Coevolutionary extremal dynamics on gasket fractal

We considered a Bak-Sneppen model on a Sierpinski gasket fractal. We calculated the avalanche size distribution and the distribution of distances between subsequent minimal sites. To observe the temporal correlations of the avalanche, we estimated the return time distribution, the first-return time, and the all-return time distribution. The avalanche size distribution follows the power law, P(s)∼s−τ, with the exponent τ=1.004(7). The distribution of jumping sites also follows the power law, P(r)∼r−π, with the critical exponent π=4.12(4). We observe the periodic oscillation of the distribution of the jumping distances which originated from the jumps of the level when the minimal site crosses the stage of the fractal. The first-return time distribution shows the power law, Pf(t)∼t−τf, with the critical exponent τf=1.418(7). The all-return time distribution is also characterized by the power law, Pa(t)∼t−τa, with the exponent τa=0.522(4). The exponents of the return time satisfy the scaling relation τf+τa=2 for τf?2.     

Fluctuations of trading volume in a stock market

We consider the probability distribution function of the trading volume and the volume changes in the Korean stock market. The probability distribution function of the trading volume shows double peaks and follows a power law, P(V/〈V〉)∼(V/〈V〉)^−α at the tail part of the distribution with α=4.15(4) for the KOSPI (Korea composite Stock Price Index) and α=4.22(2) for the KOSDAQ (Korea Securities Dealers Automated Quotations), where V is the trading volume and 〈V〉 is the monthly average value of the trading volume. The second peaks originate from the increasing trends of the average volume. The probability distribution function of the volume changes also follows a power law, , where V_r=V(t)−V(t−T) and T is a time lag. The exponents β depend on the time lag T. We observe that the exponents β for the KOSDAQ are larger than those for the KOSPI.     

A triangle model of criminality

This paper is concerned with a quantitative model describing the interaction of three sociological species, termed as owners, criminals and security guards, and denoted by X, Y and Z respectively. In our model, Y is a predator of the species X, and so is Z with respect to Y. Moreover, Z can also be thought of as a predator of X, since this last population is required to bear the costs of maintaining Z.We propose a system of three ordinary differential equations to account for the time evolution of X(t), Y(t) and Z(t) according to our previous assumptions. Out of the various parameters that appear in that system, we select two of them, denoted by H, and h, which are related with the efficiency of the security forces as a control parameter in our discussion. To begin with, we consider the case of large and constant owners population, which allows us to reduce (3), (4) and (5) to a bidimensional system for Y(t) and Z(t). As a preliminary step, this situation is first discussed under the additional assumption that Y(t)+Z(t) is constant. A bifurcation study is then performed in terms of H and h, which shows the key role played by the rate of casualties in Y and Z, that results particularly in a possible onset of bistability. When the previous restriction is dropped, we observe the appearance of oscillatory behaviours in the full two-dimensional system. We finally provide a exploratory study of the complete model (3), (4) and (5), where a number of bifurcations appear as parameter H changes, and the corresponding solutions behaviours are described.     

Scaling and memory effect in volatility return interval of the Chinese stock market

We investigate the probability distribution of the volatility return intervals τ for the Chinese stock market. We rescale both the probability distribution P_q(τ) and the volatility return intervals τ as to obtain a uniform scaling curve for different threshold value q. The scaling curve can be well fitted by the stretched exponential function , which suggests memory exists in τ. To demonstrate the memory effect, we investigate the conditional probability distribution P_q(τ|τ₀), the mean conditional interval 〈τ|τ₀〉 and the cumulative probability distribution of the cluster size of τ. The results show clear clustering effect. We further investigate the persistence probability distribution P_±(t) and find that P₋(t) decays by a power law with the exponent far different from the value 0.5 for the random walk, which further confirms long memory exists in τ. The scaling and long memory effect of τ for the Chinese stock market are similar to those obtained from the United States and the Japanese financial markets.     

Method for measurements of second-order nonlinear optical coefficient based on Z-scan

The method for measuring second-order nonlinear optical coefficients based on well-known Z-scan is presented. The influence of linear absorption coefficients on normalized transmittance is discussed. Using this method, we obtained the second-order nonlinear coefficient d₃₁(5%MgO:LiNbO₃) = 4.5 × 10⁻¹² m/v at 1064 nm, which agrees well with theoretical calculations and previous well-known values.     

