自适应网络中病毒传播的稳定性和分岔行为研究

自适应复杂网络是以节点状态与拓扑结构之间存在反馈回路为特征的网络. 针对自适应网络病毒传播模型, 利用非线性微分动力学系统研究病毒传播行为; 通过分析非线性系统对应雅可比矩阵的特征方程, 研究其平衡点的局部稳定性和分岔行为, 并推导出各种分岔点的计算公式. 研究表明, 当病毒传播阈值小于病毒存在阈值, 即R₀0^c时, 网络中病毒逐渐消除, 系统的无病毒平衡点是局部渐近稳定的; R₀^c0<1时, 网络出现滞后分岔, 产生双稳态现象, 系统存在稳定的无病毒平衡点、较大稳定的地方病平衡点和较小不稳定的地方病平衡点; R₀>1时, 网络中病毒持续存在, 系统唯一的地方病平衡点是局部渐近稳定的. 研究发现, 系统先后出现了鞍结分岔、跨临界分岔、霍普夫分岔等分岔行为. 最后通过数值仿真验证所得结论的正确性. 关键词： 自适应网络 稳定性 分岔 基本再生数     

基于交通流量的病毒扩散动力学研究

不同于经典扩散模型中节点传染力等同于节点度k的假定, 基于交通流量的病毒扩散模型中, 各个节点的传染力可以等同于节点实际介数b_k. 利用平均场近似方法, 提出基于交通流量SIS病毒修正扩散模型. 根据修正SIS模型, 以最小搜索信息路由为例, 重新研究病毒传播率β, 平均发包率λ同传播阈值β_c, 平稳状态病毒密度ρ之间的关系. 理论分析与实验结果均表明, 当网络拓扑和路由策略一定时, 传播阈值β_c为实际介数b_k的均值<b_k>与其平方的均值<b_k²>的比值. 而稳定状态时感染密度ρ同感染同病毒传播率β, 平均发包率λ 以及λ =1时节点实际介数的均值<b_λ=1> 的乘积倒数存在幂率关系.     

相对论Thomas-Fermi近似下的核半径公式

使用QHD-I的相对论核场论模型,在Thomas-Fermi近似下讨论核力作用半径公式 R=R₀A^1/3,发现理论计算R₀的结果与高能α粒子与原子核散射的实验结果很好地符合.     

核电荷半径的同位旋相关性及其微观诠释

原子核电荷半径R_c所有的实验数据都表明, R_c系统偏离A^1/3律, 即随A增大R_c/A^1/3系统地递减, 而R_c/Z^1/3则比较接近于一个常量. 原子核巨单极共振能量E_x ∝ R^－1的大量实验数据也支持这一结论. 根本原因在于A^1/3律与同位旋无关, 而Z^1/3律已部分反映了同位旋的影响. 基于壳模型, 给出了Z^1/3律的微观诠释. 壳模型中质子和中子谐振子势强度参数ω_p和ω_n的差异, 可以用Z^1/3律说明. 基于与Wigner的原子核同位旋多重态质量公式(IMME)相似的理论考虑, 提出了核电荷半径改进的Z^1/3律.     

一个八维Kaluza-Klein宇宙模型

本文讨论了一个八维Kaluza-Klein宇宙模型.它不仅自洽地包含Georgi三族SU(11)大统一模型,而且得到了与观测宇宙一致的物理解.在这一模型中,通常四维的宇宙标度因子记作R₃而额外维度的宇宙标度因子记作R₄,它们的物理性质可分成四个阶段来描述.第一阶段,R₃和R₄都在膨胀;第二阶段,R₃是一个inflation解而R₄是个常数;第三阶段,R₄开始坍缩到它的极小值,而R₃继续单调地增加;第四阶段,R₄稳定在Kaluza-Klein半径R_KK而R₃通常的FRW方式膨胀,这时四维的宇宙常数为零.     

