Noise effects in two different biological systems

We investigate the role of the colored noise in two biological systems: (i) adults of Nezara viridula (L.) (Heteroptera: Pentatomidae), and (ii) polymer translocation. In the first system we analyze, by directionality tests, the response of N. viridula individuals to subthreshold signals plus noise in their mating behaviour. The percentage of insects that react to the subthreshold signal shows a nonmonotonic behaviour, characterized by the presence of a maximum, as a function of the noise intensity. This is the signature of the non-dynamical stochastic resonance phenomenon. By using a “soft” threshold model we find that the maximum of the input-output cross correlation occurs in the same range of noise intensity values for which the behavioural activation of the insects has a maximum. Moreover this maximum value is lowered and shifted towards higher noise intensities, compared to the case of white noise. In the second biological system the noise driven translocation of short polymers in crowded solutions is analyzed. An improved version of the Rouse model for a flexible polymer is adopted to mimic the molecular dynamics by taking into account both the interactions between adjacent monomers and the effects of a Lennard-Jones potential between all beads. The polymer dynamics is simulated in a two-dimensional domain by numerically solving the Langevin equations of motion in the presence of thermal fluctuations and a colored noise source. At low temperatures or for strong colored noise intensities the translocation process of the polymer chain is delayed. At low noise intensity, as the polymer length increases, we find a nonmonotonic behaviour for the mean first translocation time of the polymer centre of inertia. We show how colored noise influences the motion of short polymers, by inducing two different regimes of translocation in the dynamics of molecule transport.     

时滞对一类单位负反馈二阶振荡系统的正面作用分析

针对一类被控对象具有二阶系统标准形式的振荡系统进行了稳定性分析,讨论了闭环系统为单位负反馈时信号传输时滞对控制系统性能的影响.通过绘制和分析相对阻尼系数在不同取值区间的Nyquist曲线,得出了时滞与闭环系统稳定性的关系,并对各种情况进行了单位阶跃响应的实例仿真.仿真结果表明了分析的正确性.     

金融动力学的时空关联与大波动特性——兼谈中西方金融市场的对比研究

文章扼要地评述了金融物理学研究进展,介绍了文章作者在金融动力学时空关联方面的最新研究成果,特别关注中西方金融市场的对比研究.唯象理论研究表明,西方金融市场的价格收益率和波动率的时间关联显示杠杆效应,而中国金融市场则显示反杠杆效应;一种价格收益率和波动率的反馈相互作用可以解释杠杆和反杠杆效应的起源.西方金融市场的个体股票价格的交叉关联呈现标准的行业板块结构,而中国金融市场展示的是一种特殊的板块结构,如"ST板块"和"蓝筹板块"等.股票价格大波动可分为动力学内部产生的和外部事件诱导的两大类.金融动力学的时间反演不对称性,主要来源于外部事件诱导的大波动.     

Reply to comment on “On the controversy around Daganzo’s requiem for and Aw-Rascle’s resurrection of second-order traffic flow models” by H.M. Zhang

This contribution compares several different approaches allowing one to derive macroscopic traffic equation directly from microscopic car-following models. While it is shown that some conventional approaches lead to theoretical problems, it is proposed to use an approach reminding of smoothed particle hydrodynamics to avoid gradient expansions. The derivation circumvents approximations and, therefore, demonstrates the large range of validity of macroscopic traffic equations, without the need of averaging over many vehicles. It also gives an expression for the “traffic pressure”, which generalizes previously used formulas. Furthermore, the method avoids theoretical inconsistencies of macroscopic traffic models, which have been criticized in the past by Daganzo and others.     

Synchronization in evolving snowdrift game model

The interaction between the evolution of the game and the underlying network structure with evolving snowdrift game model is investigated. The constructed network follows a power-law degree distribution typically showing scale-free feature. The topological features of average path length, clustering coefficient, degree-degree correlations and the dynamical feature of synchronizability are studied. The synchronizability of the constructed networks changes by the interaction. It will converge to a certain value when sufficient new nodes are added. It is found that initial payoffs of nodes greatly affect the synchronizability. When initial payoffs for players are equal, low common initial payoffs may lead to more heterogeneity of the network and good synchronizability. When initial payoffs follow certain distributions, better synchronizability is obtained compared to equal initial payoff. The result is also true for phase synchronization of nonidentical oscillators.     