Peculiar statistical properties of Chinese stock indices in bull and bear market phases

Chinese stock markets have experienced an extraordinary bull market since Jan 2006, which attracted global eyes. We investigate the statistical properties of the indices’ log-return r(t) for the bull market (Jan 2006-Oct 2007) and the previous bear market (Jan 2001-Dec 2005). Here we report three peculiar features of r(t): (i) the cumulative distribution function curve of r(t) in the bull market is similar to that in the bear market; (ii) the autocorrelation function of r(t) in the bull market has a stronger negative correlation and a shorter correlation time than that in the bear market; (iii) the bull market shows stronger long-term correlation than the bear market. This work has relevance to understanding novel statistical properties in economic systems.     

Isothermal adsorption kinetics on heterogeneous surfaces

Adsorption kinetics on energetically heterogeneous surfaces under isothermal conditions is analyzed using the uniform energy distribution model. Considering the quasi-equilibrium of surface diffusion between the adsorption sites with different energy, the kinetic equations dΘ/dt=(k_ap−A_dK_diff)(1−Θ) for first-order adsorption and dΘ/dt=k_ap(1−Θ)²−A_dK_diffΘ(1−Θ) for dissociative adsorption are obtained, where K_diff is a coefficient describing the surface diffusion equilibrium, which depends on the coverage and the energy distribution. Under isochoric conditions with p decreasing due to adsorption, surface diffusion accelerates the rate towards equilibrium significantly, as observed in static calorimetric adsorption experiments. An approximate solution in Lagergren form is derived for this condition.     

Compactification and signature transition in Kaluza-Klein spinor cosmology

We study the classical and quantum cosmology of a 4 + 1-dimensional space-time with a non-zero cosmological constant coupled to a self-interacting massive spinor field. We consider a spatially flat Robertson-Walker universe with the usual scale factor R (t) and an internal scale factor a (t) associated with the extra dimension. For a free spinor field the resulting equations admit exact solutions, whereas for a self-interacting spinor field one should resort to a numerical method for exhibiting their behavior. These solutions give rise to a degenerate metric and exhibit signature transition from a Euclidean to a Lorentzian domain. Such transitions suggest a compactification mechanism for the internal and external scale factors such that a ∼ R⁻¹ in the Lorentzian region. The corresponding quantum cosmology and the ensuing Wheeler-DeWitt equation have exact solutions in the mini-superspace when the spinor field is free, leading to wavepackets undergoing signature change. The question of stabilization of the extra dimension is also discussed.     

Influence of Nb substitution for Fe on the magnetic and magneto-impedance properties of amorphous and annealed Fe76.5−xSi13.5B9Cu1Nbx (x=0–7) ribbons

We report a systematic study of the influence of Nb substitution for Fe on the magnetic properties and magneto-impedance (MI) effect in amorphous and annealed Fe_76.5−xSi_13.5B₉Cu₁Nb_x (x=0, 1, 2, 3, 4, 5, 6, and 7) ribbons. The amorphous ribbons were annealed at different temperatures ranging from 530 to 560 °C in vacuum for different annealing times between 5 and 20 min. We have found that for the as-quenched amorphous ribbons, the substitution of Nb for Fe first increases the saturation magnetization (M_s) and decreases the coercivity (H_c) until x=3, for which the largest M_s∼152 emu/g and the smallest H_c∼1.3 Oe are obtained, then an opposite trend is found for x>3. The largest MI ratio (ΔZ/Z∼38% at f=6 MHz) is achieved in the amorphous ribbon with x=3. A similar trend has been observed for the annealed ribbons. The most desirable magnetic properties (M_s∼156 emu/g and H_c∼1.8 Oe) and the largest MI ratio (ΔZ/Z∼221% at f=6 MHz) are achieved for the x=3 sample annealed at 540 °C for 15 min. A correlation between the microstructure, magnetic properties, and MI effect in the annealed ribbons has been established.     

Incorporation of Effects of Diffusion into Advection-Mediated Dispersion in Porous Media

The distribution of solute arrival times, W(t;x), at position x in disordered porous media does not generally follow Gaussian statistics. A previous publication determined W(t;x) in the absence of diffusion from a synthesis of critical path, percolation scaling, and cluster statistics of percolation. In that publication, W(t;x) as obtained from theory, was compared with simulations in the particular case of advective solute transport through a two-dimensional model porous medium at the percolation threshold for various lengths x. The simulations also did not include the effects of diffusion. Our prediction was apparently verified. In the current work we present numerical results related to moments of W(x;t), the spatial solute distribution at arbitrary time, and extend the theory to consider effects of molecular diffusion in an asymptotic sense for large Peclet numbers, P_e. However, results for the scaling of the dispersion coefficient in the range 1<P_e<100 agree with those of other authors, while results for the dispersivity as a function of spatial scale also appear to explain experiment.     

