Some open problems in granular matter mechanics

Granular matter is a large assemblage of solid particles, which is fundamentally different from any other type of matters, such as solid and liquid. Most models presented for granular matter are phenomenological and are only suitable for solving engineering problems. Many fundamental mechanical problems remain open. By analyzing characteristics of internal state structure, we propose that granular matter is intrinsically multiscale, i.e. microscale of particle size, mesoscale of force chain, and macroscale of the bulk of granular matter. The correlations among difference scales would be crucial. The mesoscale force chain network is determined by both particle properties and macroscopic boundary conditions. The evolution of the force the chain network contributes to macroscopic mechanical properties of granular matter. In addition, we discuss the drawbacks in simplifying contact forces in the current models, and the difficulties in analyzing the interaction of interstitial fluid in wet granular matter. As an appropriate application of granular matter, debris flow can be studied with granular matter mechanics; meanwhile, debris flow brings more challenges which certainly motivate future studies on granular matter.     

Reversible stress softening of actin networks

The mechanical properties of cells play an essential role in numerous physiological processes. Organized networks of semiflexible actin filaments determine cell stiffness and transmit force during mechanotransduction, cytokinesis, cell motility and other cellular shape changes. Although numerous actin-binding proteins have been identified that organize networks, the mechanical properties of actin networks with physiological architectures and concentrations have been difficult to measure quantitatively. Studies of mechanical properties in vitro have found that crosslinked networks of actin filaments formed in solution exhibit stress stiffening arising from the entropic elasticity of individual filaments or crosslinkers resisting extension. Here we report reversible stress-softening behaviour in actin networks reconstituted in vitro that suggests a critical role for filaments resisting compression. Using a modified atomic force microscope to probe dendritic actin networks (like those formed in the lamellipodia of motile cells), we observe stress stiffening followed by a regime of reversible stress softening at higher loads. This softening behaviour can be explained by elastic buckling of individual filaments under compression that avoids catastrophic fracture of the network. The observation of both stress stiffening and softening suggests a complex interplay between entropic and enthalpic elasticity in determining the mechanical properties of actin networks.     

Contact force measurements and stress-induced anisotropy in granular materials

Interparticle forces in granular media form an inhomogeneous distribution of filamentary force chains. Understanding such forces and their spatial correlations, specifically in response to forces at the system boundaries, represents a fundamental goal of granular mechanics. The problem is of relevance to civil engineering, geophysics and physics, being important for the understanding of jamming, shear-induced yielding and mechanical response. Here we report measurements of the normal and tangential grain-scale forces inside a two-dimensional system of photoelastic disks that are subject to pure shear and isotropic compression. Various statistical measures show the underlying differences between these two stress states. These differences appear in the distributions of normal forces (which are more rounded for compression than shear), although not in the distributions of tangential forces (which are exponential in both cases). Sheared systems show anisotropy in the distributions of both the contact network and the contact forces. Anisotropy also occurs in the spatial correlations of forces, which provide a quantitative replacement for the idea of force chains. Sheared systems have long-range correlations in the direction of force chains, whereas isotropically compressed systems have short-range correlations regardless of the direction.     

Resemblance of actin-binding protein/actin gels to covalently crosslinked networks

The maintainance of the shape of cells is often due to their surface elasticity, which arises mainly from an actin-rich cytoplasmic cortex. On locomotion, phagocytosis or fission, however, these cells become partially fluid-like. The finding of proteins that can bind to actin and control the assembly of, or crosslink, actin filaments, and of intracellular messages that regulate the activities of some of these actin-binding proteins, indicates that such 'gel-sol' transformations result from the rearrangement of cortical actin-rich networks. Alternatively, on the basis of a study of the mechanical properties of mixtures of actin filaments and an Acanthamoeba actin-binding protein, alpha-actinin, it has been proposed that these transformations can be accounted for by rapid exchange of crosslinks between actin filaments: the cortical network would be solid when the deformation rate is greater than the rate of crosslink exchange, but would deform or 'creep' when deformation is slow enough to permit crosslinker molecules to rearrange. Here we report, however, that mixtures of actin filaments and actin-binding protein (ABP), an actin crosslinking protein of many higher eukaryotes, form gels rheologically equivalent to covalently crosslinked networks. These gels do not creep in response to applied stress on a time scale compatible with most cell-surface movements. These findings support a more complex and controlled mechanism underlying the dynamic mechanical properties of cortical cytoplasm, and can explain why cells do not collapse under the constant shear forces that often exist in tissues.     

