Clustering dynamics of nonlinear oscillator network: Application to graph coloring problem

The Kuramoto model is modified by introducing a negative coupling strength, which is a generalization of the original one. Among the abundant dynamics, the clustering phenomenon of the modified Kuramoto model is analyzed in detail. After clustering appears in a network of coupled oscillators, the nodes are split into several clusters by their phases, in which the phases difference within each cluster is less than a threshold and larger than a threshold between different clusters. We show that this interesting phenomenon can be applied to identify the complete sub-graphs and further applied to graph coloring problems. Simulations on test beds of graph coloring problems have illustrated and verified the scheme.     

Classical and quantum wave dynamics on time-dependent geometric graph

Geometric graph composed from a ring and a segment is considered. We deal with the Schrödinger (quantum) and the wave (classical) operators at the edges and the Kirchhoff conditions at the internal vertex. The lengths of the graph edges varies in time. Time evolution of a wave packet is studied in classical and quantum cases.     

分子动力学模拟钠硼硅酸盐玻璃电子辐照诱导的结构演化效应

钠硼硅酸盐玻璃作为高放射废物玻璃固化体的候选材料之一,已有大量实验对该类玻璃开展了电子或重离子的辐照效应研究.然而,在理论计算与模拟方面的工作却很少,目前主要集中于重离子的辐照效应,对电子的辐照效应的模拟尚未见报道.本文利用分子动力学工具提出一种新的方法,以实现对电子辐照诱导的玻璃结构演化进行模拟.该方法基于实验中玻璃的结构变化特点,即实验中的拉曼结果已经证实:在大剂量的电子辐照后的玻璃中存在分子氧的事实,由于这些分子氧不会与其他粒子发生相互作用,因而可以通过从体系中逐步地移除一定数量氧原子的方式,以达到模拟大剂量电子辐照的情形,进而得到电子辐照后的玻璃的结构信息.模拟结果显示:随着移除氧原子的数量增加,玻璃中的Si—O—Si平均键角逐渐减小;而且玻璃中的小环数量会因氧的逐渐减少而逐渐增加;玻璃中部分[BO4]结构会转变为[BO3]结构,最终这种转变会达到饱和;大量移除氧之后,玻璃中的钠元素也出现明显的相分离.这些模拟辐照的玻璃结构特性能较好地与实验中的硼硅酸盐玻璃电子辐照诱导的结构变化符合.因此,本文提出的方法有望为通过分子动力学模拟硼硅酸盐玻璃的电子辐照效应提供新思路.     

Application of statistical mechanics to combinatorial optimization problems: The chromatic number problem andq-partitioning of a graph

Methods of statistical mechanics are applied to two important NP-complete combinatorial optimization problems. The first is the chromatic number problem, which seeks the minimal number of colors necessary to color a graph such that no two sites connected by an edge have the same color. The second is partitioning of a graph intoq equal subgraphs so as to minimize intersubgraph connections. Both models are mapped into a frustrated Potts model, which is related to theq- state Potts spin glass. For the first problem, we obtain very good agreement with numerical simulations and theoretical bounds using the annealed approximation. The quenched model is also discussed. For the second problem we obtain analytic and numerical results by evaluating the groundstate energy of theq=3 and 4 Potts spin glass using Parisi's replica symmetry breaking. We also perform some numerical simulations to test the theoretical result and obtain very good agreement.     

Algebraic dynamics solutions and algebraic dynamics algorithm for nonlinear partial differential evolution equations of dynamical systems

Using functional derivative technique in quantum field theory, the algebraic dynamics approach for solution of ordinary differential evolution equations was generalized to treat partial differential evolution equations. The partial differential evolution equations were lifted to the corresponding functional partial differential equations in functional space by introducing the time translation operator. The functional partial differential evolution equations were solved by algebraic dynamics. The algebraic dynamics solutions are analytical in Taylor series in terms of both initial functions and time. Based on the exact analytical solutions, a new numerical algorithm—algebraic dynamics algorithm was proposed for partial differential evolution equations. The difficulty of and the way out for the algorithm were discussed. The application of the approach to and computer numerical experiments on the nonlinear Burgers equation and meteorological advection equation indicate that the algebraic dynamics approach and algebraic dynamics algorithm are effective to the solution of nonlinear partial differential evolution equations both analytically and numerically. Supported by the National Natural Science Foundation of China (Grant Nos. 10375039, 10775100 and 90503008), the Doctoral Program Foundation of the Ministry of Education of China, and the Center of Nuclear Physics of HIRFL of China     

An Adaptive Hierarchical Network Model for Studying the Structure of Economic Network

The interdependence of financial institutions is primarily responsible for creating a systemic hierarchy in the industry. In this paper, an Adaptive Hierarchical Network Model is proposed to study the problem of hierarchical relationships arising from different individuals in the economic domain. In the presented dynamically evolving network model, new directed edges are generated depending on the existing nodes and the hierarchical structures among the network, and these edges decay over time. When the preference of nodes in the network for higher ranks exceeds a certain threshold value, the equality state in the network becomes unstable and rank states emerge. Meanwhile, we select four real data sets for model evaluation and observe the resilience in the network hierarchy evolution and the differences formed by different patterns of hierarchy preference mechanisms, which help us better understand data science and network dynamics evolution.     

