Studies of beam propagation characteristics on apertured fractional Fourier transforming systems

Based on the principle that a rectangular function can be expanded into a sum of complex Gaussian functions with finite numbers, propagation characteristics of a Gaussian beam or a plane wave passing through apertured fractional Fourier transforming systems are analyzed and corresponding analytical formulae are obtained. Analytical formulae in different fractional orders are numerically simulated and compared with the diffraction integral formulae, the applicable range and exactness of analytical formulae are confirmed.It is shown that the calculating speed of using the obtained approximate analytical formulae, is several hundred times faster than that of using diffraction integral directly. Meanwhile, by using analytical formulae the effect of different aperture sizes on Gaussian beam propagation characteristics is numerically simulated, it is shown that the diffraction effect can be neglected when the aperture size is 5 times larger than the beam waist size.     

A general theory of harmonic wave propagation in linear periodic systems with multiple coupling

A general theory is presented of harmonic wave propagation in one-dimensional periodic systems with multiple coupling between adjacent periodic elements. The motion of each element is expressed in terms of a finite number of displacement coordinates. The nature and number of different wave propagation constants at any frequency are discussed, and the energy flow associated with waves having real, complex or imaginary propagation constants is investigated. Kinetic and potential energy functions are derived for the propagating waves and a generalized Rayleigh's Quotient and Rayleigh's Principle for the complex wave motion have been found. This is extended to yield a generalized Rayleigh-Ritz method of finding approximate, yet accurate, relationships between the frequencies and propagation constants of the propagating waves. The effect of damping is also considered, and a special class of “damped forced waves” is postulated for hysteretically damped periodic systems. An energy definition for the loss factor of these waves is found. Briefly considered is the two-dimensional multi-coupled periodic system in which a simple wave motion analogous to a plane wave propagates across the whole system.     

Assembly effect of groups in online social networks

Due to the popularity and growth of online social networks, security in these networks becomes a critical problem. Previous works have proved that a virus can spread effectively in social networks. In this paper, groups in social networks are studied. We notice that groups on social network services sites can assemble people with similar characteristics, which may promote virus propagation in these networks. After our analysis, it is found that the use of groups can shorten the distance among users, and hence it would cause faster virus spread. We propose a virus propagation model and simulate it in a group network to show the assembly effect of groups. Our result shows that even with only one random attack, a virus can still spread rapidly, and the direct contact among group members is the reason for fast spreading.     

The response of a beam to a transient pressure wave load

The dynamic behaviour of beam structures under pressure waves is investigated. The propagation of the bending waves under a moving single load is first studied for three types of beam: a Bernoulli-Euler beam, a beam with shear deflection and a Timoshenko beam. Then the responses of the Bernoulli-Euler and the Timoshenko beam are studied under moving pressure wave excitation. The results are presented as dynamic amplification factors (DAF). The influence of the load parameters (load shape, propagation speed, pressure wave duration, etc.) and the beam parameters (slenderness, damping, etc.) is discussed. The load shape (symmetrical, asymmetrical) and the propagation speed strongly influence the response. The results are compared with available approximate solutions for the corresponding lumped element, single degree of freedom model of the structure.     

无标度网络中最大传染能力限定的病毒传播问题研究

传统的病毒传播模型在无限大无标度网络上不存在病毒传播阈值,即无论病毒的传播速率多么低,病毒始终能够在网络中传播.但研究发现,这个结论是在网络中存在超级传染者的假设下得到的,然而许多真实的无标度网络中并不存在超级传染者.因此,文章提出了一个最大传染能力限定的病毒传播模型,并从理论上证明了在最大传染能力限定的无限大无标度网络上,病毒传播阈值是存在的;同时,也分析了最大传染能力限定下非零传播阈值与有限规模网络下非零传播阈值的本质区别,并解释了为什么人们总是认为传统病毒传播模型对许多真实网络病毒感染程度估计过高的 关键词： 无标度网络 最大传染能力 传播阈值 感染程度     

Power-law for axon diameters at branch point

Background

Axon calibers vary widely among different animals, neuron classes, and even within the same neuron. What determines the diameter of axon branches?

Results

We pursue the hypothesis that the axon caliber has evolved to minimize signal propagation delays, while keeping arbor volume to a minimum. For a general cost function, we show that the optimal diameters of mother and daughter branches at a bifurcation satisfy a power law. The derivation relies on the fact that the axon conduction speed scales as a power of axon diameter. Although available data are consistent with the law, there is a large spread in the data. Future experimental tests will determine whether this spread is due to biological variability or measurement error.

Conclusions

Minimization of arbor volume and signal propagation delay may have been an important factor in the evolution of the brain.

