Simulation of bacterial flagellar phase transition by non-convex and non-local continuum modeling

Bacterial flagellar filament can undergo a stress-induced polymorphic phase transition in both vitro and vivo environments. The filament has 12 different helical forms (phases) characterized by different pitch lengths and helix radii. When subjected to the frictional force of flowing fluid, the filament changes between a left-handed normal phase and a right-handed semi-coiled phase via phase nucleation and growth. This paper develops non-local finite element method (FEM) to simulate the phase transition under a displacement-controlled loading condition (controlled helix-twist). The FEM formulation is based on the Ginzburg-Landau theory using a one-dimensional non-convex and non-local continuum model. To describe the processes of the phase nucleation and growth, viscosity-type kinetics is also used. The non-local FEM simulation captures the main features of the phase transition: two-phase coexistence with an interface of finite thickness, phase nucleation and phase growth with interface propagation. The non-local FEM model provides a tool to study the effects of the interfacial energy/thickness and loading conditions on the phase transition.     

MECHANICAL MODELING OF THE BISTABLE BACTERIAL FLAGELLAR FILAMENT

We extend the 2D Landau phase transition theory to the bacterial flagellar filament which displays the phase transition between the left handed normal form and the right handed semi-coiled form. The bacterial flagellar filament is treated as an elastic thin rod based on the Kirchhoff’s thin rod theory. Mechanical analysis is performed on the periodical phase transition of the filament between the two helical structures of the opposite charity. The curvature and twist are chosen as the order parameters in constructing the phase transition model of the filament. The established model is applied to study the instability properties of the filament and to investigate the loading and deformation conditions of the phase transition. In addition, the curvature and twist gradient energy are considered to describe the interface properties of the two phases.     

铈γ→α相变的室温动态特性

通过试样组件尺寸匹配设计的被动围压SHPB实验,获得了99.8%纯铈在1.7GPa静水压内的、包含γ?α相变和逆相变过渡区的室温动态静水压-体应变连续曲线。研究显示:室温铈γ→α相变是具有明显滞后现象的一级相变,而非以往研究认为的体积跃变的一级相变;相变过渡区的静水压范围是0.8~1.3GPa。逆相变过渡区的静水压范围是0.6~1.1GPa;逆相变过渡区的静水压-体应变曲线滞后于相变过渡区的静水压-体应变曲线0.15GPa静水压;在相变和逆相变过渡区内,静水压-体应变曲线按照约4.2GPa体积模量的线性关系演化;演化机制为γ和α两相均匀混合、静水压驱动两相组份转化。基于该演化机制,构建了描述相变前后和相变过程的静水压-体应变响应的三段线性模型。     

Large conversion of energy in dielectric elastomers by electromechanical phase transition

When air is pumped in, a tubular balloon initially inflates slightly and homogeneously. A short section of the balloon then forms a bulge, which coexists with the unbulged section of the balloon. As more air is pumped in, the bulged section elongates at the expense of the unbulged section, until the entire balloon is bulged. The phenomenon is analogous to the liquid-to-vapor phase transition. Here we study the bulging transition in a dielectric elastomer tube as air is pumped into the balloon and a voltage is applied through the thickness of the membrane. We formulate the condition for coexistent budged and unbulged sections, and identify allowable states set by electrical breakdown and mechanical rupture. We find that the bulging transition dramatically amplifies electromechanical energy conversion. Energy converted in an electromechanical cycle consisting of unbulged and bulged states is thousands of times that in an electrome-chanical cycle consisting of only unbulged states.     

A continuum traffic flow model with the consideration of coupling effect for two-lane freeways

A new higher-order continuum model is proposed by considering the coupling and lane changing effects of the vehicles on two adjacent lanes. A stability analysis of the proposed model provides the conditions that ensure its linear stability. Issues related to lane changing, shock waves and rarefaction waves, local clustering and phase transition are also investigated with numerical experiments. The simulation results show that the proposed model is capable of providing explanations to some particular traffic phenomena commonly observable in real traffic flows.     

