Degree distributions of the visibility graphs mapped from fractional Brownian motions and multifractal random walks

The dynamics of a complex system is usually recorded in the form of time series, which can be studied through its visibility graph from a complex network perspective. We investigate the visibility graphs extracted from fractional Brownian motions and multifractal random walks, and find that the degree distributions exhibit power-law behaviors, in which the power-law exponent α is a linear function of the Hurst index H of the time series. We also find that the degree distribution of the visibility graph is mainly determined by the temporal correlation of the original time series with minor influence from the possible multifractal nature. As an example, we study the visibility graphs constructed from three Chinese stock market indexes and unveil that the degree distributions have power-law tails, where the tail exponents of the visibility graphs and the Hurst indexes of the indexes are close to the α∼H linear relationship.     

Polarization of atomic hydrogen lines upon collision with an electron beam

A technique is described for the analytical calculation of the degree of linear polarization of atomic hydrogen lines formed by several radiative transitions with different polarizations upon excitation by an electron impact. The degree of linear polarization of the line L of the hydrogen atom is calculated as an example. The analytical equations used are derived by the Born method. The results of the analytical calculation are compared with experiment and with other calculations. The effective excitation cross sections and the degree of linear polarization of the H_α and H_β lines of the hydrogen atom are calculated analytically for the case of electron-beam excitation. The results of the analytical calculation of the effective excitation cross section of the H_α line are compared with the available experimental and calculated data.     

Energy gap and transition temperature of highly disordered and amorphous thallium- and indium-films

Thin and pure Tl-films and In-films with different impurities (Ag, Te, Ge, Sb) are condensed onto a cooled substrate at 4 K. Measurements of the energy gap by means of the tunnel effect and the transition temperature of the weak-coupling superconductor thallium are carried out as a function of the degree of disorder of the films. The ratioα=2Δ ₀/kT _c increases proportional to the reciprocal mean free path from 3.5 for the annealed film up to 3.8 for the highly disordered film. For In-films condensed by quenching with impurity additions, one finds a linear relation between energy gap and transition temperature. In-films with Sb-additive are obtained in an amorphous phase with a ratioα=2Δ ₀/kT _c of 4.4. The amorphous state of the In/Sb-films is confirmed by measurements of the electric conductivity and the Hall-effect.     

A scale-free network with limiting on vertices

We propose and analyze a random graph model which explains a phenomena in the economic company network in which company may not expand its business at some time due to the limiting of money and capacity. The random graph process is defined as follows: at any time-step t, (i) with probability α(k) and independently of other time-step, each vertex is inactive which means it cannot be connected by more edges, where k is the degree of v_i at the time-step t; (ii) a new vertex v_t is added along with m edges incident with v_t at one time and its neighbors are chosen in the manner of preferential attachment. We prove that the degree distribution P(k) of this random graph process satisfies if α(⋅) is a constant α₀; and P(k)∝C₂k⁻³ if α(?)↓0 as ?↑∞, where C₁,C₂ are two positive constants. The analytical result is found to be in good agreement with that obtained by numerical simulations. Furthermore, we get the degree distributions in this model with m-varying functions by simulation.     

Blocking effects in irreversible adsorption of linear macromolecules

A new variant of random sequential adsorption (RSA), namely random sequential ballistic adsorption (RSBA), is proposed to explore the possible role of blocking effects in the adsorption dynamics of ballistically arriving objects. These objects upon adsorption can protrude outside the substrate and in turn can obstruct and hence reject the adsorption of newly arriving objects. Adsorption of linear macromolecules (modeled as infinitesimally thin needles), on a two-dimensional continuum substrate is studied using RSBA model. It is shown analytically that in late time regime, the number n(t) of adsorbed objects at time t follows a power law n(t) ∼ t^α, as in RSA, but with a different exponent, α = 2/3. Computer simulations are also carried out. The simulation results are found to be in close agreement with the analytical results. The exponent behavior for real experimental conditions is also analyzed.     