     

Free vibrations of a mono-coupled periodic system

Vibration problems of periodic systems can be analyzed efficiently by means of the transfer matrix method. The frequency equation for the whole system is shown to be obtained in terms of the eigenvalues, or their natural logarithms, which are often called “propagation constants”, of the transfer matrix for a single periodic subsystem. In case of a mono-coupled system this frequency equation may be solved graphically by using the propagation constant curve, thereby saving a great deal of computational effort. Two types of mono-coupled systems are considered as numerical examples: a spring-mass oscillating system and a continuous Timoshenko beam resting on regularly spaced knife-edge supports. Depending on whether the transfer matrix is derived by an analytical procedure or by the finite element method, the numerical solutions become either exact or approximate.     

Propagation of elliptical Gaussian beam passing through apertured paraxial optical systems

The propagation of elliptical Gaussian beam passing through paraxial optical systems with aperture is investigated analytically by using tensor method. The approximate formula for propagation of elliptical Gaussian beam through hard apertured optical systems is derived based on the fact that the circ function can be expanded into a finite sum of complex Gaussian functions. The derived formula provides a convenient tool for treating the propagation and transformation of elliptical Gaussian beam through apertured optical systems. As an application example, the propagation properties of elliptical Gaussian beam through apertured fractional Fourier systems are discussed.     

Online social networks—Paradise of computer viruses

Online social network services have attracted more and more users in recent years. So the security of social networks becomes a critical problem. In this paper, we propose a virus propagation model based on the application network of Facebook, which is the most popular among these social network service providers. We also study the virus propagation with an email virus model and compare the behaviors of a virus spreading on Facebook with the original email network. It is found that Facebook provides the same chance for a virus spreading while it gives a platform for application developers. And a virus will spread faster in the Facebook network if users of Facebook spend more time on it.     

基于有向网络的Email病毒传播模型及其震荡吸引子研究

基于有向Email网络和Email病毒传播特点,运用平均场方法建立Email病毒传播的时滞微分方程模型,研究Email病毒在有向网络中的震荡传播行为.理论上给出了震荡解的全局吸引子存在的充要条件,数值实验验证了吸引子的存在性和控制.研究表明,子图之间的传播概率决定吸引子的存在性,而有效传播率影响吸引子的振幅,因此这两个参数对于有效预测和控制Email病毒在网络上的传播规模具有重要意义.     

Phonon emission induced dynamic fracture phenomena

We use molecular dynamics simulations to calculate the phonon energy emitted during rapid crack propagation in brittle crystals. We show that this energy is different for different crack planes and propagation directions and that it is responsible for various phenomena at several length scales: energetically preferred crack systems and crack deflection at the atomic scale, reduced maximum crack speed with volume at the micrometer scale, and the inability of a crack to attain the theoretical limiting speed at the macroscale. We propose to include the contribution of this energy in the Freund equation of motion of a dynamically propagating crack.     

A virus spreading model for cognitive radio networks

Since cognitive radio (CR) networks could solve the spectrum scarcity problem, they have drawn much research in recent years. Artificial intelligence(AI) is introduced into CRs to learn from and adapt to their environment. Nonetheless, AI brings in a new kind of attacks specific to CR networks. The most powerful one is a self-propagating AI virus. And no spreading properties specific to this virus have been reported in the literature. To fill this research gap, we propose a virus spreading model of an AI virus by considering the characteristics of CR networks and the behavior of CR users. Several important observations are made from the simulation results based on the model. Firstly, the time taken to infect the whole network increases exponentially with the network size. Based on this result, CR network designers could calculate the optimal network size to slow down AI virus propagation rate. Secondly, the anti-virus performance of static networks to an AI virus is better than dynamic networks. Thirdly, if the CR devices with the highest degree are initially infected, the AI virus propagation rate will be increased substantially. Finally, it is also found that in the area with abundant spectrum resource, the AI virus propagation speed increases notably but the variability of the spectrum does not affect the propagation speed much.     

Finite volume evolution Galerkin method for hyperbolic conservation laws with spatially varying flux functions

We present a generalization of the finite volume evolution Galerkin scheme [M. Luká?ová-Medvid’ová, J. Saibertov’a, G. Warnecke, Finite volume evolution Galerkin methods for nonlinear hyperbolic systems, J. Comp. Phys. (2002) 183 533– 562; M. Luká?ová-Medvid’ová, K.W. Morton, G. Warnecke, Finite volume evolution Galerkin (FVEG) methods for hyperbolic problems, SIAM J. Sci. Comput. (2004) 26 1–30] for hyperbolic systems with spatially varying flux functions. Our goal is to develop a genuinely multi-dimensional numerical scheme for wave propagation problems in a heterogeneous media. We illustrate our methodology for acoustic waves in a heterogeneous medium but the results can be generalized to more complex systems. The finite volume evolution Galerkin (FVEG) method is a predictor–corrector method combining the finite volume corrector step with the evolutionary predictor step. In order to evolve fluxes along the cell interfaces we use multi-dimensional approximate evolution operator. The latter is constructed using the theory of bicharacteristics under the assumption of spatially dependent wave speeds. To approximate heterogeneous medium a staggered grid approach is used. Several numerical experiments for wave propagation with continuous as well as discontinuous wave speeds confirm the robustness and reliability of the new FVEG scheme.     