光受激发射的稳定性

本文推导出描述三能级Laser工作过程的准经典方程组,并分析了输出振动的稳定性。在阈值以上,当T₁?T₂,q^-1时,只在1/(qT₂)>1时,输出振幅是稳定的(其中T₁,T₂,q^-1分别是分子纵向、横向及谐振腔的弛豫时间)。在稳定区域,趋向平衡的时间与T₁成正比。当分子线宽小于谐振腔宽度时,输出是不稳定的,而在1/(qT₂)减小时,平衡点由稳定变到不稳定时产生一个稳定的极限环,即输出振幅逐渐开始振动。关于稳定性的结论在气体Laser中是可以检验的。本文指出,在红宝石Laser中看到的输出不稳定,可能就是谐振腔的q很大的结果。     

e+e－湮没中L=1激发态重子的产生比例

用一个简化模型概括的低激发态重子主要衰变分支比和我们在文献[2]中给出的基本关系,得出L=1激发态重子对∑⁺(1385),∑⁺,Ξ⁰(1530)和Ξ⁰的衰变贡献,进而用γ共振能量下的实验值R₁=(1530)/Ξ,R₂=∑(1385)/∑和R₃=∧(1520)/∑(1385)作输入,估算了L=1的各激发态重子的产生比例.     

MgB2超导薄膜的微波测量

报道了利用蓝宝石介质谐振器技术测量MgB₂超导薄膜的微波表面电阻R_{s、0K时的穿透深度λ(0)和超导能隙Δ(0).λ(0)和Δ(0)的值是通过先测量样品穿透深度λ(T)的变化量Δλ(T)，然后由BCS理论模型拟合Δλ(T)的实验数据得到的.测试样 品是利用化学气相沉积技术在MgO(111)基片上制备的c轴织构的MgB2超导薄膜， 薄膜的超导转变温度和转变宽度分别为38K和01K.微波测试结果表明在10K，18GHz下M gB2薄膜的Rs约为100μΩ，可以和高质量的YBCO薄膜的Rs值相比拟；BCS理论拟合得到的MgB2超导薄膜的λ(0)=102nm，Δ(0)=113k Tc.}     

关于π-π共振态

本文从解析性和么正性出发,对具有共振行为的π-π散射分波振幅的形式作了普遍的讨论。理论中包含了一个标志与Breit-Wigner共振形式偏离的函数F_(l)^I)(v),当F_(l)^I)(v)=1时,振幅恰好具有Breit-Wigner共振形式。具体计算表明,这个函数与1有一定的偏离。利用ND^-1方法、交叉对称性、ρ与f⁰的Bootstrap近似,将所得到的振幅与-90的共振解。计算中考虑了非弹性过程和负半轴色散积分的贡献。计算结果得到,对于J=1,I=1态,v_R=6.4,Г₁=0.12;对于J=2,I=0态,v_(R2)=20,Г₂=0.016。这相当于m_ρ=762MeV,m_f⁰=1283MeV,ρ的半宽度约为45MeV。它们与目前的实验数据是很好符合的。     

两原子与双模腔场喇曼相互作用(g1≠g2)的辐射谱

研究了两个有效双能级原子与双模腔场具有不同耦合常数(g₁≠g₂)时通过喇曼相互作用的辐射谱,详细讨论了双模腔场分别处于不同数态时的情形,发现其辐射谱具有如下新特点:当模1腔场处于真空态,模2腔场处于弱场中时,随着R=g₂/g₁的增加,辐射谱交替出现对称的10峰、6峰结构,与单模双原子情形相比较,更为灵敏地反映出两原子与腔场间不同的喇曼相互作用强度;当模1腔场处于真空态、模2腔场处于强场中时,0相似文献   

Global dynamics of a novel multi-group model for computer worms

In this paper, we study worm dynamics in computer networks composed of many autonomous systems. A novel multigroup SIQR (susceptible-infected-quarantined-removed) model is proposed for computer worms by explicitly considering anti-virus measures and the network infrastructure. Then, the basic reproduction number of worm R0 is derived and the global dynamics of the model are established. It is shown that if R0 is less than or equal to 1, the disease-free equilibrium is globally asymptotically stable and the worm dies out eventually, whereas, if R0 is greater than 1, one unique endemic equilibrium exists and it is globally asymptotically stable, thus the worm persists in the network. Finally, numerical simulations are given to illustrate the theoretical results.     

