肝脏中生物流体流动的多重介质渗流模型和数值模拟

本文采用生物渗流理论，建立了肝脏内不同生物流体流动的多重介质渗流模型，采用有限元法求解这种特殊的渗流问题，根据数值计算结果揭示了肝内血液、组织液以及胆汁等的流动规律，并探讨了肝脏血流动力学的一些问题。论文将肝脏内部与生物代谢功能有关的肝血窦和窦周间隙当作两重并存的多孔介质，血液在肝血窦中，以及组织液在窦周间隙中的流动均当作渗流处理，通过Starling公式考虑了两重介质之间的流量交换，从而建立了肝血窦-窦周间隙的双重介质模型。针对肝脏胆汁分泌功能，将肝脏内密布的毛血肝管网当作多孔介质，以受静压及渗透压驱动的流体跨壁流动表示肝汁从肝细胞向毛细肝管的分泌，肝汁在毛细胆管网中的流动作为渗流处理，从而建立了肝汁分泌与输运的双重介质模型。采用有限元法求解了生物流体的双重介质渗流问题，针对非牛顿渗流和两重介质的相互作用，本文发展了一种嵌套迭代方法，即采用直接迭代求解血液在肝血窦中的非线性渗流，采用交替迭代解决双重介质渗流中由跨壁流支引起的相互流体交换，直接迭代嵌套于交替迭代中。这种算法比较有效的解决了包含非牛顿渗流的双重介质渗流问题。根据生物多孔介质中微细管系统的构筑方式以及不同微细管系统之间的联系方式，论文提出将生物多孔介质划分为分级多孔介质和多重多孔介质两种主要类型。基于多相混合物的平均化的理论，论文推导了双重多孔介质中的动量守恒方程、质量守恒方程以及相应的渗流方程，建立了双重多孔介质渗流的平均化模型。基于分级多孔介质渗流的理论，论文将脏器中的血管树按管径分为不同级别的多孔介质，各级血管中和血液流动均作为渗流处理，从而提出了计算脏器整体血流的一种渗流方法。采用这种方法，在论文提出的肝血窦 - 窦周间隙双重介质渗流流模型的基础之上，初步研究了肝脏门静脉系统的血液动力学规律。采用本文提出的肝血窦 - 窦周间隙双重介质模型和胆汁分泌 - 流动的双重介质模型，得到了血液、组织液和胆汁在肝小叶中的压力分布和速度分布，并分析了肝血窦壁的跨壁流动模式，胆汁流量的影响因素，以及窦周间隙中组织液流量与肝血窦中血液流动及肝血窦壁渗透系数等因素的关系，揭示了肝脏内血液、组织液及胆汁等生物流体流动的一般规律。

Parameters Inversion of Fluid-Saturated Porous Media Based on Neural Networks

The multi-layers feedforward neural network is used for inversion of material constants of fluid-saturated porous media. The direct analysis of fluid-saturated porous media is carried out with the boundary element method. The dynamic displacement responses obtained from direct analysis for prescribed material parameters constitute the sample sets training neural network. By virtue of the effective L-M training algorithm and the Tikhonov regularization method as well as the GCV method for an appropriate selection of regularization parameter, the inverse mapping from dynamic displacement responses to material constants is performed. Numerical examples demonstrate the validity of the neural network method.

Kramers Escape Rate in Nonlinear Diffusive Media

In this paper, we study nonlinear Kramers problem by investigating overdamped systems ruled by the one-dimensional nonlinear Fokker-Planck equation. We obtain an analytic expression for the Kramers escape rate under quasistationary conditions by employing

State Vector: A New Approach to Prediction of the Failure of Brittle Heterogeneous Media and Large Earthquakes

The concept of state vector stems from statistical physics, where it is usually used to describe activity patterns of a physical field in its manner of coarsegrain. In this paper, we propose an approach by which the state vector was applied to describe quantitatively the damage evolution of the brittle heterogeneous systems, and some interesting results are presented, i.e., prior to the macro-fracture of rock specimens and occurrence of a strong earthquake, evolutions of the four relevant scalars time series derived from the state vectors changed anomalously. As retrospective studies, some prominent large earthquakes occurred in the Chinese Mainland (e.g., the M 7.4 Haicheng earthquake on February 4, 1975, and the M 7.8 Tangshan earthquake on July 28, 1976, etc) were investigated. Results show considerable promise that the time-dependent state vectors could serve as a kind of precursor to predict earthquakes.

Catastrophic Rupture Induced Damage Coalescence in Heterogeneous Brittle Media

In heterogeneous brittle media, the evolution of damage is strongly influenced by the multiscale coupling effect. To better understand this effect, we perform a detailed investigation of the damage evolution, with particular attention focused on the catastrophe transition. We use an adaptive multiscale finite-element model (MFEM) to simulate the damage evolution and the catastrophic failure of heterogeneous brittle media. Both plane stress and plane strain cases are investigated for a heterogeneous medium whose initial shear strength follows the Weibull distribution. Damage is induced through the application of the Coulomb failure criterion to each element, and the element mesh is refined where the failure criterion is met. We found that as damage accumulates, there is a stronger and stronger nonlinear increase in stress and the stress redistribution distance. The coupling of the dynamic stress redistribution and the heterogeneity at different scales result in an inverse cascade of damage cluster size, which represents rapid coalescence of damage at the catastrophe transition.

Long-Range Stress Redistribution Resulting From Damage in Heterogeneous Media

It has been shown in CA simulations and data analysis of earthquakes that declustered or characteristic large earthquakes may occur with long-range stress redistribution. In order to understand long-range stress redistribution, we propose a linear-elastic but heterogeneous-brittle model. The stress redistribution in the heterogeneous-brittle medium implies a longer-range interaction than that in an elastic medium. Therefore, it is surmised that the longer-range stress redistribution resulting from damage in heterogeneous media may be a plausible mechanism governing main shocks.

