Synchronized regions of pinned complex networks: spectral analysis

The synchronization problem for a complex dynamical network is investigated in this paper from a spectral analysis approach. It is assumed that only a small portion of the nodes in the network are chosen to be controlled, known as the pinning control scheme. Some new types of synchronized regions for networks with different node dynamics and inner-coupling structures are discovered, especially for the case of the special chaotic node systems with a stable equilibrium point under fully anti-diagonal and partially anti-diagonal couplings. The eigenvalue distributions of the coupling and control matrices for different types of complex networks are obtained. The effects of the network topology, global coupling strength, pinning density, and pinning strength on the network synchronizability are examined through extensive numerical simulations. It is shown that the synchronizability of the pinned network can be effectively improved by increasing the overall coupling strength, pinning density, and pinning strength for some classes of synchronized regions, whereas too large the pinning density and pinning strength will lead to desynchronization for other classes. It is found that small-world networks are not always easier to synchronize than regular rings, and a denser eigenvalue distribution may not always imply better synchronizability.     

图论与复杂网络

近10年来迅猛发展起来的复杂网络理论为研究复杂性与复杂系统科学提供了一个重要支撑点,它高度概括了复杂系统的重要特征,无论是在理论还是在应用方面都具有很强的生命力,而且在各个方面都得到了很大发展.重点讨论图论在复杂网络中的应用,特别是代数图论在复杂网络同步问题中的应用.首先给出一些图的最小非零与最大特征值以及同步能力的估计,并且讨论了子图与图特征向量在同步能力估计中的作用.其次以两个简单图指出同步能力与网络结构参数的关系复杂,并给出补图与加边对同步研究的意义,然后给出图运算在复杂网络同步中的作用.最后从图论与控制理论角度展望了复杂网络领域未来可能的发展方向.      

Discontinuous synchrony in an array of Van der Pol oscillators

We show the phenomenon of complete synchronization in an network of coupled oscillators. We confirm that non-diagonal coupling can lead to the appearance or disappearance of synchronous windows (ragged synchronizability phenomenon) in the coupling parameter space. We also show the appearance of clusters (synchronization in one or more group) between coupled systems. Our numerical studies are confirmed by an electronic experiment.     

On the connections between the functionals of equivalent variational principles

It is proved in this paper that the functionals of equivalent variational principles are different essentially only in terms of weighted residues. Consequently, the simplest method for constructing equivalent variational principles is to add weighted residues to known functionals as first used by Courant [4].     

The collective bursting dynamics in a modular neuronal network with synaptic plasticity

In this study, how the synaptic plasticity influences the collective bursting dynamics in a modular neuronal network is numerically investigated. The synaptic plasticity is described by a modified Oja’s learning rule. The modular network is composed of some sub-networks, each of them having small-world characteristic. The result indicates that bursting synchronization can be induced by large coupling strength between different neurons, which is robust to the local dynamical parameter of individual neurons. With the emergence of synaptic plasticity, the bursting dynamics in the modular neuronal network, particularly the excitability and synchronizability of bursting neurons, is detected to be changed significantly. In detail, upon increasing synaptic learning rate, the excitability of bursting neurons is greatly enhanced; on the contrary, bursting synchronization between interacted neurons is a little suppressed by the increase in synaptic learning rate. The presented findings could be helpful to understand the important role of synaptic plasticity on neural coding in realistic neuronal network.     

The energy of a growing elastic surface

The potential energy of the elastic surface of an elastic body which is growing by the coherent addition of material is derived. Several equivalent expressions are presented for the energy required to add a single atom, also known as the chemical potential. The simplest involves the Eshelby stress tensors for the bulk medium and for the surface. Dual Lagrangian/Eulerian expressions are obtained which are formally similar to each other. The analysis employs two distinct types of variations to derive the governing bulk and surface equations for an accreting elastic solid. The total energy of the system is assumed to comprise bulk and surface energies, while the presence of an external medium can be taken into account through an applied surface forcing. A detailed account is given of the various formulations possible in material and current coordinates, using four types of bulk and surface stresses: the Piola-Kirchhoff stress, the Cauchy stress, the Eshelby stress and a fourth, called the nominal energy-momentum stress. It is shown that inhomogeneity surface forces arise naturally if the surface energy density is allowed to be position dependent.     

An Alternative Stability Analysis Technique for the Simplest Walker

We revisit the simplest walker studiedearlier by Garcia and co-workers. We extend the small-slope stability analysis to second order, substantially improving accuracy, andalso provide some details left out of the earlier work.We develop an alternative (reverse) approach for the stabilityanalysis, which involves shorter calculations: for stability analysis upto any given order, the new procedure requires calculations to one order less than the previous (forward) procedure. The stabilityresults obtained by the two methods are, nevertheless, equivalent.     