Recoil ranges of nuclei produced in α-induced reactions on 1107 109Ag and 115In

Integral recoil ranges of evaporation residues for the reactions ¹⁰⁷Ag(α, 3n), ¹⁰⁷Ag(α, α2n), ¹⁰⁹Ag(α, 2n), ¹⁰⁹Ag(α, 3n), ¹⁰⁹Ag(α, 4n), ¹¹⁵In(α, 2n), ¹¹⁵In(α, 3n) and ¹¹⁵In(α, αn) have been measured in the energy range of 202 - 60 MeV α-particles using the conventional thick target thick catcher technique. Transfer of linear momenta to the product nuclei for the above reactions have been deduced from experimental recoil range data. Detailed comparisons of the observations with predictions of theoretical calculations based on statistical model are presented and discussed. For (α, xn) reactions, overall agreement between the theory and the experiment is found to be satisfactory specially at low projectile energy. In cases of (α, αxn) reactions, the theory failed to reproduce the experimental linear momentum transfer even at low incident alpha energy.     

Scaling laws of nonlinear Rayleigh-Taylor and Richtmyer-Meshkov instabilities in two and three dimensions

The late-time nonlinear evolution of the Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities for random initial perturbations is investigated using a statistical mechanics model based on single-mode and bubble-competition physics at all Atwood numbers ( A ) and full numerical simulations in two and three dimensions. It is shown that the RT mixing zone bubble and spike fronts evolve as h∼α·A·gt² with different values of α for the bubble and spike fronts. The RM mixing zone fronts evolve as h∼t^θ with different values of θ for bubbles and spikes. Similar analysis yields a linear growth with time of the Kelvin–Helmholtz mixing zone. The dependence of the RT and RM scaling parameters on A and the dimensionality will be discussed. The 3D predictions are found to be in good agreement with recent Linear Electric Motor (LEM) experiments.     

Impact of initial lattice structures on networks generated by traces of random walks

We show that the platform stage of network evolution plays a principal role in the topology of resulting networks generated by short-cuts stimulated by the movements of a random walker, the mechanism of which tends to produce power-law degree distributions. To examine the numerical results, we have developed a statistical method which relates the power-law exponent γ to random properties of the subgraph developed in the platform stage. As a result, we find that an important exponent in the network evolution is α, which characterizes the size of the subgraph in the form V∼t^α, where V and t denote the number of vertices in the subgraph and the time variable, respectively. 2D lattices can impose specific limitations on the walker’s diffusion, which keeps the value of α within a moderate range and provides typical properties of complex networks. 1D and 3D cases correspond to different ends of the spectrum for α, with 2D cases in between. Especially for 2D square lattices, a discontinuous change of the network structure is observed, which varies according to whether γ is greater or less than 2. For 1D cases, we show that emergence of nearly complete subgraphs is guaranteed by α<1/2, although the transient power-law is permitted at low increase rates of edges. Additionally, the model exhibits a spontaneous emergence of highly clustered structures regardless of its initial structure.     

Three-alpha force and the 3-α model of12C

We postulate a Gaussian three-body potential amongα particles and adjust its parameters so that, when it is added to the Ali-Bodmerα-α potential, a good fit to experimental energies of low-lying 0⁺ and 2⁺ states of¹²C is achieved. With these potentials we made a linear variational calculation in a basis of harmonic oscillator functions which are translationally invariant, completely symmetric, and have a definite orbital angular momentum. We study the influence of this three-body potential on elastic and inelastic form factors, transition widths, Coulomb energy and charge radius of the 3-α system. The 3-α potential improved results found with the Ali-Bodmer potential alone. We find the 0 ₂ ⁺ state to be a (non-rigid) linear chain and the ground state to be a triangle ofα particles.     

Choice of Efficient Linear Scale and Generalized Description of Internal Heat Transfer Coefficient in Porous Structures

The expedience of using the ratio of inertial β and viscous α hydraulic coefficients of a fluid flow in porous structures as the characteristic linear scale, when generalizing the experimental data on internal heat transfer in porous media, is shown. It is demonstrated that the correlation Nu = A · Pe, with both criteria based on β/α ratio, most efficiently describes the experimental data for a wide set of ordered and disordered porous structures, including sintered spheres, network materials, sintered felt and cellular foams of high porosity. The coefficient A depends on porosity and is equal to 0.004 for spheres, networks and felts, and 0.0004 for foams. For any specific case the values of α and β coefficients can be readily obtained from testing materials under consideration, control samples, or full-scale articles.     

