三类白细胞核孔筛滤试验的双参数模型

白细胞核孔筛滤试验是估计白细胞变形性的主要方法之一．我们对这一试验的三类情形提出了生物流体力学模型，这三类情形是：（i）自身重力过滤；（ii）恒压过滤；（iii）恒流量过滤．在以前的模型中，细胞阻力被假定为一常数，而在本文中，我们考虑细胞阻力时，同时顾及了驱动压力和白细胞个体变形性差异的影响．而且，我们在Moessmer实验基础上，对多形核粒性白细胞通过核孔的时间假定了一个概率分布函数．最后我们得到了以上三种情形的数值解，第一种情形的解与实验结果的对比是令人满意的．文中的双参数，A和B，代表了不同压力下白细胞变形性的不同．     

一种未血管化肿瘤生长模型整体解的证明

研究了一种未血管化肿瘤生长模型的自由边界问题,模型与此类其它模型有着明显的不同,它引入新的运动项来描述肿瘤内细胞的运动,反映了肿瘤内细胞运动的"接触抑制"性质.运用Banach不动点理论和抛物型方程的L~P理论,证明了模型存在唯一整体解.     

扁球旋转大气阻力对人造卫星运动的影响

描述了在地球扁率和大气阻力联合作用的人造卫星运动。导出了系统的哈密顿运动方程，其中包括括直到J4的重力热带调和函数的阻力加速度。大气模型采用带扁椭球旋转模型，随着离地距离的增加，大气旋转滞后于地球旋转，首先，借助两次正则变换，接连消去短期项和长期项求得无阻力问题的解，然后再定义一个算子，并利用无阻力问题中带“两撇形式的变量”，给出求解阻力速度的公式。     

基于弹性壳的三维群体细胞动力学模型

群体细胞迁移常见于胚胎发育、伤口愈合和肿瘤侵袭等各种生理和病理过程中,关于其动力学的研究对于揭示群体细胞迁移机理、深刻理解有关生物过程十分重要.该文构建了群体细胞的三维可变形壳状模型,提出了一种考虑细胞弹性形变和细胞间接触与黏附相互作用的群体细胞动力学理论,并发展了相应的数值算法.基于所发展的动力学模型与算法,对多细胞在嚢腔里的受限旋转运动进行了模拟,复现了相关实验现象,分析了细胞极性、细胞形变、胞间相互作用等因素对多细胞三维动力学的影响规律.     

悬移质与推移质分层管流的阻力特性

本文着重探讨管道中悬移质与推移质分层流动的阻力特性.文中提出,粗颗粒、高浓度的两相流动中,颗粒间的碰撞力对颗粒的悬浮和运动起着重要的作用.在这个理论基础上,导出了阻力系数公式,并得到验证.试验证明,扩散理论不足以描述这类流动.粗颗粒的悬浮运动是否增耗水流的能量,主要取决于碰撞力与紊动力之间的对比消长.在高浓度情况下,粗颗粒悬移质明显地增大了水流的能量损失.推移质的存在将使两相流动的阻力损失显著增大,其增阻率与水流条件及颗粒特性之间存在有一定的函数关系.     

弹性膜对部分充液罐车内液体晃动的抑制效果研究

为了提高液罐车的制动性能和侧倾稳定性极限,建立了流固耦合模型,研究了弹性膜对部分充液罐车内液体晃荡的抑制效果.进行了实验室实验,实验结果验证了数值模型的有效性.验证后的模型被进一步用于研究不同的弹性膜配置对晃荡响应的影响,如液体载荷传递、晃荡力、俯仰力矩和罐壁压强.研究中考虑了两种不同的储罐配置,即没有任何阻尼装置的储罐和具有各种弹性膜组合的储罐,以进行比较.结果表明,添加弹性膜可以显著限制液体的运动,从而显著降低由晃动引起的俯仰力矩,这将提高罐车的制动性能和侧倾稳定性极限.     

浅孔爆破在沿空留巷切顶卸压中的应用研究

分析了浅孔爆破岩体裂隙分布和厚层坚硬顶板破断规律,提出采用浅孔爆破切顶卸压技术与充填体相结合的留巷方式,建立充填体切顶卸压力学模型,研究表明:相邻炮孔爆炸时,裂隙区相互贯通,留巷顶板强度降低,改善了沿空留巷顶板结构和应力环境,降低了充填体切顶阻力和宽度.以某煤矿11304工作面厚坚硬顶板沿空留巷试验工程为背景,利用LS-DYNA数值模拟,最终确定炮孔孔深3200mm、孔径42 mm、间距850 mm,充填体强度为6.5 MPa,留巷巷内顶板保持完整,巷旁充填体维护效果良好.     