等价变分原理泛函之间的联系

本文证明了等价变分原理的泛函,实质上都只相差某种加权残差项,这也就表明了,在已知的泛函后附加加权残差项,是建立等价变分原理最简便的方法.     

细胞骨架生物力学进展

细胞骨架力学作为力学细胞生物学的一个新兴领域, 其研究方法突破传统细胞力学思想, 不再把活细胞简化为皮质膜包着的弹性、黏性或黏弹性连续介质体, 而是基于在细胞变形和功能中发挥重要作用的细胞骨架离散网络结构, 在微/纳米尺度建立一种集细胞形态和功能于一体的离散网络结构. 这种细胞骨架模型作为细胞变形和生化事件调控的纽带, 能从分子层次上阐述细胞运动、能量转换、信息传递、基因表达等重大生命活动的潜在机制,同时也能解释生物大分子间相互作用、受体/配体特异性相互作用、大分子自装配、细胞及分子层次的力学-化学耦合, 为定量研究细胞-亚细胞-生物大分子等在多种力学刺激下的响应建立了良好的平台, 对于理解生物模式形成、生物复杂性以及解决重大生物学难题具有深远意义. 本文基于细胞骨架三维离散网络结构特点及其生物学背景, 从生物力学角度详细阐述近几年国际上流行的细胞骨架模型理论分析和研究成果的最新进展.      

Synchronization in complex dynamical networks with interval time-varying coupling delays

This paper deals with the synchronization problem of complex dynamical networks with interval time-varying coupling delays. A simple local linear feedback controller is introduced to guarantee the synchronizability of the networks. Some delay-dependent synchronization conditions for the controlled complex dynamical networks are presented by using the Lyapunov–Krasovskii functional method and the reciprocally convex combination approach. Theoretical analysis and numerical examples show that the obtained conditions have less computational complexity and less conservatism than some recently reported ones.     

Hysteresis and phase transition in many-particle storage systems

We study the behavior of systems that can be described as ensembles of interconnected storage particles. Our examples concern the storage of lithium in many-particle electrodes of rechargeable lithium-ion batteries and the storage of air in a system of interconnected rubber balloons. We are particularly interested in those storage systems whose constituents exhibit non-monotone material behavior leading to transitions between two coexisting phases and to hysteresis. In the current study, we consider the case that the time to approach equilibrium of a single storage particle is much smaller than the time for full charging of the ensemble. In this regime, the evolution of the probability to find a particle of the ensemble in a certain state may be described by a non-local conservation law of Fokker–Planck type. The resulting equation contains two parameter which control whether the ensemble transits the 2-phase region along a Maxwell line or along a hysteresis path, or whether the ensemble shows the same non-monotone behavior as its constituents.     

A new micromechanical approach of micropolar continuum modeling for 2-D periodic cellular material

In this paper, we present a new united approach to formulate the equivalent micropolar constitutive relation of two-dimensional (2-D) periodic cellular material to capture its non-local properties and to explain the size effects in its structural analysis. The new united approach takes both the displacement compatibility and the equilibrium of forces and moments into consideration, where Taylor series expansion of the displacement and rotation fields and the extended aver-aging procedure with an explicit enforcement of equilibrium are adopted in the micromechanical analysis of a unit cell. In numerical examples, the effective micropolar constants obtained in this paper and others derived in the literature are used for the equivalent micropolar continuum simulation of cellular solids. The solutions from the equivalent analysis are compared with the discrete simulation solutions of the cellu-lar solids. It is found that the micropolar constants developed in this paper give satisfying results of equivalent analysis for the periodic cellular material.     

Analysis of the mechanics of perforation of projectiles in metallic plates

A mathematical model has been developed to describe the mechanism of normal perforation of projectiles in metallic targets. The perforation process is considered to be divided into three interconnected stages. The analysis accounts for an effective mass of the bullet due to part of the target material moving with the bullet, the deformation of the bullet during penetration, and the increased strength of the target material at high rates of loading. The analysis enables the residual velocity to be calculated as a function of the target thickness and its mechanical and physical properties, and of the mass, geometry and impact velocity of the projectile. The geometry of the cavity, i.e. entrance and exit diameters and plug thicknesses, are factors in the analysis and are empirical quantities. The present theory can also predict the force-time curve and the contact time for the perforation process.     