冲击下宏观相边界的传播

研究了具有CdS型相变本构材料的宏观相边界传播规律。相边界包括纯新相和混合相两段。纯新相段可用逐步近似法,混合相段则必须用数值方法求解。给出了三种加卸载应力边界条件下的算例。在突加突卸的应力边界条件下,给出了相边界传播的解析解。在算例中,各种解法得到的结果彼此很好符合。     

Change in the structure of a polymer solution in a longitudinal hydrodynamic field

There are two qualitatively different conditions for the stretching of liquid fibers formed by moderately concentrated polymer solutions [1]. If the longitudinal gradient of the drawing rate is rather small the structure of the solution remains unchanged. If this gradient exceeds a certain critical value, some of the solvent is expressed from the solution in and the liquid filament is converted into a slightly swollen fiber. The solvent released settles as droplets on the filament surface. This effect is of very great importance for a number of industrial processes pertaining to the production of filaments and films from polymer solutions. In addition, as was reported in [1], the drawing of a liquid filament, accomapnied by orientational formation of the solid phase, can serve as a most simple imitation of the formation of silk and gossamer filaments in nature.This paper presents a qualitative theory for this phenomenon, based on investigation of the thermodynamic stability of a polymer solution in a longitudinal hydrodynamic field.In conclusion the author thanks S. Ya. Frenkel for kindly providing information about the experiments conducted in his laboratory.     

非均匀颗粒材料的类固-液相变行为及本构方程

以非均匀颗粒介质为研究对象，采用三维离散元方法对其在不同密集度和剪切速率下的动 力过程进行了数值模拟，分析了其在由瞬时接触的快速流动向持续接触的准静态流动的转变 过程及其行为特点. 通过对不同材料性质下相变过渡区内颗粒材料的宏观应力、接触时间数、 配位数、团聚颗粒数量、有效摩擦系数等参量的计算，更加全面地描述了非均匀颗粒材料在 类固-液相变过程中的基本特征. 基于以上数值计算结果，建立了一个适用于颗粒材料 类固态、类液态以及其相变过程的本构方程，并通过剪切室实验结果验证了它的合理性.     

Representation of robotic fractional dynamics in the pseudo phase plane

This paper analyses robotic signals in the perspective of fractional dynamics and the pseudo phase plane (PPP).It is shown that the spectra of several experimental signals can be approximated by trend lines whose slope characterizes their fractional behavior.For the PPP reconstruction of each signal,the time lags are calculated through the fractal dimension.Moreover,to obtain a smooth PPP,the noisy signals are filtered through wavelets.The behavior of the spectra reveals a relationship with the fractal dimension of the PPP and the corresponding time delay.     

Combined stress waves with phase transition in thin-walled tubes简

The incremental constitutive relation and governing equations with combined stresses for phase transition wave propagation in a thin-walled tube are established based on the phase transition criterion considering both the hydrostatic pressure and the deviatoric stress. It is found that the centers of the initial and subsequent phase transition ellipses are shifted along the σ-axis in the στ-plane due to the tension-compression asymmetry induced by the hydrostatic pressure. The wave solution offers the "fast" and "slow" phase transition waves under combined longitudinal and torsional stresses in the phase transition region. The results show some new stress paths and wave structures in a thin-walled tube with phase transition, differing from those of conventional elastic-plastic materials.     

Packing induced bistable phenomenon in granular flow:analysis from complex network perspective

The effects of packing configurations on the phase transition of straight granular chute flow with two bottlenecks axe studied. The granular flow shows a dilute- to-dense flow transition when the channel width is varied, accompanied with a peculiar bistable phenomenon. The bistable phenomenon is induced by the initial packing config- uration of particles. When the packing is dense, the initial flux is small and will induce a dense flow. When the packing is loose, the initial flux is large and will induce a di- lute flow. The fabric network of granulax packing is analyzed from a complex network perspective. The degree distribution shows quantitatively different characteristics for the configurations. A two-dimensional （2D） packing clustering coefficient is defined to better quantify the fabric network.     