Analysis of epidemic models with demographics in metapopulation networks

In this paper, two susceptible–infected–susceptible (SIS) epidemic models are presented and analyzed by reaction–diffusion processes with demographics in metapopulation networks. Firstly, an SIS model with constant-inputting is discussed. The model has a disease-free equilibrium, which is locally asymptotically stable when the basic reproduction number is less than unity, otherwise it is unstable. It has an endemic equilibrium, which is globally asymptotically stable. Secondly, in another SIS model, the birth rate is the form of Logistic. Similarly, the stability of disease-free equilibrium and endemic equilibrium is also proved. Finally, numerical simulations are performed to illustrate the analytical results.     

Internal symmetry groups of quantum geons

In canonical quantum gravity asymptotically trivial diffeomorphisms not deformable to the identity can act nontrivially on the quantum state space. We show that for many 3-manifolds, the inequivalent diffeomorphisms comprise coverings in SU(2) of crystallographic groups. When the diffeomorphism R_2π associated with 2π-rotation is nontrivial, state vectors can have half-integral angular momentum; we list all 3-manifolds with R_2π trivial.     

Improved Ligand-Field Theory with Effect of Electron-Phonon Interaction

Traditional ligand-field theory has to be improved by taking into account both “pure electronic” contribution and electron-phonon interaction one (including lattice-vibrational relaxation energy). By means of improved ligand-field theory, R₁, R₂, R₃', R₂', and R₁' lines, U band, ground-state zero-field-splitting (GSZFS), and ground-state g factors of ruby and/or GSGG:Cr³⁺ as well as thermal shifts of GSZFS, R₁ line and R₂ line of ruby have been calculated. The results are in very good agreement with the experimental data. Moreover, it is found that the value of cubic-field parameter given by traditional ligand-field theory is inappropriately large. For thermal shifts of GSZFS, R₁ line and R₂ line of ruby, several conclusions have also been obtained.     

The effect of infected external computers on the spread of viruses: A compartment modeling study

Inevitably, there exist infected computers outside of the Internet. This paper aims to understand how infected external computers affect the spread of computer viruses. For that purpose, a new virus–antivirus spreading model, which takes into account the effect of infected/immune external computers, is established. A systematic study shows that, unlike most previous models, the proposed model admits no virus-free equilibrium and admits a globally asymptotically stable viral equilibrium. This result implies that it would be practically impossible to eradicate viruses on the Internet. As a result, inhibiting the virus prevalence to below an acceptable level would be the next best thing. A theoretical study reveals the effect of different parameters on the steady virus prevalence. On this basis, a number of suggestions are made so as to contain virus spreading.     

Energy Spectrum of La3Lu2Ga3O12：Cr^3＋ and Its Pressure-Induced R-Line-Shift Reversal

By means of both the theory for pressure-induced Shifts （PS） of energy spectra and the theory for shifts of energy spectra due to electron-phonon interaction （EPI）, the normal-pressure energy spectra of α and β centers of Cr^3＋ ions for LLGG：Cr^3＋ and the PS＇s of R1 lines and U band of these centers have been calculated at 10 K, respectively. The total calculated results are in very good agreement with the experimental data. For LLGG：Cr^3＋, the pressureinduced low-high crystal-field transition and the reversal of R1-line PS take place. The pressure-dependent variation of Rmix^ei （2E - 4T2） [mixing-degree of （t2^2 （^3T1）e^4T2） and （t2^3 E） base-wavefunctions in the wavefunction of R1 state without EPI] plays a key role for the reversal of R1-line PS. The behavior of the pure electronic PS of R1 line is quite different from that of the PS of R1 line due to EPI. It is the combined effect of them that gives rise to the total PS of R1 line. The comparison between R1-line PS＇s of GSGG：Cr^3＋ and LLGG：Cr^3＋ has been made. It is found that a peak of R1-line PS appears at Rmix^ei （^2E - ^4T2） ≈ 0.08.     