Domain growth dynamics in multicomponent vesicles composed of BSM/DOPC/cholesterol

We have investigated the domain growth dynamics in vesicles composed of BSM/DOPC/cholesterol using fluorescence microscopy. A ternary mixture of equimolar BSM, DOPC, and cholesterol was employed, and two fluorescent dyes were added for comparison studies. We found that in the early stage the number of the domains on the vesicle surface, N(t), decayed with time as N(t)∼t^−2/3, which confirmed previous theoretical prediction and numerical simulation, while in the late stage N(t) decreased more quickly, as ∼t^−β, with β≈2. We discuss the faster growth dynamics based on the collision-induced collision mechanism.     

Magnetic collapse and electronic phase transitions at high pressure in transition metal oxides

A review of electronic and magnetic phase transition in metal oxides with strong electron correlations (SEC) is given. The bandwidth control of the insulator gap is expected in the Hubbard model when the decreasing of the interatomic distance results in the bandwidth W(P) increase and at some critical value P_c, W(P_c)∼U and the Mott–Hubbard gap disappears. The other situation takes place in transition metal boroxides FeBO₃ and GdFe₃(BO₃)₄, where the increase of crystal field parameter Δ(P) results in the high spin–low spin crossover.     

The energy spectral analysis of the strong-coupled superlattice

We study the energy spectrum of the strong-coupled superlattice. The barriers affect the energy spectral statistics in a small scale. The nearest-neighbor energy-level distribution P(s) and the spectral rigidity Δ₃(L) demonstrated the GOE (Gaussian Orthogonal Ensemble) distribution. In the whole scale, with the electric field increasing, the spectral rigidity Δ₃(L) changes from the Poisson-type like distribution to the Wigner-type like distribution due to the change of the energy-level long-correlation, while the P(s) indicates that the system demonstrates to be integrable. The near-degeneracy of levels makes the level statistics complex.     

A new deterministic complex network model with hierarchical structure

We introduce a new simple pseudo tree-like network model, deterministic complex network (DCN). The proposed DCN model may simulate the hierarchical structure nature of real networks appropriately and have the unique property of ‘skipping the levels’, which is ubiquitous in social networks. Our results indicate that the DCN model has a rather small average path length and large clustering coefficient, leading to the small-world effect. Strikingly, our DCN model obeys a discrete power-law degree distribution P(k)∝k^−γ, with exponent γ approaching 1.0. We also discover that the relationship between the clustering coefficient and degree follows the scaling law C(k)∼k⁻¹, which quantitatively determines the DCN's hierarchical structure.     

Current fluctuations in chain of nanoparticles

We have fabricated and analyzed devices where an electrode gap was bridged by a chain of citrate stabilized gold particles. The current-voltage characteristic I∼ζ(V−Vt) with voltage threshold Vt≈0 and scaling exponent ζ=0.91 is attributed to charge transport in a one-dimensional path. We observe current fluctuations in the frequency range 3-100 mHz as function of time as a result of conformational changes in the citrate molecules induced by charge transfer across the molecules.     

Magnetic relaxation in pulse-magnetized high-temperature superconductors

A magnetic filed relaxation at the center of a pulse-magnetized single-domain Y–Ba–Cu–O superconductor at 78 K has been studied. In case of a weak magnetization, the magnetic flux density increases logarithmically and normalized relaxation rate defined as S = −d(lnB)/d(lnt) is negative (S = −0.037). When an external magnetic field magnitude increases, the relaxation rate first decreases in absolute value, then changes sign (becomes positive, S > 0) and after reaching some maximum finally reduces to a very small value. Non-monotonous dependence of S vs. H_a is explained by a non-homogeneous local temperature distribution during a pulse magnetization.     