On hydrodynamic instabilities,chaos and phase transition

Ellipticity as the underlying mechanism for instabilities of physical systems is highlighted in the study of model nonlinear evolution equations with dissipation and the study of phase transition in Van der Waals fluid. Interesting results include spiky solutions, chaotic behavior in the context of partial differential equations, as well as the nucleation process due to ellipticity in phase transition.     

纳米晶钽在单向拉伸载荷下的分子动力学模拟

利用分子动力学方法模拟了纳米晶钽在单轴拉伸载荷作用下的微观结构演化情况. 结果表明纳米晶钽在塑性变形过程中可以发生从BCC到FCC, HCP结构的应力诱导相变. FCC 结构原子百分比的最大值和试样的抗拉强度成线性关系，据此可推出一个相变发生的临界应 力值. 应变率越大，相变滞后于应力越严重. 当应变达到一定值时，试样会发生晶间断裂现 象，定量分析发现纳米晶钽晶间裂纹初始形成应变不受平均晶粒尺寸的影响，而与应变率和 模拟温度有着密切的关系.     

Evolution of a long-wave train in loss of stability of a phase interface in geothermal systems

The transition to instability of phase interfaces in geothermal systems when a water stratum overlies a steam stratum and the most unstable mode corresponds to zero wavenumber is considered. The nonlinear Kolmogorov-Petrovskii-Piskunov equation describing the evolution of a narrow strip of weakly unstable modes is obtained. This equation is an analog of the well-known Ginzburg-Landau equation corresponding to the case of destabilization of modes with finite wavenumbers. It is shown that in the neighborhood of the critical points there exist two locations of the plane phase interface which coincide at the instant at which the instability threshold is reached and then disappear.     

Numerical simulations of a filament in a flowing soap film

Experiments concerning the properties of soap films have recently been carried out and these systems have been proposed as experimental versions of theoretical two‐dimensional liquids. A silk filament introduced into a flowing soap film, was seen to demonstrate various stable modes, and these were, namely, a mode in which the filament oscillates and one in which the filament is stationary and aligns with the flow of the liquid. The system could be forced from the oscillatory mode into the non‐ oscillatory mode by varying the length of the filament. In this article we use numerical and computational techniques in order to simulate the strongly coupled behaviour of the filament and the fluid. Preliminary results are presented for the specific case in which the filament is seen to oscillate continuously for the duration of our simulation. We also find that the filament oscillations are strongly suppressed when we reduce the effective length of the filament. We believe that these results are reminiscent of the different oscillatory and non‐oscillatory modes observed in experiment. The numerical solutions show that, in contrast to experiment, vortices are created at the leading edge of the filament and are preferentially grown in the curvature of the filament and are eventually released from the trailing edge of the filament. In a similar manner to oscillating hydrofoils, it seems that the oscillating filaments are in a minimal energy state, extracting sufficient energy from the fluid to oscillate. In comparing numerical and experimental results it is possible that the soap film does have an effect on the fluid flow especially in the boundary layer where surface tension forces are large. Copyright © 2004 John Wiley & Sons, Ltd.     

Tensile behaviors of pre-twisted composite strands

In this paper, we address the tensile behaviors of pre-twisted composite strands, which consists of a pre-twisted single core filament surrounded by n-helical side filaments. Based on the extensible rod with zero bending and small twisting moduli for the core filament and inextensible rod for the side filaments, we develop the analytical method of the tensile behaviors of pre-twisted composite strands. Using a numerical continuation scheme, we elucidate the effects of microscopic factors such as initial helical angle, pre-twist of core filament, ratio of elastic modulus of core to that of side filament, and the number of the side filaments on the macroscopic tensile behavior of the strand as a whole structure. As a result, we show that the behavior is not trivial, even though the filament is a linear elastic due to the interplay of both geometrical constraint and finite deformation of the strand.     