水滴撞击倾斜非Newton除冰液液膜动力学行为特性数值研究

为了探究降雨天气下水滴撞击除冰液液膜后引发的非Newton动力学行为,耦合相界面控制方程及组分输运方程,构建了多相、多组分、多体系耦合作用的液滴撞击非Newton液膜的动力学行为模型.开展了水滴撞击除冰液液膜非稳态演化行为特性数值研究,以实验结果验证并修正了模型.此外,进一步分析了除冰液的剪切稀化特性和斜面坡度对撞击过程的影响机制.研究结果表明：液滴撞击倾斜液膜后会产生非对称的液冠,而除冰液非Newton特性引发的黏度差异进一步导致撞击后的非对称运动;在液冠的形成过程中,除冰液被带离液膜,与水分的稀释效应共同降低了液膜的黏度;坡度的增加限制了水滴在液膜上游的作用范围,促进了下游液冠的生长进而加快了除冰液的脱离,因此液膜在下游的黏度显著降低.     

多层簿膜厚度XQMA测定及Monte Carlo计算方法

本文提出了应用X射线显微分析实验及Monte Carlo模拟计算电子散射、X射线激发来确定多层薄膜样品每一层厚度的方法.在几种加速电压下,对不同组成、不同厚度的多层膜进行了测定,所得结果与核背散法测定值一致.相对误差小于10％.文中给出了计算程序流程图.     

泥浆的力学性质和砂粒在泥浆中运动时所受的阻力

一般认为泥浆在运动时候,它的力学性质已经有别于通常的牛顿流体而是宾汉体了.因此剪应力应该用宾汉体的剪应力关系式.本文作者则持另外一种见解.认为泥浆是一种接近于沥青一类的粘性极大,弛豫时间极长的流体.本文讨论了泥浆的力学性质,并且进一步讨论了圆球在泥浆中作匀速直线运动时所受到的阻力.在讨论过程中,我们利用了人们熟知的粘性流体绕圆球运动的Stokes解,得到了一个简单的阻力公式.当圆球在重力和浮力作用下在泥浆中作沉淀运动时候,我们求出了沉降速度.在沉降速度为零时候,我们就可以求出"不沉粒径"和"宾汉体极限剪应力"的关系.我们把计算结果得到的理论公式和陕西水科所及黄委会水科所等单位的实验数据[1][2]进行了比较,结果是令人满意的.     

A DLM/FD/IB Method for Simulating Compound Cell Interacting with Red Blood Cells in a Microchannel

In this article, a computational model and related methodologies have been tested for simulating the motion of a malaria infected red blood cell (iRBC for short) in Poiseuille flow at low Reynolds numbers. Besides the deformability of the red blood cell membrane, the migration of a neutrally buoyant particle (used to model the malaria parasite inside the membrane) is another factor to determine the iRBC motion. Typically an iRBC oscillates in a Poiseuille flow due to the competition between these two factors. The interaction of an iRBC and several RBCs in a narrow channel shows that, at lower flow speed, the iRBC can be easily pushed toward the wall and stay there to block the channel. But, at higher flow speed, RBCs and iRBC stay in the central region of the channel since their migrations are dominated by the motion of the RBC membrane.     

Two-fluid Casson model for pulsatile blood flow through stenosed arteries: A theoretical model

Pulsatile flow of blood through mild stenosed narrow arteries is analyzed by treating the blood in the core region as a Casson fluid and the plasma in the peripheral layer as a Newtonian fluid. Perturbation method is used to solve the coupled implicit system of non-linear differential equations. The expressions for velocity, wall shear stress, plug core radius, flow rate and resistance to flow are obtained. The effects of pulsatility, stenosis, peripheral layer and non-Newtonian behavior of blood on these flow quantities are discussed. It is found that the pressure drop, plug core radius, wall shear stress and resistance to flow increase with the increase of the yield stress or stenosis size while all other parameters held constant. The percentage of increase in the resistance to flow over the uniform diameter tube is considerably very low for the present two-fluid model compared with those of the single-fluid model.     

On a model of a flexural prestressed shell

E. Sanchez‐Palencia We derive a linearized prestressed elastic shell model from a nonlinear Kirchhoff model of elastic plates. The model is given in terms of displacement and micro‐rotation of the cross‐sections. In addition to the standard membrane, transverse shear, and flexural terms, the model also contains a nonstandard prestress term. The prestress is of the same order as flexural effects; hence, the model is appropriate when flexural effects dominate over membrane ones. We prove the existence and uniqueness of the solutions by Lax–Milgram theorem and compare solution with the solution of the standard shell model via numerical examples. Copyright © 2015 John Wiley & Sons, Ltd.     

