Attack vulnerability of scale-free networks due to cascading failures

In this paper, adopting the initial load of a node i to be with k_i being the degree of the node i, we propose a cascading model based on a load local redistribution rule and examine cascading failures on the typical network, i.e., the BA network with the scale-free property. We find that the BA scale-free network reaches the strongest robustness level in the case of α=1 and the robustness of the network has a positive correlation with the average degree 〈k〉, where the robustness is quantified by a transition from normal state to collapse. In addition, we further discuss the effects of two different attacks for the robustness against cascading failures on our cascading model and find an interesting result, i.e., the effects of two different attacks, strongly depending to the value α. These results may be very helpful for real-life networks to avoid cascading-failure-induced disasters.     

Sub-coercive field dynamic hysteresis in morphotropic phase boundary composition of Pb(Zr1/2Ti1/2)O3-Pb(Zn1/3Nb2/3)O3 ceramic and its scaling behavior

Sub-coercive field dynamic ferroelectric hysteresis of a morphotropic phase boundary composition of the PZT-PZN ceramic was investigated under influence of the compressive stress. The scaling relation of hysteresis area 〈A〉 against frequency f, field amplitude E₀, and stress σ took a form of , which is not different significantly to that of other PZT-PZN compositions with pure tetragonal or rhombohedral structure, as well as to that of soft and hard PZT bulk ceramics. This study suggested that the domain structures, not ceramic compositions, played a key role in controlling dynamic hysteresis behavior of ferroelectric materials.     

The nature of the rectilinear diameter singularity

The rigorous explanation for the term |t|^2β in the rectilinear diameter equation is given (t=(T_c−T)/T_c, β is the critical exponent for the asymptotic form of the equation of state). The optimal order parameter, for which the branches of binodal are symmetric, is constructed within the canonical formalism. It is shown that the ratio of the amplitudes for the diameter singularity of the order parameter before |t|^1−α and |t|^2β, where α determines the behavior of the heat capacity and β is the critical exponent of the order parameter, takes the universal character modulo non-universal factor which depends on the thermodynamic class of the corresponding states. The analysis of entropy for argon and water leads to β=0.33 and the corresponding amplitude ratio .     

Statistical properties of volatility return intervals of Chinese stocks

The statistical properties of the return intervals τ_q between successive 1-min volatilities of 30 liquid Chinese stocks exceeding a certain threshold q are carefully studied. The Kolmogorov-Smirnov (KS) test shows that 12 stocks exhibit scaling behaviors in the distributions of τ_q for different thresholds q. Furthermore, the KS test and weighted KS test show that the scaled return interval distributions of 6 stocks (out of the 12 stocks) can be nicely fitted by a stretched exponential function with γ≈0.31 under the significance level of 5%, where is the mean return interval. The investigation of the conditional probability distribution P_q(τ|τ₀) and the mean conditional return interval 〈τ|τ₀〉 demonstrates the existence of short-term correlation between successive return interval intervals. We further study the mean return interval 〈τ|τ₀〉 after a cluster of n intervals and the fluctuation F(l) using detrended fluctuation analysis, and find that long-term memory also exists in the volatility return intervals.     

The inversion of diatomic Born-Oppenheimer-breakdown corrections

The inversion of diatomic vibration-rotation data to give the r dependence of operators is considered. For the Born-Oppenheimer energy levels E_vJ and for the expectation values 〈vJ|X(r)|vJ〉 of an operator X(r), the inversion is unambiguous if the reduced mass is known, leading to the potential energy function V(r) and to X(r). The breakdown of the Born-Oppenheimer approximation is represented in terms of three functions Qⁱ(r), Rⁱ(r), and Sⁱ(r) for each atom i. The function Qⁱ(r) can be removed by a transformation that changes the other functions to and , which still have one degree of indeterminacy. The effects of this indeterminacy in fits to truncated Hamiltonians is considered for the extensive data for isotopomers of the LiH molecule. This discussion is relevant to a recent claim that the dipole moment and rotational g_J factor of LiH can be determined from a fit to field-free vibration-rotation spectra. The values obtained for these quantities are unreliable because they are strongly dependent on the constraints used in the Born-Oppenheimer-breakdown functions.     

Effects of attachment preferences on coevolution of opinions and networks

In the coevolution of network structures and opinion formation, we investigate the effects of a mixed population with distinctive relinking preferences on both the convergence time and the network structures. It has been found that a heterogeneous network structure is easier to be reached with more high-degree-preferential (HDP) nodes. There exists high correlation between the convergence time and the network heterogeneity. The heterogeneous degree distribution caused by preferential attachment accelerates the convergence to a consensus state and the shortened convergence time inhibits the occurrence of the following disquieting situation that occurs in a continuously evolving network: with preferential attachment and long-time evolvement, most of the nodes would become separated and only a few leaders would have immediate neighbors. Analytical calculations based on mean field theory reveal that both the transition point p_tr and the consensus time τ depend upon the standard deviation of the degree distribution σ_d. p_tr increases while τ decreases with the rise of σ_d. Functions of p_tr=〈k〉/(〈k〉+1) and are found. Theoretical analyses are in accordance with simulation data.     