西北太平洋副热带模态水区域声传播特性*

西北太平洋副热带模态水(STMW)是在西北太平洋夏季出现的温跃层中温度、盐度和密度具有垂向均一性的水团。由于西北太平洋副热带模态水(STMW)的存在,深海声速剖面呈现出双跃层结构,对深海远程声传播产生较大的影响。本文对比分析了西北太平洋副热带模态水(STMW)区域夏冬两季典型声速剖面环境下的声传播规律。分析结果表明,夏季声速剖面环境下,声源位于浅层声道宽度内时,声传播为浅层声道的类深海声道传播与会聚区传播的复合形式。掠射角较小的声线被限制于浅层声道中,增加了会聚区内的到达结构,并且增强了在影区的声能量,在第二影区内的传播损失比冬季声速剖面环境下最多低近60dB。本文推导了浅层声道的截止频率的近似表达式,分析结果表明,截止频率主要由浅层声道的宽度和正梯度段的声速差值决定,夏季STMW区域浅层声道截止频率主要集中在100Hz左右。     

水声通信近似L0范数约束的BP网络均衡器*

针对稀疏水声信道的长时延扩展及梯度下降的权值迭代方案导致的神经网络均衡器收敛速度慢的问题,提出了近似L₀范数约束的BP神经网络均衡器。首先在传统BP网络均衡器基础上增加判决反馈项,然后在代价函数中对均衡器输入层到隐含层的权值增加L₀范数约束,构造新的代价函数,利用高斯族函数近似L₀范数约束,并根据不同隐层神经元节点输出权值的L₂范数设定近似参数。仿真结果表明,稀疏信道条件下,本方法相比传统的BP网络均衡器收敛速度更快,误码率更低,可以有效提升神经网络均衡器的性能。     

Augmented Riemann solvers for the shallow water equations over variable topography with steady states and inundation

We present a class of augmented approximate Riemann solvers for the shallow water equations in the presence of a variable bottom surface. These belong to the class of simple approximate solvers that use a set of propagating jump discontinuities, or waves, to approximate the true Riemann solution. Typically, a simple solver for a system of m conservation laws uses m such discontinuities. We present a four wave solver for use with the the shallow water equations—a system of two equations in one dimension. The solver is based on a decomposition of an augmented solution vector—the depth, momentum as well as momentum flux and bottom surface. By decomposing these four variables into four waves the solver is endowed with several desirable properties simultaneously. This solver is well-balanced: it maintains a large class of steady states by the use of a properly defined steady state wave—a stationary jump discontinuity in the Riemann solution that acts as a source term. The form of this wave is introduced and described in detail. The solver also maintains depth non-negativity and extends naturally to Riemann problems with an initial dry state. These are important properties for applications with steady states and inundation, such as tsunami and flood modeling. Implementing the solver with LeVeque’s wave propagation algorithm [R.J. LeVeque, Wave propagation algorithms for multi-dimensional hyperbolic systems, J. Comput. Phys. 131 (1997) 327–335] is also described. Several numerical simulations are shown, including a test problem for tsunami modeling.     

Approximate analytical expression for the kurtosis parameter of off-axial Hermite-cosine-Gaussian beams propagating through apertured and misaligned ABCD optical systems

The approximate analytical expression for the kurtosis parameter of off-axial Hermite-cosine-Gaussian beams (HCosGBs) propagating through apertured and misaligned ABCD optical systems is derived based on the approximate propagation equation of off-axial HCosGBs and an example is given to illustrate for its application. The method used in this paper could be extended to studying the kurtosis parameter of the Hermite-sinusoidal-Gaussian beams passing through apertured and misaligned ABCD optical systems.     

Propagation of the Hermite–Gaussian beams through misaligned optical system with a circular aperture

By means of expanding a hard-edged aperture into a finite sum of complex Gaussian functions, the approximate analytical formula of one kind of higher-order Gaussian beams called the Hermite–Gaussian beams (HGBs) passing through circular apertured and misaligned optical system is obtained in this paper. The result provides more convenience for studying its propagation than the usual way by using diffraction integral directly. Some numerical simulations are also given for illustrating the propagation properties of the HGBs through the circular apertured optical systems.     

Struggle for space: viral extinction through competition for cells

The design of protocols to suppress the propagation of viral infections is an enduring enterprise, especially hindered by limited knowledge of the mechanisms leading to viral extinction. Here we report on infection extinction due to intraspecific competition to infect susceptible hosts. Beneficial mutations increase the production of viral progeny, while the host cell may develop defenses against infection. For an unlimited number of host cells, a feedback runaway coevolution between host resistance and progeny production occurs. However, physical space limits the advantage that the virus obtains from increasing offspring numbers; thus, infection clearance may result from an increase in host defenses beyond a finite threshold. Our results might be relevant to devise improved control strategies in environments with mobility constraints or different geometrical properties.