Directed transport and complex dynamics of vortices in a Josephson junction network driven by modulated currents

Directed transport of vortices in a Josephson junction network (JJN) with structural disorder is studied using a numerical simulation. Using spatiotemporal modulation of driving currents, the directed transport of vortices occurs even in the presence of disorder under certain conditions. From the analyses of the current–voltage and local voltage characteristics, it is found that the collective motion of vortices has an importance for the occurrence of directed transport.     

两相流有限穿越可视图演化动力学研究

针对小管径两相流流动特性, 全新优化设计弧形对壁式电导传感器. 通过动态实验在获取传感器测量信号的基础上, 采用有限穿越可视图理论构建对应于不同流型的两相流复杂网络. 通过分析发现, 有限穿越可视图网络异速生长指数和网络平均度值的联合分布可实现对小管径两相流的流型辨识; 有限穿越可视图度分布曲线峰值可有效刻画与泡径大小分布相关的流动物理结构细节特征; 网络平均度值可表征流动结构的宏观特性; 网络异速生长指数对流体动力学复杂性十分敏感, 可揭示不同流型演化过程中的细节演化动力学特性. 两相流测量信号的有限穿越可视图分析为揭示两相流流型的形成及演化动力学机理提供了新途径. 关键词： 两相流 复杂网络 有限穿越可视图 网络异速生长指数     

Antiferromagnetic-vortex dynamics driven by spin-polarized current in small thin disks

We investigate vortex configuration confined in antiferromagnetic thin disks. By virtue of sublattice mismatch at the disk borders, we propose a model that takes such a magnetostatic-like cost into account. The model predicts that onion-like configuration interpolates between curly and divergent vortex. Concerning its dynamics, it is shown that the vortex acquires oscillatory dynamics with well-defined amplitude and frequency that may be controlled on demand by an alternating spin-polarized current. These findings may be useful for the emerging field of antiferromagnetic topological spintronics, once vortex dynamics may be controlled by purely electronic means.     

Real-time evolution of strongly coupled fermions driven by dissipation

We consider the real-time evolution of a strongly coupled system of lattice fermions whose dynamics is driven entirely by dissipative Lindblad processes, with linear or quadratic quantum jump operators. The fermion 2-point functions obey a closed set of differential equations, which can be solved with linear algebra methods. The staggered occupation order parameter of the t$t$-V$V$ model decreases exponentially during the dissipative time evolution. The structure factor associated with the various Fourier modes shows the slowing down of low-momentum modes, which is due to particle number conservation. The processes with nearest-neighbor-dependent Lindblad operators have a decay rate that is proportional to the coordination number of the spatial lattice.     

Investigating the time dynamics of seismicity by using the visibility graph approach: Application to seismicity of Mexican subduction zone

By using the method of the visibility graph (VG), five magnitude time series extracted from the seismic catalog of the Mexican subduction zone were investigated. The five seismic sequences represent the seismicity which occurred between 2005 and 2012 in five seismic areas: Guerrero, Chiapas, Oaxaca, Jalisco and Michoacán. Among the five seismic sequences, the Jalisco sequence shows VG properties significantly different from those shown by the other four. Such a difference could be inherent in the different tectonic settings of Jalisco with respect to those characterizing the other four areas. The VG properties of the seismic sequences have been put in relationship with the more typical seismological characteristics (b$b$-value and a$a$-value of the Gutenberg–Richter law).     

Nonequilibrium dynamics of a diffusion-limited reaction driven by a cluster-memory mechanism

The diffusion-limited reaction A+AA+B is studied in general dimension. The asymptotic decay of the system is found to depend nontrivially upon the initial concentration of A particles for certain ranges of the diffusion constant, backward reaction rate, and total concentration of particles. This nonequilibrium behavior is due to the formation of clusters centered about the initial A particles. A perturbative analysis ind=1 shows that the transition to the nonequilibrium dynamics is sharp and is quite similar to another previously studied reaction A+AA. Ford>1, a scaling argument is presented which describes the dependence of the asymptotic decay on the initial concentration of A particles and the equilibrium concentration for large backward reaction rates. Monte Carlo data are shown which confirm the analytic work ind=1, 2, and 3.     

Fractal analysis on human dynamics of library loans

In this paper, the fractal characteristic of human behaviors is investigated from the perspective of time series constructed with the amount of library loans. The values of the Hurst exponent and length of non-periodic cycle calculated through rescaled range analysis indicate that the time series of human behaviors and their sub-series are fractal with self-similarity and long-range dependence. Then the time series are converted into complex networks by the visibility algorithm. The topological properties of the networks such as scale-free property and small-world effect imply that there is a close relationship among the numbers of repetitious behaviors performed by people during certain periods of time. Our work implies that there is intrinsic regularity in the human collective repetitious behaviors. The conclusions may be helpful to develop some new approaches to investigate the fractal feature and mechanism of human dynamics, and provide some references for the management and forecast of human collective behaviors.     