Random walks and diameter of finite scale-free networks

Dynamical scalings for the end-to-end distance R_ee and the number of distinct visited nodes N_v of random walks (RWs) on finite scale-free networks (SFNs) are studied numerically. 〈R_ee〉 shows the dynamical scaling behavior , where is the average minimum distance between all possible pairs of nodes in the network, N is the number of nodes, γ is the degree exponent of the SFN and t is the step number of RWs. Especially, in the limit t→∞ satisfies the relation , where d is the diameter of network with for γ≥3 or for γ<3. Based on the scaling relation 〈R_ee〉, we also find that the scaling behavior of the diameter of networks can be measured very efficiently by using RWs.     

Multifractal Detrended Cross-Correlation Analysis of sunspot numbers and river flow fluctuations

We use the Detrended Cross-Correlation Analysis (DCCA) to investigate the influence of sun activity represented by sunspot numbers on one of the climate indicators, specifically rivers, represented by river flow fluctuation for Daugava, Holston, Nolichucky and French Broad rivers. The Multifractal Detrended Cross-Correlation Analysis (MF-DXA) shows that there exist some crossovers in the cross-correlation fluctuation function versus time scale of the river flow and sunspot series. One of these crossovers corresponds to the well-known cycle of solar activity demonstrating a universal property of the mentioned rivers. The scaling exponent given by DCCA for original series at intermediate time scale, , is λ=1.17±0.04 which is almost similar for all underlying rivers at 1σ confidence interval showing the second universal behavior of river runoffs. To remove the sinusoidal trends embedded in data sets, we apply the Singular Value Decomposition (SVD) method. Our results show that there exists a long-range cross-correlation between the sunspot numbers and the underlying streamflow records. The magnitude of the scaling exponent and the corresponding cross-correlation exponent are λ∈(0.76,0.85) and γ_×∈(0.30,0.48), respectively. Different values for scaling and cross-correlation exponents may be related to local and external factors such as topography, drainage network morphology, human activity and so on. Multifractal cross-correlation analysis demonstrates that all underlying fluctuations have almost weak multifractal nature which is also a universal property for data series. In addition the empirical relation between scaling exponent derived by DCCA and Detrended Fluctuation Analysis (DFA), is confirmed.     

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.     

Multifractal analysis of the fracture surfaces of foamed polypropylene/polyethylene blends

The two-dimensional multifractal detrended fluctuation analysis is applied to reveal the multifractal properties of the fracture surfaces of foamed polypropylene/polyethylene (PP/PE) blends at different temperatures. Nice power-law scaling relationship between the detrended fluctuation function F_q and the scale s is observed for different orders q and the scaling exponent h(q) is found to be a nonlinear function of q, confirming the presence of multifractality in the fracture surfaces. The multifractal spectra f(α) are obtained numerically through Legendre transform. The shape of the multifractal spectrum of singularities can be well captured by the width of spectrum and the difference of dimension . With the increase of the PE content, the fracture surface becomes more irregular and complex, as is manifested by the facts that increases and decreases from positive to negative. A qualitative interpretation is provided based on the foaming process.     

Quantum tomograms from intermediate entangled states

We show that for quantum tomography there exist two mutually conjugating intermediate coordinate-momentum entangled states |η₁,η_2〉λ,ν and |?₁,?_2〉σ,τ. The Radon transforms of the Wigner operators are just the pure-state density matrices and , respectively. As a result, the tomogram of quantum states is the module-square of their wave function in these representations. A new convenient formalism of quantum tomogram is thus established.     

The off-axis pyroelectric effect observed for lithium tetraborate

We find a pyroelectric current along the 〈110〉 direction of stoichiometric Li₂B₄O₇ so that the pyroelectric coefficient is nonzero but roughly 10⁻³ smaller than along the 〈001〉 direction of spontaneous polarization. Abrupt decreases in the pyroelectric coefficient along the 〈110〉 direction can be correlated with anomalies in the elastic stiffness contributing to concept that the pyroelectric coefficient is not simply a vector but has qualities of a tensor, as expected. The time dependent surface photovoltaic charging suggests that an inverse piezoelectric effect occurs at the (110) surface but not the (100) surface. Both effects along the 〈110〉 direction or at the (110) surface are distinct the conventional as a bulk pyroelectric effect.     