高速弓网系统动力学参数敏度分析及优化

随着高速列车运行速度的提升, 弓网关系这一基础力学问题备受关注. 良好的弓网关系是确保列车安全高效运行、稳定可靠受流、降低接触线与受电弓滑板磨耗等的基本前提. 其中, 受电弓和接触网的动力学参数对弓网耦合作用起至关重要的作用. 本文采用弓网接触力随机统计特征作为优化目标函数,进行受电弓动力学参数的敏度分析和优化设计. 首先, 建立了二维弹性链悬挂接触网-三质量块受电弓动力学模型,根据EN50318: 2018标准验证了动力学建模和分析结果的正确性. 然后, 基于高速弓网系统的动力学仿真, 进行了DSA380型高速受电弓三质量块参数的动力学敏度分析, 确定了9个动力学参数的敏感度级别, 弓头等效质量敏度评级最高,下框架等效阻尼次之, 下框架等效质量和上框架等效阻尼第三. 最后, 研究了弓头等效刚度和等效阻尼联合变化对弓网耦合动力学性能的影响,给出了提升弓网耦合性能的弓头双参数优化方案, 建议同时减小弓头等效阻尼和增大弓头等效刚度, 能够实现比单参数优化更好的弓网耦合性能.      

A Theoretical Model with Experimental Verification to Predict Hydrodynamics of Foams

An experimentally validated theoretical model, based on hydraulic resistance network and scale analysis at the pore level, is developed to predict the pressure drop for flow through foams. The complex microstructure of the foams is modeled as a matrix of interconnected solid ligaments forming simple cubic arrays of cylinders. New correlations for permeability and form drag (inertia) coefficient are presented as functions of the mean pore and ligament diameter as well as the foam porosity. The present model makes it possible to conduct parametric studies. Results obtained from the proposed model are successfully compared with our experimental data as well those found in the literature to observe good agreement.     

Kinematic Analysis of Robotic Bevel-Gear Trains: An Application of Network Model Approach

The network model approach for rigid and multi-rigid body systems developed recently [1,2] can also be used conveniently in formulating system equations or equations of motion of three-dimensional mechanical systems of interconnected rigid bodies. In this article, this method is further elaborated for establishing only the kinematics of spatial robotic bevel-gear trains. However the dynamic analysis of such systems using the same method is also possible and will be taken up in a future publication.     

Continuum models of multi-walled carbon nanotubes

Molecular mechanics (MM) simulations have been carried out to determine energetically favorable double-walled carbon nanotube (DWNT) structures, and analyze their infinitesimal extensional, torsional, radial expansion/contraction, and bending deformations. Loads are applied either to one wall or simultaneously to both walls of an open-ended DWNT. These results are compared against single-walled carbon nanotube (SWNT) results to determine differences and similarities between responses of SWNTs and DWNTs, and the validity of using SWNT results to predict the response of a DWNT. It is found that for small deformations such as simple tension and torsion, results for a DWNT can be derived from those for its constituent SWNTs within 3% error. Results of radial expansion/contraction of a SWNT are used to deduce an expression for the van der Waals force. Based on these results, a continuum model is proposed for a MWNT whose response to mechanical deformations computed using engineering theories is the same as that of the MWNT obtained via MM simulations. The continuum structure is comprised of concentric cylindrical tubes interconnected by truss elements. Young’s modulus, Poisson’s ratio, the thickness of each concentric tube, and the stiffness of the truss elements are given. The proposed continuum model is validated by studying bending and the onset of global buckling deformations of a DWNT and its proposed equivalent continuum structure. Carbon nanotubes can be replaced by their equivalent continuum structures when deriving mechanical properties of nanotube reinforced polymeric composites.     

Effects of the Correlation Length on the Hydraulic Parameters of a Fracture Network

We consider the influences of correlation length and aperture variability on the REV, the equivalent permeability of a fracture network, and the uncertainty in the equivalent permeability using a two-dimensional orthogonal bond percolation model. The percolation threshold, correlation length, effective conductivity, and coefficient of variation of the effective conductivity are investigated over statistically representative multiple realizations with Monte Carlo simulations in 2D fracture networks that have log-normally distributed individual fracture permeabilities. We show that although the aperture variability is large, the REV and the correlation length are similar near the percolation threshold. In contrast, when the fracture density is much larger than the percolation threshold they diverge as the aperture variability increases. We characterize the effects of correlation length and aperture variability on effective conductivity with a simple function. From the coefficient of variation analysis, the correlation length can be a criterion for evaluating which conceptual model is appropriate for describing the flow system for a given fracture network when aperture variability is sufficiently small. However, discrete fracture network models are recommended for flow simulation models because of the difficulty of REV estimation and the uncertainty in equivalent hydraulic parameters when aperture variability is large.     

工程结构优化的神经网络方法

本文阐述了神经网络优化计算的基本原理，构造了工程结构优化的神经网络模型。采用模拟退火技术进行模型求解，且巧妙地将退火温度Ｔ的倒数作为Ｌａｇｒａｎｇｅ乘子，以改善增广目标函数的收敛性。实例计算表明，由非线性模拟神经元组成的大规模并行、互连的网络在工程结构的优化设计中是可行且有效的。