Deterministic and stochastic equations of motion arising in Oldroyd fluids of order one: existence,uniqueness, exponential stability and invariant measures

Abstract

In this work, we consider the two-dimensional viscoelastic fluid flow equations, arising from the Oldroyd model for the non-Newtonian fluid flows. We investigate the well-posedness of such models in two-dimensional bounded and unbounded (Poincaré domains) domains, both in deterministic and stochastic settings. The existence and uniqueness of weak solution in the deterministic case is proved via a local monotonicity property of the linear and nonlinear operators and a localized version of the Minty-Browder technique. Some results on the exponential stability of stationary solutions are also established. The global solvability results for the stochastic counterpart are obtained by a stochastic generalization of the Minty-Browder technique. The exponential stability results in the mean square as well as in the pathwise (almost sure) sense are also discussed. Using the exponential stability results, we finally prove the existence of a unique invariant measure, which is ergodic and strongly mixing.     

双重伪补代数的假值理想的一点注记

介绍了双重伪补代数的假值理想和假值同余的概念,并刻画了它们的某些性质.特别地,给出了双重伪补代数的假值理想和假值同余的特征表示.     

强向量均衡问题与不动点问题的粘性逼近算法

讨论了强向量均衡问题与非扩张映射不动点问题的公共解.首先,给出了强向量均衡问题的辅助问题,并在适当的条件下,证明了其解的存在性和唯一性结果.然后,利用这些结果,提出了强向量均衡问题与非扩张映射不动点问题公共解的粘性逼近算法,并进一步证明了,在适当的条件下,由该算法产生的迭代序列强收敛于强向量均衡问题和非扩张映射不动点问题的公共解.     

Normal systems over ANR’s, rigid embeddings and nonseparable absorbing sets

Most of results of Bestvina and Mogilski [Characterizing certain incomplete infinite-di-mensional absolute retracts. Michigan Math. J., 33, 291-313 (1986)] on strong Z-sets in ANR's and absorbing sets is generalized to nonseparable case. It is shown that if an ANR X is locally homotopy dense embeddable in infinite-dimensional Hilbert manifolds and w(U ) = w(X ) (where "w"is the topological weight) for each open nonempty subset U of X , then X itself is homotopy dense embeddable in a Hilbert manifold. It is also demonstrated that whenever X is an AR, its weak product W (X, ) = {(x n ) ∞ n=1 ∈ X ω : x n = for almost all n} is homeomorphic to a pre-Hilbert space E with E ～ = ΣE. An intrinsic characterization of manifolds modelled on such pre-Hilbert spaces is given.     

Demonstration of the approximation of eliminating atomic excited populations in an atom-cavity system

Using the master equation approach to a V-type three-level atom inside a high-finesse single-mode cavity in the strong coupling condition,we demonstrate the approximation of eliminating populations of atomic excited states,which is widely used in the field of the atom-cavity systems [Hechenblaikner G,Gangl M,Horak P and Ritsch H 1998 Phys.Rev.A 58 3030];Liu L W,Tan T and Xu Y 2008 J.Mod.Opt.56 968;Cho J,Angelakis D G and Bose S 2008 Phys.Rev.A 78 062338.This is reflected in the deviation of the population δ,of which the value is 10～(-3)～10～(-2).We further find the deviation of the dipole force and demonstrate that the deviation of atomic population will not notably affect the dipole force of the atom in the strong coupling condition.A relevant experimental case is also presented.     

共晶基陶瓷复合材料的强度模型

根据细观结构内界面的强约束特性,通过纤维-基体内界面切应力确定了共晶陶瓷棒体的细观应力场.然后分析了两相界面处位错塞积产生的应力集中,获得基体内的最大应力,当最大拉应力等于基体理论断裂强度时,得到共晶棒体的断裂强度的解析表达式.考虑共晶陶瓷棒体长度和方位的随机性,根据概率理论得到共晶陶瓷基复合材料的宏观强度的理论模型.结果表明复合材料的宏观强度与亚微米纤维的直径和长度、以及亚微米纤维、基体、共晶陶瓷棒体的弹性常数有关.理论与实验结果十分接近,说明文中理论模型是合理的,同时证明了共晶界面对陶瓷复合材料的重要影响.     

两指标B值强鞅空间的强原子分解

定义了两指标B值强鞅空间和强原子,利用Banach空间的光滑性建立了两指标B值强鞅空间s~∑α^p的强原子分解定理,应用强原子分解定理证明了一些两指标B值强鞅不等式.     

用改进的ghost fluid方法模拟强激波与界面的相互作用

为了解决原来的ghost fluid方法在计算强激波和界面相互作用时界面附近出现的速度和压力振荡问题,对原来的ghost fluid方法进行了改进,通过在界面处构造Riemann问题并求出界面的压力和速度,ghost fluid流体的压力和速度分别用界面的压力和速度代替,ghost流体的密度通过熵常数外推得到。改进的ghost fluid保持了原来的ghost fluid的简单性,对一维强激波与气-气、气-液界面的相互作用问题以及射流问题进行了数值计算,得到了分辨率较高的计算结果。     

Teleportation of Unknown Atomic Entangled States Using GHZ Class States

We propose two physical schemes, which can teleport unknown atomic entangled states from user A （Alice） to user B （Bob） via GHZ class states as quantum channel The two schemes are both based on cavity QED techniques. In the two schemes, teleportation and distillation procedures can be realized simultaneously. The second teleportation scheme is more advantageous than the first one.     

Neutrino energy loss by electron capture in magnetic field at the crusts of neutron stars

Based on the p-f shell model,the effect of strong magnetic field on neutrino energy loss rates by electron capture is investigated.The calculations show that the magnetic field has only a slight effect on the neutrino energy loss rates in the range of 108-1013 G on the surfaces of most neutron stars.But for some magnetars,the range of the magnetic field is 1013-1018 G,and the neutrino energy loss rates are greatly reduced,even by more than four orders of magnitude due to the strong magnetic field.