广义相变原理及其临界理论

广义相变是指物质系统由一定套向一定态的跃迁过程,包括平衡态相变,非平衡相变,以及介于这两者之间的相变。本文介绍了作者近年来在非平衡相变与平衡相变临界标度关系方面的一些研究结果,对平衡相变的临界标度理论进行了推广,提出了一个更为普适的议相变临界标度理论,     

Universal scaling relations in food webs

The structure of ecological communities is usually represented by food webs. In these webs, we describe species by means of vertices connected by links representing the predations. We can therefore study different webs by considering the shape (topology) of these networks. Comparing food webs by searching for regularities is of fundamental importance, because universal patterns would reveal common principles underlying the organization of different ecosystems. However, features observed in small food webs are different from those found in large ones. Furthermore, food webs (except in isolated cases) do not share general features with other types of network (including the Internet, the World Wide Web and biological webs). These features are a small-world character and a scale-free (power-law) distribution of the degree (the number of links per vertex). Here we propose to describe food webs as transportation networks by extending to them the concept of allometric scaling (how branching properties change with network size). We then decompose food webs in spanning trees and loop-forming links. We show that, whereas the number of loops varies significantly across real webs, spanning trees are characterized by universal scaling relations.     

Hidden complexity in the mechanical properties of titin

Individual molecules of the giant protein titin span the A-bands and I-bands that make up striated muscle. The I-band region of titin is responsible for passive elasticity in such muscle, and contains tandem arrays of immunoglobulin domains. One such domain (I27) has been investigated extensively, using dynamic force spectroscopy and simulation. However, the relevance of these studies to the behaviour of the protein under physiological conditions was not established. Force studies reveal a lengthening of I27 without complete unfolding, forming a stable intermediate that has been suggested to be an important component of titin elasticity. To develop a more complete picture of the forced unfolding pathway, we use mutant titins--certain mutations allow the role of the partly unfolded intermediate to be investigated in more depth. Here we show that, under physiological forces, the partly unfolded intermediate does not contribute to mechanical strength. We also propose a unified forced unfolding model of all I27 analogues studied, and conclude that I27 can withstand higher forces in muscle than was predicted previously.     

Sierpinski镂垫上Gauss模型的普适性

应用实空间重整化群变换的方法，研究了标度系数l=3的Sierpinski镂垫上Gauss模型的相变和临界性质，求出了系统的临界点和临界指数．结果表明，l=2和l=3的Sierpinski镂垫上的Gauss系统属于不同的普适类．说明其普适性除了决定于系统的空间维数外，还与分形维数有关．     

Sound scattering in dense granular media

The sound propagation in a dense granular medium is basically characterized by the ratio of wavelength to the grain size. Two types of wave transport are distinguished： one corresponds to coherent waves in the long wavelength limit, the other to short-wavelength scattered waves by the inhomogeneous contact force networks. These multiply scattered elastic waves are shown to exhibit a diffusive characteristics of transport over long distances of propagation. Determination of the transport mean free path l^＊ and the inelastic absorption （Q^-1） allows the inference of the structural properties of the material such as the heterogeneity and internal dissipation. The relevance of our experiments for seismological applications is discussed. Moreover, we apply the correlation technique of the configuration-specific sound scattering to monitoring the dynamic behaviour of the granular medium （irreversible rearrangements） under strong vibration, shearing and thermal cycling, respectively.     

Friction enhances elasticity in granular solids

For years, engineers have used elastic and plastic models to describe the properties of granular solids, such as sand piles and grains in silos. However, there are theoretical and experimental results that challenge this approach. Specifically, it has been claimed that stress in granular solids propagates in a manner described by wave-like (hyperbolic) equations, rather than the elliptic equations of static elasticity. Here we report numerical simulations of the response of a two-dimensional granular slab to an external load, revealing that both approaches are valid--albeit on different length scales. For small systems that can be considered mesoscopic on the scale of the grains, a hyperbolic-like, strongly anisotropic response is expected. However, in large systems (those typically considered by engineers), the response is closer to that predicted by traditional isotropic elasticity models. Static friction, often ignored in simple models, plays a key role: it increases the elastic range and renders the response more isotropic, even beyond this range.     