Effect of exchange-coupling interaction on anisotropy of grain in nanoscaled magnets

The effect of inter-grain exchange-coupling interaction on the anisotropy of grain in nanoscaled magnets has been investigated by putting forward an expression of anisotropy at grain boundary, , which is suitable for different coupling conditions, and expresses well the coherency between soft and hard grains. The average anisotropy of grain 〈K^ij〉 has been calculated based on and the theory of partial exchange-coupling interaction. It has been found that the average anisotropy of hard or soft grain, 〈K^hh〉 or 〈K^ss〉, increases with increasing grain size D monotonously when hard-hard or soft-soft grains couple. When soft-hard grains touch each other, with increasing D, the variation of average anisotropy of soft-hard grain 〈K〉 depends on the anisotropy at grain interface , which denotes the affection degree of hard grain on the anisotropy of soft grain. Compared with other results, it is more reasonable that ranges from to . The variations of anisotropy with D we calculated are consistent with those of coercivities given by other authors when is fixed in a certain range.     

Detection of changes in the fractal scaling of heart rate and speed in a marathon race

The aim of this study was to detect changes in the fractal scaling behavior of heart rate and speed fluctuations when the average runner’s speed decreased with fatigue. Scaling analysis in heart rate (HR) and speed (S) dynamics of marathon runners was performed using the detrended fluctuation analysis (DFA) and the wavelet based structure function. We considered both: the short-range (α₁) and the long-range (α₂) scaling exponents for the DFA method separated by a change-point, (box length), the same for all the races. The variability of HR and S decreased in the second part of the marathon race, while the cardiac cost time series (i.e. the number of cardiac beats per meter) increased due to the decreasing speed behavior. The scaling exponents α₁ and α₂ of HR and α₁ of S, increased during the race () as did the HR wavelet scaling exponent (τ). These findings provide evidence of the significant effect of fatigue induced by long exercise on the heart rate and speed variability.     

Origin of photoluminescence in nanocrystalline Si:H films

We have studied the origin of photoluminescence (PL) from hydrogenated nanocrystalline silicon (nc-Si:H) films produced by a plasma-enhanced chemical vapor deposition technique using SiF₄/SiH₄/H₂ gas mixtures. The nc-Si:H films were characterized using X-ray diffraction, infrared, Raman spectroscopy, optical absorption and stress, and were examined for PL by varying the deposition temperature (T_d) under two different hydrogen flow rate ([H₂]) conditions. The PL exhibited two peaks at around 1.7-1.75 and 2.2-2.3 eV. The peak energy, E_PL, of the 1.7-1.75-eV PL band was found to shift as T_d or [H₂] changes. It was found that the decrease in T_d acts to decrease the average grain size, 〈δ〉, and to increase both the optical band gap, , and the E_PL values. By contrast, the increase in [H₂] decreased the 〈δ〉 value, while increased the values of and E_PL. Thus, as either T_d decreases or [H₂] increases, it is found that a decrease in 〈δ〉 corresponds well with increases in and E_PL. As a consequence, it was suggested that an increase in E_PL of the 1.7-1.75-eV PL band can be connected with an increase in , through a decrease in 〈δ〉. However, the PL process cannot be connected with the transition between both the bands, related to formation of nanocrystals. Based on these results, it was proposed that the use of both low T_d and high [H₂] conditions would allow to grow nc-Si:H films with small grains.     

Finite and infinite dynamical systems of identical interacting particles

A dynamical system of infinite volume and of infinite number of identical interacting particles occupying energy levels has been constructed as the limit of an infinite sequence of finite, equivalent systems of increasing size and particle number. Systems both in equilibrium and in non-equilibrium state (designated S_∞=limS_k, , respectively, k=1,2,…) were investigated. The main results are:(i) The values in the T-limit (thermodynamic limit) of the physical quantities characterizing these systems are determined.(ii) The time evolution process both in and in systems is governed by the non-linear rate equations with common initial conditions p_i(t₀), where p_i(t)=n_i(t)/N are the occupation probabilities at time t. The time evolution process in the and systems is the same. The asymptotic approach to the equilibrium state is proved.(iii) For the case of the equilibrium state, the Boltzmann probability distribution p_i is given by the equation −lnp_i+a+e_ib=0 common to S_k and S_∞ systems with the same value of a and b. The term a=β⁻¹a_e, where a_e is the free energy per particle, and .(iv) The conditions for the equivalence of the systems being in equilibrium and also of the ones in non-equilibrium are stated.     

Complex Wavelet Transform of the Two-mode Quantum States

By employing the bipartite entangled state representation and the technique of integration within an ordered product of operators, the classical complex wavelet transform of a complex signal function can be recast to a matrix element of the squeezing-displacing operator U ₂(μ, σ) between the mother wavelet vector 〈ψ| and the two-mode quantum state vector |f〉 to be transformed. 〈ψ|U ₂(μ, σ)|f〉 can be considered as the spectrum for analyzing the two-mode quantum state |f〉. In this way, for some typical two-mode quantum states, such as two-mode coherent state and two-mode Fock state, we derive the complex wavelet transform spectrum and carry out the numerical calculation. This kind of wavelet-transform spectrum can be used to recognize quantum states.