Annealing induced microstructural evolution of electrodeposited electrochromic tungsten oxide films

A significant influence of microstructure on the electrochromic and electrochemical performance characteristics of tungsten oxide (WO₃) films potentiostatically electrodeposited from a peroxopolytungstic acid (PPTA) sol has been evaluated as a function of annealing temperature. Powerful probes like X-ray diffractometry (XRD), transmission electron microscopy (TEM), UV-vis spectrophotometry, multiple step chronoamperometry and cyclic voltammetry have been employed for the thin film characterization. The as-deposited and the film annealed at 60 °C are composed of nanosized grains with a dominant amorphous phase, as well as open structure which ensues from a nanoporous matrix. This ensures a greater number of electroactive sites and a higher reaction area thereby manifesting in electrochromic responses superior to that of the films annealed at higher temperatures. The films annealed at temperatures ≥250 °C are characterized by a prominent triclinic crystalline structure and a hexagonal phase co-exists at temperatures ≥400 °C. The deleterious effect on the electrochromic properties of the film with annealing is ascribed to the loss of porosity, densification and the increasing crystallinity and grain size. Amongst all films under investigation, the film annealed at 60 °C exhibits a high transmission modulation (ΔT ∼ 68%) and coloration efficiency (η ∼ 77.6 cm² C⁻¹) at λ = 632.8 nm, charge storage capacity (Q_ins ∼ 21 mC cm⁻²), diffusion coefficient (6.08 × 10⁻¹⁰ cm² s⁻¹), fast color-bleach kinetics (t_c ∼ 275 s and t_b ∼ 12.5 s) and good electrochemical activity, as well as reversibility for the lithium insertion-extraction process upon cycling. The remarkable potential, which the film annealed at 60 °C has, for practical “smart window” applications has been demonstrated.     

Quasi-Debye response of ion-hopping conduction at lowest frequencies

On the basis of the relaxation mode theory, quasi-Debye response in the dynamic conductivity by hopping ions is theoretically investigated in three-dimensional random lattices with a uniform distribution of activation energies. It is shown at lowest frequencies that the dynamic conductivity is approximately given by σ(ω)∼σ(0)+A″ω^s″, s″=2−n, where n is a non-integer exponent originated from the mode diffusion length and density of states. The numerical analyses give rise to some values of s″<2, for example s″∼1.5, which behaves as s″→2 with increasing temperature.     

Optical investigation of charge-transfer transitions in spinel Co3O4

Optical transitions in normal-spinel Co₃O₄ have been identified by investigating the variation of its optical absorption spectrum with the replacement of Co by Zn. Three optical-transition structures were located at about 1.65, 2.4, and 2.8 eV from the measured dielectric function of Co₃O₄ by spectroscopic ellipsometry. The variation of the absorption structures with the Zn substitution (Zn_xCo_3−xO₄) can be explained in terms of charge-transfer transitions involving d states of Co ions. The 1.65 eV structure is assigned to a d-d charge-transfer transition between the t_2g states of octahedral Co³⁺ ion and t₂ states of tetrahedral Co²⁺ ion, t_2g(Co³⁺)→t₂(Co²⁺). The 2.4 and 2.8 eV structures are interpreted as due to charge-transfer transitions involving the p states of O²⁻ ion: p(O²⁻)→t₂(Co²⁺) for the 2.4 eV absorption and p(O²⁻)→e_g(Co³⁺) for the 2.8 eV absorption. The observed gradual reduction of the 1.65 and 2.4 eV absorption strength with the increase of the Zn composition for Zn_xCo_3−xO₄ can be explained in terms of the substitution of the tetrahedral Co²⁺ sites by Zn²⁺ ions. The crystal-field splitting Δ_Oh between the e_g and the t_2g states of the octahedral Co³⁺ ion is estimated to be 2 eV.     

Kinetic Limit of N-Body Description of Wave–Particle Self-Consistent Interaction

A system of N particles $\xi ^N = x_1 ,\upsilon_1,...,x_N ,\upsilon _N )$ interacting self-consistently with one wave Z = A exp(iφ) is considered. Given initial data (Z ^(N)(0), ξ ^N (0)), it evolves according to Hamiltonian dynamics to (Z ^(N)(t), ξ ^N (t)). In the limit N → ∞, this generates a Vlasov-like kinetic equation for the distribution function f(x, v, t), abbreviated as f(t), coupled to the envelope equation for Z: initial data (Z ^(∞)(0), f(0)) evolve to (Z ^(∞)(t), f(t)). The solution (Z, f) exists and is unique for any initial data with finite energy. Moreover, for any time T>0, given a sequence of initial data with N particles distributed so that the particle distribution f ^N(0) → f(0) weakly and with Z ^(N)(0) → Z(0) as N → ∞, the states generated by the Hamiltonian dynamics at all times 0 ≤ t ≤ T are such that (Z ^(N)(t), f ^N(t)) converges weakly to (Z ^(∞)(t), f(t)).