基于分子动力学模拟的单晶硅冲击压缩相变研究

晶体硅具有复杂的相变机制,在相图研究中受到广泛关注,其在动载荷下的变形机制是当前研究热点。为揭示晶体硅在强动加载下的变形和相变行为特征,基于分子动力学方法,采用平板冲击加载方式,模拟研究了单晶硅在初始环境温度为300 K时分别沿[001]、[110]和[111]晶向的不同强度下的冲击压缩行为,冲击粒子速度为0.3～3.2 km/s。研究发现,随着冲击粒子速度的增加,单晶硅剪切应力在逐渐增加后由于结构相变发生急剧下降,相变阈值和相变机制均呈现各向异性。其中,沿[001]晶向冲击压缩下观察到多种固-固相变以及固-液相变,并观察到与最新文献的实验高度一致的固-液共存现象。研究结果可为动加载下晶体硅的相变研究提供纳米尺度的结果支撑。     

Computational and theoretical modeling of intermediate filament networks: Structure, mechanics and disease

Intermediate filaments,in addition to microtubules and actin microfilaments,are one of the three major components of the cytoskeleton in eukaryotic cells.It was discovered during the recent decades that in most cells,intermediate filament proteins play key roles to reinforce cells subjected to large-deformation,and that they participate in signal transduction,and it was proposed that their nanomechanical properties are critical to perform those functions.However,it is still poorly understood how the nanoscopic structure,as well as the combination of chemical composition,molecular structure and interfacial properties of these protein molecules contribute to the biomechanical properties of filaments and filament networks.Here we review recent progress in computational and theoretical studies of the intermediate filaments network at various levels in the protein’s structure.A multiple scale method is discussed,used to couple molecular modeling with atomistic detail to larger-scale material properties of the networked material.It is shown that a finer-trains-coarser methodology as discussed here provides a useful tool in understanding the biomechanical property and disease mechanism of intermediate filaments,coupling experiment and simulation.It further allows us to improve the understandingof associated disease mechanisms and lays the foundation for engineering the mechanical properties of biomaterials.     

颗粒材料剪切流动状态转变的环剪试验研究

颗粒材料的剪切流动行为广泛地存在于滑坡、泥石流等自然灾害以及矿物原料传输、泵送等工业过程中.颗粒材料在不同体积分数、剪切速率和应力约束下会表现出不同的流动状态并发生相互转化.对颗粒材料在剪切流动过程中力学特性的研究有助于加深理解其发生不同流动状态的内在机理,为解决相应的颗粒材料问题提供理论依据.为此,本文研制了颗粒材料剪切流动的中型环剪仪,并对颗粒材料在不同法向约束应力和剪切速率下的剪切应力和体积膨胀率进行了测试.结果表明,剪切应力和体积膨胀率均随剪切速率的增大而增大,但增长速率在临界剪切速率处发生转变,使其随剪切速率的平方呈分段式线性增长.通过对颗粒材料在不同剪切速率和惯性数下有效摩擦系数变化趋势的分析,讨论了颗粒材料由慢速流向快速流转化的基本规律,以及在临界剪切速率处发生流动状态转化的内在条件.此外,通过对不同法向应力下临界剪切速率以及快速流动下运动规律的测试,发现临界剪切速率随法向应力的增加而减小,即法向应力可促进颗粒材料由慢速流向快速流的转化,但在快速流动状态下的有效摩擦系数对法向应力不敏感.以上对颗粒材料在不同剪切速率、法向应力下流动状态的环剪试验研究有助于揭示其发生不同流动状态转化的内在机理.      

马氏体相变过程中形核、失稳及多界面微结构的动力学模拟

材料发生相变的过程中会出现失稳、滞后回线及多界面的微结构等复杂现象，而稳定性的丧失使其动力学方程的求解十分困难。对于形状记忆合金中的马氏体相变，相变过程中材料的等效杨氏模量变为负值，使得传统的动力学方程成为病态的，无法直接求解，必须要进行正则化。而相变的滞后回线与微结构的出现也说明经典的弹性理论不再适用，必须要引入新的能量项以能刻画这些现象。本文在非线性弹性理论的框架下，引入应变梯度界面能和位移非均匀能，利用变分原理建立了材料相变的一维动力学模型。高阶项的引入极大地改善了方程的性质，使数值求解成为可能。计算结果表明，该模型确能较有效地描述相变时的失稳与微结构。