Large strain constitutive modelling of cellulose aerogels

In this contribution, we propose a non-linear constitutive model for cellulose aerogels subject to compression. The model is based on the cellular microstructure of aerogels formed of square shaped unit cells of varying pore sizes with an isotropic spatial distribution. Under uniaxial compression, these cells tend to bend non-linearly until pore collapse. This cell bending is described by the extended version of the Euler-Bernoulli beam theory for large deflections. The macroscopic free energy of the whole network is obtained by integration of the microscopic energies of cells over all spatial directions. Cellulose aerogels with different cellulose content are simulated using the proposed model. The model predictions show good agreement with experimental data. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On noise modeling in a nerve fibre

We present a novel mathematical approach to model noise in dynamical systems. We do so by considering the dynamics of a chain of diffusively coupled Nagumo cells affected by noise. We show that the noise in a variable representing the transmembrane current can be effectively modeled as fluctuations in the model parameters corresponding to electric resistance and capacitance of the membrane. These fluctuations may account for the interactions between the membrane and the surrounding (physiological) solution as well as for the thermal effects. The proposed approach to model noise in a nerve fibre is an alternative to the standard technique based on the consideration of additive stochastic current perturbation (the Langevin type equations) and differs from it in important mathematical aspects, particularly, it points out to the non-Markov dynamics of transmembrane potential. Our scheme relates to a time scale which is shorter than the relaxation times of involved physiological processes.     

Numerical Simulation of Red Blood Cell Suspensions Behind a Moving Interface in a Capillary

Computational modeling and simulation are presented on the motion of red blood cells behind a moving interface in a capillary. The methodology is based on an immersed boundary method and the skeleton structure of the red blood cell (RBC) membrane is modeled as a spring network. As by the nature of the problem, the computational domain is moving with either a designated RBC or an interface in an infinitely long two-dimensional channel with an undisturbed flow field in front of the computational domain. The tanking-treading and the inclination angle of a cell in a simple shear flow are briefly discussed for the validation purpose. We then present and discuss the results of the motion of red blood cells behind a moving interface in a capillary, which show that the RBCs with higher velocity than the interface speed form a concentrated slug behind the moving interface.     

A DLM/FD/IB Method for Simulating Cell/Cell and Cell/Particle Interaction in Microchannels

A spring model is used to simulate the skeleton structure of the red blood cell （RBC） membrane and to study the red blood cell （RBC） rheology in Poiseuille flow with an immersed boundary method. The lateral migration properties of many cells in Poiseuille flow have been investigated. The authors also combine the above methodology with a distributed Lagrange multiplier/fictitious domain method to simulate the interaction of cells and neutrally buoyant particles in a microchannel for studying the margination of particles.     

The optimal periodic motions of a two-mass system in a resistant medium

The rectilinear motions of a two-mass system, consisting of a container and an internal mass, in a medium with resistance, are considered. The displacement of the system as a whole occurs due to periodic motion of the internal mass with respect to the container. The optimal periodic motions of the system, corresponding to the greatest velocity of displacement of the system as a whole, averaged over a period, are constructed and investigated using a simple mechanical model. Different laws of resistance of the medium, including linear and quadratic resistance, isotropic and anisotropic, and also a resistance in the form of dry-friction forces obeying Coulomb's law, are considered.     

The effects of post-stenotic dilatations on the flow of a blood analogue through stenosed coronary arteries

Previous work on the resistance to flow ratio and wall shear ratio of non-Newtonian blood flow through arteries containing aneurisms and stenoses has considered only Power Law and Casson models of fluid behaviour. Here a Bingham fluid is used to model blood. Flow through both constrictions and dilatations is considered. The effects of both a single diseased portion and pairs of abnormal wall segments in close proximity to each other are investigated. Comparison is made with earlier studies. Particular attention is paid to the effects of a post-stenotic dilatation as the ameorlation of the increase in resistance to flow ratio caused by such a situation is clinically relevant.     

Effects of stenosis on arterial rheology through a mathematical model

The paper presents an analytical study of blood flow through a stenosed artery using a suitable mathematical model. The artery is modelled as an anisotropic viscoelastic cylindrical tube containing a non-Newtonian viscous incompressible fluid representing blood. The blood flow is assumed to be characterized by the Herschel–Bulkley model. The effect of the surrounding connective tissues on the motion of the arterial wall has been incorporated. Initially, the relevant solutions of the boundary value problem are obtained in the Laplace transform space, through the use of a suitable finite difference technique. Laplace inversion is carried out by employing suitable numerical techniques. Finally, the variations of the vascular wall displacements, the velocity distribution of the blood flow, the flux, the resistance to flow and the wall shear stress in the stenotic region are quantified through numerical computations and presented graphically.