The definition of the product δ(x)χx-α (α>0, real) and its applications

We introduce new space of continuous test functions S? having at x=0 an asymptotic expansion in Dirichlet series. It is shown that on the space S? the product δ(x)χx^-α(α>0, real) is a local linear continuous functional, proportional to the derivative of continuous order δ^(α) of Dirac delta. It is shown that the product δ(x)χx^-α occurs in quantum field theory asymptotically invariant with respect to the dilatation group, if we differentiate causal or retarded propagators.     

Alpha clustering in 4n nuclei from 4He to 40Ca

The α clustering in nuclei from ⁴He to ⁴⁰Ca has been presented on a systematic footing which depicts the similarities from nucleus to nucleus. Here, the isomorphic shell model has been employed, which is a hybrid between the conventional shell model and liquid drop model in conjunction with the nucleon finite size and which, in addition, uses no adjustable parameters. In the framework of the model an α-like particle is defined as four close-by nucleons (two neutrons and two protons) in relative angular momentum zero. Thus, up to ⁴⁰Ca nine such α-like particles and two deuterons are formed whose average positions are well specified in the model. Hence, each time an α-like particle is formed (following the aforementioned definition), this could have an average position only at one of the above nine available positions for such particles. Any 4n nucleus arranges its n α-like particles in the same way and any such arrangement corresponds to the ground state or to an excited state of this nucleus and serves as the band head of a rotational band. For ²⁰Ne nine such bands have been found, while for ¹²C and ²⁸Si two and five bands, respectively. The linear α-chain for ¹²C and persisting α-planar structures for heavier nuclei appear in a natural way in the framework of the model and are supported by many observables. The real novelty of this presentation is the fact that the axis of rotation and the number of rotating nucleons inside the same rotational band may change in such a way that the relevant moment of inertia increases monotonically in steps forming for each step a new branch of the band. Thus, several such bands have the same band head, a fact which closely resembles the phenomenon of superdeformation. This phenomenon here is the result of existence of several axes of symmetry and of several axes of rotation which, by changing the axis of rotation, permit the moment of inertia to increase up to the solid body limit.     

Evolutionary games on scale-free networks with a preferential selection mechanism

Considering the heterogeneity of individuals’ influence in the real world, we introduce a preferential selection mechanism to evolutionary games (the Prisoner’s Dilemma Game and the Snowdrift Game) on scale-free networks and focus on the cooperative behavior of the system. In every step, each agent chooses an individual from all its neighbors with a probability proportional to k^α indicating the influence of the neighbor, where k is the degree. Simulation results show that the cooperation level has a non-trivial dependence on α. To understand the effect of preferential selection mechanism on the evolution of the system, we investigate the time series of the cooperator frequency in detail. It is found that the cooperator frequency is greatly influenced by the initial strategy of hub nodes when α>0. This observation is confirmed by investigating the system behavior when some hub nodes’ strategies are fixed.     

Comments on “Scale-free networks without growth”

In [Y.-B. Xie, T. Zhou, B.-H. Wang, Scale-free networks without growth, Physica A 387 (2008) 1683-1688], a nongrowing scale-free network model has been introduced, which shows that the degree distribution of the model varies from the power-law form to the Poisson form as the free parameter α increases, and indicates that the growth may not be necessary for a scale-free network structure to emerge. However, the model implicitly assumes that self-loops and multiple-links are allowed in the model and counted in the degree distribution. In many real-life networks, such an assumption may not be reasonable. We showed here that the degree distribution of the emergent network does not obey a power-law form if self-loops and multiple-links are allowed in the model but not counted in the degree distribution. We also observed the same result when self-loops and multiple-links are not allowed in the model. Furthermore, we showed that the effect of self-loops and multiple-links on the degree distribution weakens as α increases and even becomes negligible when α is sufficiently large.     

