 224412], in which the excited state of the whole system may be described as a linear combination of local excitations, has been implemented at ab initio level. Its performance is tested on the ionization potential and the energy gap between singlet ground state and lowest triplet for linear molecular hydrogen chains and more realistic systems, such as polyenes and polysilenes, using full configuration interaction (FCI) wave functions with a minimal basis set. The influence of different block sizes and the extent of interblock interactions are investigated. It has been demonstrated that satisfactory results can be obtained if the near degeneracies between the model space and the outer space are avoided and if interactions between the next-nearest neighbor blocks are considered. The method can be used with larger basis sets and other accurate enough ab initio evaluations (instead of FCI) of local excited states, from blocks, or from dimers or trimers of blocks. It provides a new possibility to accurately and economically describe the low-lying delocalized excited states of large systems, even inhomogeneous ones.     

Viscosity analysis on the Boltzmann equation

This paper is devoted to investigating the asymptotic properties of the renormalized solution to the viscosity equation tfε + v ·▽xfε = Q (fε,fε ) + εΔvfε as ε→ 0+ . We deduce that the renormalized solution of the viscosity equation approaches to the one of the Boltzmann equation in L1 ((0 , T ) × RN × RN ). The proof is based on compactness analysis and velocity averaging theory.     

Low-temperature effective potential of the Ising model

We study the low-temperature effective potential of the Ising model. We evaluate the three-point and four-point zero-momentum renormalized coupling constants that parametrize the expansion of the effective potential near the coexistence curve. These results are obtained by a constrained analysis of the ε-expansion that uses accurate estimates for the two-dimensional Ising model.     

利用重归一化Numerov方法研究超冷双原子碰撞

采用重归一化Numerov算法求解关于超低温双原子碰撞问题的非含时薛定谔方程组.以39K-133Cs碰撞为例,研究了超低温下双原子Feshbach共振的性质.结果表明,重归一化Numerov算法可以很精确地描述超冷条件下碰撞过程.与改进的logarithmic derivative算法相比,在同等参数条件下,重归一化Numerov方法在计算效率上虽然有一定劣势,但在大格点步长参数范围内有着更好的稳定性.提出重归一化Numerov和logarithmic derivative算法相结合的传播方法,在保证结果精度的同时大大减少了计算时间.此项算法也可以应用于求解任意温度下的两体碰撞耦合薛定谔方程组.     

On the existence of finite energy weak solutions to the Navier–Stokes equations in irregular domains

This paper studies the existence of weak solutions of the Navier–Stokes system defined on a certain class of domains in ?³ that may contain cusps. The concept of such a domain and weak energy solution for the system is defined and its existence is proved. However, thinness of cusps must be related to the adiabatic constant appearing in the pressure law. Copyright © 2008 John Wiley & Sons, Ltd.