Partial clustering prevents global crystallization in a binary 2D colloidal glass former

A mixture of two types of super-paramagnetic colloidal particles with long-range dipolar interaction is confined by gravity to the flat interface of a hanging water droplet. The particles are observed by video microscopy and the dipolar interaction strength is controlled via an external magnetic field. The system is a model system to study the glass transition in 2D, and it exhibits partial clustering of the small particles (N. Hoffmann et al., Phys. Rev. Lett. 97, 078301 (2006)). This clustering is strongly dependent on the relative concentration of big and small particles. However, changing the interaction strength reveals that the clustering does not depend on the interaction strength. The partial clustering scenario is quantified using Minkowski functionals and partial structure factors. Evidence that partial clustering prevents global crystallization is discussed.     

Electronic properties close to Dirac cone in two-dimensional organic conductor α-(BEDT-TTF)<Subscript>2</Subscript>I<Subscript>3</Subscript>

A zero-gap state (ZGS) has been found in a bulk system of two-dimensional organic conductor, α-(BEDT-TTF)₂I₃ salt which consists of four sites of donor molecules in a unit cell. In the present paper, the characteristic of the ZGS is analyzed in detail and the electronic properties are examined in the vicinity of the Dirac point where the conduction and valence bands degenerate to form the zero-gap. The eigenvectors of the energy band have four components of respective sites, where two of them correspond to inequivalent sites and the other two correspond to equivalent sites. It is shown that the former exhibits an exotic momentum dependence around the contact point and the latter shows almost a constant dependence. The density of states of each site close to the Dirac point is calculated to demonstrate the temperature dependence of the local magnetic susceptibility and the local nuclear magnetic relaxation rate. Further, the robust property of the ZGS against the anion potential is also shown by using the second-order perturbation.     

The equilibrium limit of a constitutive model for two-phase granular mixtures and its numerical approximation

In this paper we analyze the equilibrium limit of the constitutive model for two-phase granular mixtures introduced in Papalexandris (2004) [13], and develop an algorithm for its numerical approximation. At, equilibrium, the constitutive model reduces to a strongly coupled, overdetermined system of quasilinear elliptic partial differential equations with respect to the pressure and the volume fraction of the solid granular phase. First we carry a perturbation analysis based on standard hydrostatic-type scaling arguments which reduces the complexity of the coupling of the equations. The perturbed system is then supplemented by an appropriate compatibility condition which arises from the properties of the gradient operator. Further, based on the Helmholtz decomposition and Ladyzhenskaya’s decomposition theorem, we develop a projection-type, Successive-Over-Relaxation numerical method. This method is general enough and can be applied to a variety of continuum models of complex mixtures and mixtures with micro-structure. We also prove that this method is both stable and consistent hence, under standard assumptions, convergent. The paper concludes with the presentation of representative numerical results.     

Upwind-biased FORCE schemes with applications to free-surface shallow flows

In this paper we develop numerical fluxes of the centred type for one-step schemes in conservative form for solving general systems of conservation laws in multiple-space dimensions on structured meshes. The proposed method is an extension of the multidimensional FORCE flux developed by Toro et al. (2009) [14]. Here we introduce upwind bias by modifying the shape of the staggered mesh of the original FORCE method. The upwind bias is evaluated using an estimate of the largest eigenvalue, which in any case is needed for selecting a time step. The resulting basic flux is first-order accurate and monotone. For the linear advection equation, the proposed UFORCE method reproduces exactly the upwind Godunov method. Extension to non-linear systems has been done empirically via the two-dimensional inviscid shallow water equations. Second order of accuracy in space and time on structured meshes is obtained in the framework of finite volume methods. The proposed method improves the accuracy of the solution for small Courant numbers and intermediate waves associated with linearly degenerate fields (contact discontinuities, shear waves and material interfaces). It achieves comparable accuracy to that of upwind methods with approximate Riemann solvers, though retaining the simplicity and efficiency of centred methods. The performance of the schemes is assessed on a suite of test problems for the two-dimensional shallow water equations.