Effective medium theory of semiflexible filamentous networks

We develop an effective medium approach to the mechanics of disordered, semiflexible polymer networks and study the response of such networks to uniform and nonuniform strain. We identify distinct elastic regimes in which the contributions of either filament bending or stretching to the macroscopic modulus vanish. We also show that our effective medium theory predicts a crossover between affine and nonaffine strain, consistent with both prior numerical studies and scaling theory.     

Mechanics of bundled semiflexible polymer networks

While actin bundles are used by living cells for structural fortification, the microscopic origin of the elasticity of bundled networks is not understood. Here, we show that above a critical concentration of the actin binding protein fascin, a solution of actin filaments organizes into a pure network of bundles. While the elasticity of weakly cross-linked networks is dominated by the affine deformation of tubes, the network of bundles can be fully understood in terms of nonaffine bending undulations.     

Visualizing the strain field in semiflexible polymer networks: strain fluctuations and nonlinear rheology of F-actin gels

We image semiflexible polymer networks under shear at the micrometer scale. By tracking embedded probe particles, we determine the local strain field, and directly measure its uniformity, or degree of affineness, on scales of 2-100 microm. The degree of nonaffine strain depends upon the polymer length and cross-link density, consistent with theoretical predictions. We also find a direct correspondence between the uniformity of the microscale strain and the nonlinear elasticity of the networks in the bulk.     

Deformation of cross-linked semiflexible polymer networks

Networks of filamentous proteins play a crucial role in cell mechanics. These cytoskeletal networks, together with various cross-linking and other associated proteins largely determine the (visco)elastic response of cells. In this Letter we study a model system of cross-linked, stiff filaments in order to explore the connection between the microstructure under strain and the macroscopic response of cytoskeletal networks. We find two distinct regimes as a function primarily of cross-link density and filament rigidity: one characterized by affine deformation and one by nonaffine deformation. We characterize the crossover between these two.     

Internal stresses, normal modes, and nonaffinity in three-dimensional biopolymer networks

We numerically investigate deformations and modes of networks of semiflexible biopolymers as a function of crosslink coordination number z and strength of bending and stretching energies. In equilibrium filaments are under internal stress, and the networks exhibit shear rigidity below the Maxwell isostatic point. In contrast to two-dimensional networks, ours exhibit nonaffine bending-dominated response in all rigid states, including those near the maximum of z=4 when bending energies are less than stretching ones.     

Alternative explanation of stiffening in cross-linked semiflexible networks

Strain stiffening of filamentous protein networks is explored by means of a finite strain analysis of a two-dimensional network model of cross-linked semiflexible filaments. The results show that stiffening is caused by nonaffine network rearrangements that govern a transition from a bending-dominated response at small strains to a stretching-dominated response at large strains. Filament undulations, which are key in the existing explanation of stiffening, merely postpone the transition.     

Experimental measures of affine and nonaffine deformation in granular shear

Through 2D granular Couette flow experiments, we probe failure and deformation of disordered solids under shear. Shear produces a mean azimuthal flow, smooth affine deformations, and irreversible so-called nonaffine particle displacements. We find that these processes are all of comparable magnitude and depend on the local shear rate. We compute the parameter of Falk and Langer characterizing nonaffine motion, Dmin2, and find that it is reasonably well described in terms of collections of single particles making locally nearly isotropic random steps, delta ri. Distributions for single particle nonaffine displacements, delta ri, satisfy P1(delta ri) proportional, variantexp[-|delta ri/Delta r|alpha] (alpha < or approximately 2).     

Structural signature of plastic deformation in metallic glasses

The structure feature of a model CuZr metallic glass during deformation is investigated by molecular dynamics simulations. A spatially heterogeneous irreversible rearrangement is observed in terms of nonaffine displacement. We find that regions with smaller nonaffine displacement have more Voronoi pentagons, while in those with larger nonaffine displacement other types of faces are more populated. We use the degree of local fivefold symmetry (LFFS) as the structural indicator to predict plastic deformation of local structures and find that the plastic events prefer to be initiated in regions with a lower degree of LFFS and propagate toward regions with a higher degree of LFFS.     

Correlations in the elastic response of dense random packings

Results are presented for the autocorrelation function of the vortexlike nonaffine piece of the linear elastic displacement field in dense random bidisperse packings of harmonically repulsive disks in 2D. The autocorrelation function is shown to scale precisely with the length of the simulation cell in systems ranging from 20 to 100 particles across. It is shown that, to first order, the displacement fields can be thought to arise from the action of uncorrelated local random forcing of a homogeneous elastic sheet, and a theory is presented which gives excellent quantitative agreement with the form of the correlation functions. These results suggest measurements to be made in many types of densely packed, random materials where the elastic displacement fields are accessible experimentally such as granular materials, dense emulsions, colloidal suspensions, etc.     

An Improved Heterogeneous Mean-Field Theory for the Ising Model on Complex Networks

Heterogeneous mean-field theory is commonly used methodology to study dynamical processes on complex networks,such as epidemic spreading and phase transitions in spin models.In this paper,we propose an improved heterogeneous mean-field theory for studying the Ising model on complex networks.Our method shows a more accurate prediction in the critical temperature of the Ising model than the previous heterogeneous mean-field theory.The theoretical results are validated by extensive Monte Carlo simulations in various types of networks.     