尾矿坝变形细观力学机理的颗粒流数值模拟

以新建四川省盐源县平川铁矿黄草坪尾矿库为工程背景,通过堆坝模型试验与室内土工试验,获得尾矿坝干滩面几何特征、颗粒分布规律及尾矿力学性质。基于离散元理论,采用PFC2D数值模拟软件进行双轴试验,与土工试验结果对比,得到尾矿细观力学参数,并分析尾矿坝颗粒接触力分布、颗粒位移与坝体结构变形特征。结果显示:1)初期坝中颗粒间接触力较大,形成的力链大致呈45°倾斜向上;坝体尾矿颗粒接触力随着埋深的增加而增大,在基岩凸起处接触力较大且集中。2)初期坝颗粒位移不明显,堆积坝少数尾矿颗粒沿坡面向下滚动,具有较大位移;尾矿堆积坝存在较为典型的滑移面,滑移面上部区域颗粒位移较大。3)初期坝结构变化不明显,尾矿堆积坝中靠近初期坝内坡面附近结构变形显著。     

混合颗粒体光弹力链定量提取方法

岩土工程和采矿工程涉及大量的颗粒物质科学和技术难题,定量识别和提取光弹试验颗粒体系的力链网络结构和分布特征,对于认识和掌握其内部细观力学机理和研究宏观力学行为至关重要.采用彩色梯度均方值(G2)算法,建立了不同粒径的圆形颗粒和方形颗粒的接触力(F)和G2的关系;基于数字图像处理技术,提出了识别和区分图像中不同粒径圆形颗粒和方形颗粒的方法,获得了光弹图片中力链网络结构和力链分布方位.以煤矿综放开采为实例,对所提出的力链定量提取方法进行了验证分析,清晰揭示了综放采面矿压形成机理和本质特征.研究表明:单颗粒的F值与G2呈单调递增关系,且粒径越大,F随G2值的增长速度越快;颗粒体系接触力集中分布在0.5F~F(F为平均接触力),方颗粒、φ12 mm圆形颗粒平均接触力较大,多为强力链;φ10 mm、φ8 mm圆形颗粒的平均接触力较小,多为弱力链.综放开采顶煤和覆岩中力链主要为树状力链,以竖向发育为主的强力链传递上部主要荷载,横向发育的弱力链对强力链起到侧向支撑的作用.顶煤放出口附近,由于颗粒侧向移动弱力链丧失,导致强力链减弱甚至消失.     

颗粒材料力学特性的数值模拟

针对颗粒介质特殊的力学特性,研究了二维颗粒堆积体中力的传递与分布,应用离散元理论建立数值模拟模型,并计算了堆积体中的接触力.结果表明,计算结果与物理试验现象较为吻合,在模拟中同时反映了颗粒介质中的拱效应和双峰现象.     

基于碳纳米线圈的细胞应激性测试探针

外界力、电刺激对细胞行为具有显著影响,细胞的力、电应激特性研究广受关注. 使用碳纳米线圈对单个活体细胞定量施加局域力学和电学刺激,探究了细胞的应激特性. 研究发现碳纳米线圈的局域力刺激可以引起细胞的整体响应,且受激响应程度与外力的作用形式和大小有关. 另外,细胞在碳纳米线圈施加的局域电刺激下会产生显著极性响应,并可在撤掉电刺激后逐渐恢复至初始状态,表明其生理结构和功能未受到破坏. 基于碳纳米线圈的非侵入性柔性生物探针具有安全可控、易操作和低成本等优点,在活体细胞对的应激和传导机制研究、细胞行为调控等领域具有广阔的应用前景.     

MD模拟温度对TATB和TATB/F2311 PBX力学性能的影响

为探讨高聚物粘结炸药(polymer-bonded explosive,PBX)的力学性能和结合能随温度变化的规律,该文用分子动力学(MD)方法和compass力场,在NPT系综下对钝感炸药TATB(1,3,5-三氨基-2,4,6-三硝基苯)及其与氟橡胶F2311所构成的阳X,进行不同温度下的周期性模拟.结果表明:与TATB单体炸药相比,PBX的力学性能显著改善,拉伸模量、体积模量和剪切模量均有所下降;随温度升高,PBX的刚性减小,弹性增强;结合能随温度升高呈先降后升再降的复杂变化趋势.     