Adaptive Mesh Refinement FEM for Damage Evolution of Heterogeneous Brittle Media

Damage evolution of heterogeneous brittle media involves a wide range of length scales. The coupling between these length scales underlies the mechanism of damage evolution and rupture. However, few of previous numerical algorithms consider the effects of the trans-scale coupling effectively. In this paper, an adaptive mesh refinement FEM algorithm is developed to simulate this trans-scale coupling. The adaptive serendipity element is implemented in this algorithm, and several special discontinuous base functions are created to avoid the incompatible displacement between the elements. Both the benchmark and a typical numerical example under quasi-static loading are given to justify the effectiveness of this model. The numerical results reproduce a series of characteristics of damage and rupture in heterogeneous brittle media.

Permeability of Fractal Porous Media by Monte Carlo Simulations

The permeability of the fractal porous media is simulated by Monte Carlo technique in this work. Based oil the fractal character of pore size distribution in porous media, the probability models for pore diameter and for permeability are derived. Taking the bi-dispersed fractal porous media as examples, the permeability calculations are performed by the present Monte Carlo method. The results show that the present simulations present a good agreement compared with the existing fractal analytical solution in the general interested porosity range. The proposed simulation method may have the potential in prediction of other transport properties (such as thermal conductivity, dispersion conductivity and electrical conductivity) in fractal porous media, both saturated and unsaturated.

A generalized model for the effective thermal conductivity of porous media based on self-similarity

A generalized model for the effective thermal conductivity of porous media is derived based on the fact that statistical self-similarity exists in porous media. The proposed model assumes that porous media consist of two portions: randomly distributed non-touching particles and self-similarly distributed particles contacting each other with resistance. The latter are simulated by Sierpinski carpets with side length L = 13 and cutout size C = 3, 5, 7 and 9, respectively, depending upon the porosity concerned. Recursive formulae are presented and expressed as a function of porosity, ratio of areas, ratio of component thermal conductivities and contact resistance, and there is no empirical constant and every parameter has a clear physical meaning. The model predictions are compared with the existing experimental data, and good agreement is found in a wide range of porosity of 0.14-0.80, and this verifies the validity of the proposed model.

A geometry model for tortuosity of flow path in porous media

A simple geometry model for tortuosity of flow path in porous media is proposed based on the assumption that some particles in a porous medium are unrestrictedly overlapped and the others are not. The proposed model is expressed as a function of porosity and there is no empirical constant in this model. The model predictions are compared with those from available correlations obtained numerically and experimentally, both of which are in agreement with each other. The present model can also give the tortuosity with a good approximation near the percolation threshold. The validity of the present tortuosity model is thus verified.

Fractal geometry model for effective thermal conductivity of three-phase porous media

An approximate model, a fractal geometry model, for the effective thermal conductivity of three-phase/unsaturated porous media is proposed based on the thermal-electrical analogy technique and on statistical self-similarity of porous media. The proposed thermal conductivity model is expressed as a function of porosity (related to stage n of Sierpinski carpet), ratio of areas, ratio of component thermal conductivities, and saturation. The recursive algorithm for the thermal conductivity by the proposed model is presented and found to be quite simple. The model predictions are compared with the existing measurements. Good agreement is found between the present model predictions and the existing experimental data. This verifies the validity of the proposed model. (C) 2004 American Institute of Physics.

Fractal dimensions for unsaturated porous media

The analytical expressions of the fractal dimensions for wetting and non-wetting phases for unsaturated porous media are derived and are found to be a function of porosity, maximum and minimum pore sizes as well as saturation. There is no empirical constant in the proposed fractal dimensions. It is also found that the fractal dimensions increase with porosity of a medium and are meaningful only in a certain range of saturation S-w, i.e. S-w > S-min for wetting phase and S-w < S-max for non-wetting phase at a given porosity, based on real porous media for requirements from both fractal theory and experimental observations. The present analysis of the fractal dimensions is verified to be consistent with the existing experimental observations and it makes possible to analyze the transport properties such as permeability, thermal dispersion in unsaturated porous media by fractal theory and technique.

Wave propagation and the frequency domain Green's functions in viscoelastic Biot/squirt (BISQ) media

In this paper, we examine the characteristics of elastic wave propagation in viscoelastic porous media, which contain simultaneously both the Biot-flow and the squirt-flow mechanisms (BISQ). The frequency-domain Green's functions for viscoelastic BISQ media are then derived based on the classic potential function methods. Our numerical results show that S-waves are only affected by viscoelasticity, but not by squirt-flows. However, the phase velocity and attenuation of fast P-waves are seriously influenced by both viscoelasticity and squirt-flows; and there exist two peaks in the attenuation-frequency variations of fast P-waves. In the low-frequency range, the squirt-flow characteristic length, not viscoelasticity, affects the phase velocity of slow P-waves, whereas it is opposite in the high-frequency range. As to the contribution of potential functions of two types of compressional waves to the Green's function, the squirt-flow length has a small effect, and the effects of viscoelastic parameter are mainly in the higher frequency range. Crown Copyright (C) 2006 Published by Elsevier Ltd. All rights reserved.

Stress-distribution around a rigid line in dissimilar media

The elastic plane problem of a rigid line inclusion between two dissimilar media was considered. By solving the Riemann-Hilbert problem, the closed-form solution was obtained and the stress distribution around the rigid line was investigated. It was found that the modulus of the singular behavior of the stress remains proportional to the inverse square root of the distance from the rigid line end, but the stresses possess a pronounced oscillatory character as in the case of an interfacial crack tip.