Doubly nonlinear parabolic-type equations as dynamical systems

In this paper, we study a class of doubly nonlinear parabolic PDEs, where, in addition to some weak nonlinearities, also some mild nonlinearities of porous media type are allowed inside the time derivative. In order to formulate the equations as dynamical systems, some existence and uniqueness results are proved. Then the existence of a compact attractor is shown for a class of nonlinear PDEs that include doubly nonlinear porous medium-type equations. Under stronger smoothness assumptions on the nonlinearities, the finiteness of the fractal dimension of the attractor is also obtained.     

Mathematical modelling of flow through consolidated isotropic porous media

A new mathematical model is proposed for time-independent laminar flow through a rigid isotropic and consolidated porous medium of spatially varying porosity. The model is based upon volumetric averaging concepts. Explicit assumptions regarding the mean geometric properties of the porous microstructure lead to a relationship between tortuosity and porosity. Microscopic inertial effects are introduced through consideration of flow development within the pores. A momentum transport equation is derived in terms of the fluid properties, the porous medium porosity and a characteristic length of the microstructure. In the limiting cases of porosity unity and zero, the model yields the required Navier-Stokes equation for free flow and no flow in a solid, respectively.     

横观各向同性三维热弹性力学通解及其势理论法

通过引入两个位移函数，对用位移表达的运动平衡方程作了简化．利用算子理论，严格地导出了横观各向同性非耦合热弹性动力学问题的通解．对于静力学问题，通解的形式可进一步简化成用4个准调和函数来表示．具体考察了横观各向同性体内平面裂纹上下表面有对称分布温度作用的问题，推广了势理论方法，导出了一个积分方程和一个微分-积分方程．针对币状裂纹表面受均布温度作用情形，给出了具体的解。     

水相中RuCl2(TPPTS)2-(S,S)-DPENDS催化苄叉丙酮的不对称加氢反应

 将水溶性手性二胺 (S,S)-1,2-二苯基乙二胺二磺酸钠 ((S,S)-DPENDS) 与钌膦配合物 ([RuCl2(TPPTS)2]2) 原位生成的催化剂用于催化水相中苄叉丙酮的不对称加氢反应. 在优化条件下, 羰基加氢产物 4-苯基-3-丁烯-2-醇的选择性可达 96.0%, 对映选择性可达 71.2%. 经正己烷简单萃取后即可实现催化剂与加氢产物的分离, 循环使用 5 次后, 目标产物 4-苯基-3-丁烯-2-醇选择性和对映选择性没有明显下降.     

Two analytic methods applied to radiative transfer in the linear-anisotropic scattering medium with graded index and diffuse gray boundaries

The curved ray-tracing method is extended to radiative transfer in the graded index medium with diffuse gray boundary conditions instead of black boundary conditions and the pseudo-source adding method is extended to the case of the linear-anisotropic scattering medium with graded index from non-scattering medium. Furthermore, the equivalence of the two methods is verified by formulation derivation. As exact analytical solutions, both the methods have high accuracy and fast computational speed. The predicted temperature distributions and dimensionless radiative heat flux at radiative equilibrium are determined by the proposed methods, and the numerical results are compared with the data in references. The results show that the present methods have a good accuracy. Influences of various combinations of refractive index and boundary emissivities on the temperature distributions and dimensionless radiative heat flux are also investigated.     

Curved ray tracing method for one-dimensional radiative transfer in the linear-anisotropic scattering medium with graded index

The curved ray tracing method (CRT) is extended to radiative transfer in the linear-anisotropic scattering medium with graded index from non-scattering medium. In this paper, the CRT is presented to solve one-dimensional radiative transfer in the linear-anisotropic scattering gray medium with a linear refractive index and two black boundaries. The predicted temperature distributions and radiative heat flux at radiative equilibrium are determined by the proposed method, and numerical results are compared with the data in references. The results show that the CRT has a good accuracy for radiative transfer in the linear-anisotropic scattering medium with graded index and the dimensionless emissive power and dimensionless radiative heat flux depend on the dimensionless refractive index gradient. It can also be seen that the dimensionless refractive index gradient has important effects on the temperature discontinuity at the boundaries.     

Temporal characteristics of few-cycle pulse on- and non-resonance propagating in a ladder-type atomic medium

Time evolution characteristic of few-cycle pulse propagating in a ladder-type atomic medium is investigated. It is shown that, time evolution of few-cycle pulse has significant difference in the both cases on- and non-resonance. In the non-resonant case, if the pulse central frequency is twice as large as medium atomic transition frequency, the pulse form (including carry-envelope phase, pulse duration, oscillation amplitude and frequency) remains unchanging or remains unchanging basically (only carry-envelope phase has some variation) in the propagation process, which means that self-induced transparency (SIT) or approximate transparency phenomenon appears. However, in the resonant case, the pulse form changes obviously in the propagation process. In addition, there is evident difference in the propagating velocity for on- and non-resonance when the pulse area is smaller.     

一阶速度-应力Biot双相各向同性介质弹性波

提出一种等价的一阶双曲型速度一应力Biot双相各向同性介质弹性波波动方程,以实现双相介质混合波场中纯快慢纵波和纯横波波场分离的问题.应用散度和旋度理论证明双相介质等价方程波场分离的可行性,采用高阶交错网格有限差分法构建高精度正演算子,推导其PML吸收边界条件和稳定性条件,并对均匀双相介质和层状非均匀双相介质模型进行数值...     

热管冰蓄冷结构设计

从技术角度研究和探讨了热管做为冰蓄冷装置的适用性;对各种热管用金属管材与工质的特性进行了科学比较;从而最终确定了适宜冰蓄冷工作的热管管材、热管工质及其基本尺寸;为热管冰蓄冷装置的深入研究及推广应用,提供了强有力的理论依据。     

胶体铁磁流体的光子特性研究

这篇综述回顾了我们今年来在铁磁流体方面的一些研究工作。铁磁流体是一种纳米磁颗粒或亚铁磁颗粒悬浮在基液（如：水或煤油）中形成的悬浮液。铁磁流体之所以受到广泛关注,是因为它们在许多方面都有着潜在应用,例如在机械工程和生物医学等领域。再次综述中,我们首先介绍了铁磁流体的场感应各向异性结构,然后,介绍了几种铁磁流体基软物质材料的光学性质,即：光学负折射、磁控光子待隙和非线性光学响应。我们采用的研究方法主要是分子动力学模拟,有效煤质近似和有限元模拟.