Evolutionary dynamics of imatinib-treated leukemic cells by stochastic approach

The evolutionary dynamics of a system of cancerous cells in a model of chronic myeloid leukemia (CML) is investigated by a statistical approach. Cancer progression is explored by applying a Monte Carlo method to simulate the stochastic behavior of cell reproduction and death in a population of blood cells which can experience genetic mutations. In CML front line therapy is represented by the tyrosine kinase inhibitor imatinib which strongly affects the reproduction of leukemic cells only. In this work, we analyze the effects of a targeted therapy on the evolutionary dynamics of normal, first-mutant and cancerous cell populations. Several scenarios of the evolutionary dynamics of imatinib-treated leukemic cells are described as a consequence of the efficacy of the different modelled therapies. We show how the patient response to the therapy changes when a high value of the mutation rate from healthy to cancerous cells is present. Our results are in agreement with clinical observations. Unfortunately, development of resistance to imatinib is observed in a fraction of patients, whose blood cells are characterized by an increasing number of genetic alterations. We find that the occurrence of resistance to the therapy can be related to a progressive increase of deleterious mutations.      

两种方法求解外场驱动含时谐振子系统

应用代数动力学规范变换方法和相干态平均的方法,求解外场驱动下含时变频谐振子系统的时间演化算符,比较了两种方法所得的结果.研究结果表明,两种方法所得结果一致.     

Pattern dynamics and optimization by reaction diffusion systems

Reaction-diffusion systems show a fast and rather complex response on patterns produced by external space- and/or time-dependent perturbations. For example, one-component autocatalytic reactions rapidly find the loci where the given space-dependent reaction rates have relatively high values by following a kind of Darwinian strategy (combining self-reproduction and diffusion). It is shown that a simulation of this strategy in combination with annealing (decreasing the diffusion rates in time) may be used as an alternative to thermodynamic annealing strategies. Many-component reactions, such as the light-sensitive Belousov-Zhabotinsky reaction, show a more complex response to patterns impressed by illumination, for example. The response behavior and possible applications to dynamic information processing are discussed.     

Nanoplasma dynamics in Xe clusters driven by ultraintense laser fields

We present a theoretical and computational study of the properties and the response of the nanoplasma and of outer ionization in Xe_n clusters (n = 55–2171, initial cluster radius R₀ = 8.7–31.0 ?) driven by ultraintense near-infrared laser fields (peak intensity I_M = 10¹⁵–10²⁰ Wcm^-2, temporal pulse length τ= 10–100 fs, and frequency ν= 0.35 fs^-1). The positively charged high-energy nanoplasma produced by inner ionization nearly follows the oscillations of the fs laser pulse and can either be persistent (at lower intensities of I_M = 10¹⁵–10¹⁶ Wcm^-2 and/or for larger cluster sizes, where the electron energy distribution is nearly thermal) or transient (at higher intensities of I_M = 10¹⁸–10²⁰ Wcm^-2 and/or for smaller cluster sizes). The nanoplasma is depleted by outer ionization that was semiquantitatively described by the cluster barrier suppression electrostatic model, which accounts for the cluster size, laser intensity and pulse length dependence of the outer ionization yield. The electrostatic model was further utilized for estimates of the laser intensity and pulse width dependence of the border radius R₀ ^(I) for the attainment of complete outer ionization at , while at R₀ > R₀ ^(I) a persistent nanoplasma prevails. R₀ ^(I) establishes an interrelationship between electron dynamics and nuclear Coulomb explosion dynamics in ultraintense laser-cluster interactions.     

交流源作用下介观RLC电路系统量子态随时间的演化

根据量子不变量理论，同时考虑介观电容器极板间电子波函数的耦合作用和电路的耗散,研究介观RLC电路系统在交流电流源作用下动力学的演化过程，并且得到描述系统量子态随时间的演化算符.进一步的分析结果表明，介观RLC电路系统的波函数将由任意的初态演化到一般的压缩态. 关键词： 介观RLC电路 交变电源 不变量理论 时间演化算符     

A fast parallel Poisson solver on irregular domains applied to beam dynamics simulations

We discuss the scalable parallel solution of the Poisson equation within a Particle-In-Cell (PIC) code for the simulation of electron beams in particle accelerators of irregular shape. The problem is discretized by Finite Differences. Depending on the treatment of the Dirichlet boundary the resulting system of equations is symmetric or ‘mildly’ nonsymmetric positive definite. In all cases, the system is solved by the preconditioned conjugate gradient algorithm with smoothed aggregation (SA) based algebraic multigrid (AMG) preconditioning. We investigate variants of the implementation of SA-AMG that lead to considerable improvements in the execution times. We demonstrate good scalability of the solver on distributed memory parallel processor with up to 2048 processors. We also compare our iterative solver with an FFT-based solver that is more commonly used for applications in beam dynamics.