Planar polarized actomyosin contractile flows control epithelial junction remodelling

Force generation by Myosin-II motors on actin filaments drives cell and tissue morphogenesis. In epithelia, contractile forces are resisted at apical junctions by adhesive forces dependent on E-cadherin, which also transmits tension. During Drosophila embryonic germband extension, tissue elongation is driven by cell intercalation, which requires an irreversible and planar polarized remodelling of epithelial cell junctions. We investigate how cell deformations emerge from the interplay between force generation and cortical force transmission during this remodelling in Drosophila melanogaster. The shrinkage of dorsal-ventral-oriented ('vertical') junctions during this process is known to require planar polarized junctional contractility by Myosin II (refs 4, 5, 7, 12). Here we show that this shrinkage is not produced by junctional Myosin II itself, but by the polarized flow of medial actomyosin pulses towards 'vertical' junctions. This anisotropic flow is oriented by the planar polarized distribution of E-cadherin complexes, in that medial Myosin II flows towards 'vertical' junctions, which have relatively less E-cadherin than transverse junctions. Our evidence suggests that the medial flow pattern reflects equilibrium properties of force transmission and coupling to E-cadherin by α-Catenin. Thus, epithelial morphogenesis is not properly reflected by Myosin II steady state distribution but by polarized contractile actomyosin flows that emerge from interactions between E-cadherin and actomyosin networks.     

Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies

Atomic force microscopes and optical tweezers are widely used to probe the mechanical properties of individual molecules and molecular interactions, by exerting mechanical forces that induce transitions such as unfolding or dissociation. These transitions often occur under nonequilibrium conditions and are associated with hysteresis effects-features usually taken to preclude the extraction of equilibrium information from the experimental data. But fluctuation theorems allow us to relate the work along nonequilibrium trajectories to thermodynamic free-energy differences. They have been shown to be applicable to single-molecule force measurements and have already provided information on the folding free energy of a RNA hairpin. Here we show that the Crooks fluctuation theorem can be used to determine folding free energies for folding and unfolding processes occurring in weak as well as strong nonequilibrium regimes, thereby providing a test of its validity under such conditions. We use optical tweezers to measure repeatedly the mechanical work associated with the unfolding and refolding of a small RNA hairpin and an RNA three-helix junction. The resultant work distributions are then analysed according to the theorem and allow us to determine the difference in folding free energy between an RNA molecule and a mutant differing only by one base pair, and the thermodynamic stabilizing effect of magnesium ions on the RNA structure.     

非平衡相变与平衡相变的临界相似关系及其统一性(英文)

在ＮＰＣ规格化模型的基础上,充分注意了平衡相变与非平衡相变两类临界现象间的主要差异和相似之处,从参考态、势函数、相关函数、临界可标度性、临界指数、标度律、临界普适性等方面考察了这两类临界观象的相互关系．结果表明,平衡相变临界观象（ＥＰＣ） 可看作是非平衡相变临界现（ＮＰＣ） 的一种特殊情况,平衡相变的临界标度律是非平衡相变临界标度律关系族中的一组关系式,即ＮＰＣ标度律具有更大的普适范围,这说明ＥＰＣ与ＮＰＣ 在临界标度性方面可由统一的理论来描述,在一定的条件下两者可统一起来．     

Longitudinal Mechanical Properties of Small-Diameter Polyurethane Vascular Graft Reinforced by Tubular Knitted Fabric

The vascular graft with 4 mm diameter was prepared by casting one layer of polyurethane (PU) film onto the knitting tubular fabric as the reinforced support. The effects of different PU content and wall thickness on the longitudinal mechanical properties of vascular graft were investigated. The breaking elongation, breaking force, initial modulus and breaking work were studied. The results showed that the longitudinal mechanical properties of vascular graft were enhanced as the content of polyurethane increased, which resulted from the combination of PU excellent elasticity and fabric preferable strength.