Local preferential attachment model for hierarchical networks

In real-life networks, incomers may only connect to a few others in a local area for their limited information, and individuals in a local area are likely to have close relations. Accordingly, we propose a local preferential attachment model. Here, a local-area-network stands for a node and all its neighbors, and the new nodes perform nonlinear preferential attachment, , in local areas. The stable degree distribution and clustering-degree correlations are analytically obtained. With the increasing of α, the clustering coefficient increases, while assortativity decreases from positive to negative. In addition, by adjusting the parameter α, the model can generate different kinds of degree distribution, from exponential to power-law. The hierarchical organization, independent of α, is the most significant character of this model.     

Preconditioning the bidomain model with almost linear complexity

The bidomain model is widely used in electro-cardiology to simulate spreading of excitation in the myocardium and electrocardiograms. It consists of a system of two parabolic reaction diffusion equations coupled with an ODE system. Its discretisation displays an ill-conditioned system matrix to be inverted at each time step: simulations based on the bidomain model therefore are associated with high computational costs. In this paper we propose a preconditioning for the bidomain model either for an isolated heart or in an extended framework including a coupling with the surrounding tissues (the torso). The preconditioning is based on a formulation of the discrete problem that is shown to be symmetric positive semi-definite. A block LU decomposition of the system together with a heuristic approximation (referred to as the monodomain approximation) are the key ingredients for the preconditioning definition. Numerical results are provided for two test cases: a 2D test case on a realistic slice of the thorax based on a segmented heart medical image geometry, a 3D test case involving a small cubic slab of tissue with orthotropic anisotropy. The analysis of the resulting computational cost (both in terms of CPU time and of iteration number) shows an almost linear complexity with the problem size, i.e. of type nlog^α(n) (for some constant α) which is optimal complexity for such problems.     

Mean π-electron energy and ionization potential in linear polyacenes with many rings,and Hückel parameters

In n-ring linear polyacenes, it is argued that the mean energy per π-electron is a constant as n → ∞, affording a many-electron interpretation of the Hückel parameter β, while |α| is identified with the ionization potential I(n) as n → ∞.     

Effect of annealing atmosphere on microstructural and photoluminescence characteristics of multiferroic BiFeO3 thin films prepared by pulsed laser deposition technique

The effect of annealing atmosphere on microstructural and photoluminescence characteristics of multiferroic BiFeO₃ (BFO) thin films deposited by pulsed laser deposition (PLD) technique is reported. The films annealed in oxygen environment showed improved microstructure and photoluminescence (PL) characteristics. The PL spectra of oxygen-annealed BFO thin films at room temperature show a strong emission in the blue region. A plot of (αE)² vs. photon energy (E) (α-absorption coefficient) and the linear extrapolation to (αE)²=0 indicates a direct gap at 2.69±0.02 eV, which is in agreement with the previous reports. The results obtained in this study are accordingly expected to facilitate the understanding and optimization of BFO thin films for photovoltaic applications.     

Pre-equilibrium alpha emission accompanying deep-inelastic16O+58Ni collisions

α particles were measured in coincidence with projectile-like reaction products (oxygen and carbon) produced in deep-inelastic¹⁶O+⁵⁸Ni collisions at about 6 MeV/N bombarding energy. The kinematic analysis of the HI andα energies measured as a function ofΘ _α gives strong evidence for a sequential process: the target-like fragments are excited by the deep-inelastic collision and undergo subsequentα decay. In contrast, the angular correlations show a pronounced forward peak, indicative of direct or pre-equilibriumα emission. The emission time for the latter is estimated to be of the order of 2×10^?21 s. To resolve this conflict of co-existing statistical and direct features of the pre-equilibrium emission, the concept of a hot spot is proposed. From the angular correlation and from theα multiplicities, a local temperature ofT?3.5 MeV is deduced which agrees well with the temperature derived from the shape of theα spectra. The spot size is estimated to be 1/5 of the sphere.