Critical scaling in linear response of frictionless granular packings near jamming

We study the origin of the scaling behavior in frictionless granular media above the jamming transition by analyzing their linear response. The response to local forcing is non-self-averaging and fluctuates over a length scale that diverges at the jamming transition. The response to global forcing becomes increasingly nonaffine near the jamming transition. This is due to the proximity of floppy modes, the influence of which we characterize by the local linear response. We show that the local response also governs the anomalous scaling of elastic constants and contact number.     

Inhomogeneous elastic response of silica glass

Using large scale molecular dynamics simulations we investigate the properties of the nonaffine displacement field induced by macroscopic uniaxial deformation of amorphous silica, a strong glass according to Angell's classification. We demonstrate the existence of a length scale xi characterizing the correlations of this field (corresponding to a volume of about 1000 atoms), and compare its structure to the one observed in a standard fragile model glass. The "boson-peak" anomaly of the density of states can be traced back in both cases to elastic inhomogeneities on wavelengths smaller than xi where classical continuum elasticity becomes simply unapplicable.     

基于传播免疫的复杂网络可控性研究

复杂网络控制反映了人类对复杂系统的认识深度和改造能力. 最新研究成果基于线性系统控制理论建立了复杂网络可控性的理论架构, 能够发现任意拓扑结构的线性时不变复杂网络中控制全部节点状态的最小驱动节点集, 但是该模型未考虑免疫节点或失效节点对控制信号传播的阻断.在继承该模型优点的前提下, 重新构建了基于传播免疫的复杂网络控制模型.在采用分属于随机免疫和目标免疫两种策略的 4个方法确定免疫节点的情况下,分析14个真实网络的可控性.结果表明:如果将网络中度数、 介数和紧密度指标较高的节点作为免疫节点,将极大地提高控制复杂网络的难度. 从而在一定程度上丰富了以往模型的结论.     

Speed of synchronization in complex networks of neural oscillators: analytic results based on Random Matrix Theory

We analyze the dynamics of networks of spiking neural oscillators. First, we present an exact linear stability theory of the synchronous state for networks of arbitrary connectivity. For general neuron rise functions, stability is determined by multiple operators, for which standard analysis is not suitable. We describe a general nonstandard solution to the multioperator problem. Subsequently, we derive a class of neuronal rise functions for which all stability operators become degenerate and standard eigenvalue analysis becomes a suitable tool. Interestingly, this class is found to consist of networks of leaky integrate-and-fire neurons. For random networks of inhibitory integrate-and-fire neurons, we then develop an analytical approach, based on the theory of random matrices, to precisely determine the eigenvalue distributions of the stability operators. This yields the asymptotic relaxation time for perturbations to the synchronous state which provides the characteristic time scale on which neurons can coordinate their activity in such networks. For networks with finite in-degree, i.e., finite number of presynaptic inputs per neuron, we find a speed limit to coordinating spiking activity. Even with arbitrarily strong interaction strengths neurons cannot synchronize faster than at a certain maximal speed determined by the typical in-degree.     

Elementary proof of Zeeman's theorem

We prove that the nonaffine conformal transformations of four-dimensional Minkowski space are necessarily global causality violators, and use this fact to obtain an elementary group-theoretic proof of the theorem that global causality implies the Lorentz group.     

The interaction between multiplex community networks

Multiplex community networks, consisting of several different types of simplex networks and interconnected among them, are ubiquitous in the real world. In this paper, we carry out a quantitative discussion on the interaction among these diverse simplex networks. First, we define two measures, mutual-path-strength and proximity-node-density, based on twoplex community networks and then propose an impact-strength-index (ISI) to describe the influence of a simplex network on the other one. Finally, we apply the measure ISI to make an explanation for the challenge system of social relations from the viewpoint of network theory. Numerical simulations show that the measure ISI can describe the interaction between multiplex community networks perfectly.     

Modelling the air transport with complex networks: A short review

Air transport is a key infrastructure of modern societies. In this paper we review some recent approaches to air transport, which make extensive use of theory of complex networks. We discuss possible networks that can be defined for the air transport and we focus our attention to networks of airports connected by flights. We review several papers investigating the topology of these networks and their dynamics for time scales ranging from years to intraday intervals, and consider also the resilience properties of air networks to extreme events. Finally we discuss the results of some recent papers investigating the dynamics on air transport network, with emphasis on passengers traveling in the network and epidemic spreading.     

Normalized Sombor Indices as Complexity Measures of Random Networks

We perform a detailed computational study of the recently introduced Sombor indices on random networks. Specifically, we apply Sombor indices on three models of random networks: Erdös-Rényi networks, random geometric graphs, and bipartite random networks. Within a statistical random matrix theory approach, we show that the average values of Sombor indices, normalized to the order of the network, scale with the average degree. Moreover, we discuss the application of average Sombor indices as complexity measures of random networks and, as a consequence, we show that selected normalized Sombor indices are highly correlated with the Shannon entropy of the eigenvectors of the adjacency matrix.     

Diffusion processes on power-law small-world networks

We consider diffusion processes on power-law small-world networks in different dimensions. In one dimension, we find a rich phase diagram, with different transient and recurrent phases, including a critical line with continuously varying exponents. The results were obtained using self-consistent perturbation theory and can also be understood in terms of a scaling theory, which provides a general framework for understanding processes on small-world networks with different distributions of long-range links.