Stability analysis of multi-group deterministic and stochastic epidemic models with vaccination rate

We discuss in this paper a deterministic multi-group MSIR epidemic model with a vaccination rate, the basic reproduction number R0, a key parameter in epidemiology, is a threshold which determines the persistence or extinction of the disease. By using Lyapunov function techniques, we show if R0 is greater than 1 and the deterministic model obeys some conditions, then the disease will prevail, the infective persists and the endemic state is asymptotically stable in a feasible region. If R0 is less than or equal to 1, then the infective disappear so the disease dies out. In addition, stochastic noises around the endemic equilibrium will be added to the deterministic MSIR model in order that the deterministic model is extended to a system of stochastic ordinary differential equations. In the stochastic version, we carry out a detailed analysis on the asymptotic behavior of the stochastic model. In addition, regarding the value of R0, when the stochastic system obeys some conditions and R0 is greater than 1, we deduce the stochastic system is stochastically asymptotically stable.Finally, the deterministic and stochastic model dynamics are illustrated through computer simulations.     

Energy Spectra of the Tunable Laser Crystal Gd3Ga5O12:Cr3+ and Their Pressure-Induced Shifts

By means of both the theory for pressure-induced shifts (PS) of energy spectra and the theory for shifts of energy spectra due to electron-phonon interaction (EPI), at 300 K, the `pure electronic' contributions and the contributions from EPI to R₁ line, R₂ line, and U band of GGG:Cr³⁺ as well as their PS have been calculated, respectively. The total calculated results are in good agreement with all the experimental data. Their physical origins have been explained. It is found that the mixing-degree of |t₂²(³T₁)e ⁴T₂> and |t₂³²E> base-wavefunctions in the wavefunctions of R₁ level of GGG:Cr³⁺ is considerable under normal pressure, and the mixing-degree rapidly decreases with increasing pressure. The change of the mixing-degree with pressure plays a key role for PS of R₁ line or R₂ line. At 300 K, both the temperature-independent contribution to R₁ line (or R₂ line or U band) from EPI and the temperature-dependent one are important. The remarkable difference between pressure-dependent behaviors of PS of R₁ lines of GGG:Cr³⁺ and GSGG:Cr³⁺ results from the differences of their microscopic properties. The features of emission spectra of GGG:Cr³⁺ at various pressures have satisfactorily been explained.     

Energy Spectrum of YAG:Cr3+ and Thermal Shifts of Its R Lines

Traditional ligand-field theory has to be improved by taking into account both “pure electronic” contribution and electron-phonon interaction one (including lattice-vibrational relaxation energy). By means of improved ligand-field theory, R₁, R₂, R'₃, R'₂, and R'₁ lines, U band, ground-state zero-field-splitting (GSZFS) and ground-state g factors as well as thermal shifts of R₁ line and R₂ line of YAG:Cr³⁺ have been calculated. The results are in very good agreement with the experimental data. In contrast with ruby, the octahedron of ligand oxygen ions surrounding the central Cr³⁺ ion in YAG:Cr³⁺ is compressed along the [111] direction. Thus, for YAG:Cr³⁺ and ruby, the splitting of t₂³⁴A₂ (or t₂³²E) has opposite order, and the trigonal-field parameters of the two crystals have opposite signs. In thermal shifts of R₁ and R₂ lines of YAG:Cr³⁺, the temperature-dependent contributions due to EPI are dominant.