Invasion percolation between two sites in two, three, and four dimensions

The mass distribution of invaded clusters in non-trapping invasion percolation between an injection site and an extraction site has been studied, in two, three, and four dimensions. This study is an extension of the recent study focused on two dimensions by Araújo et al. [A.D. Araújo, T.F. Vasconcelos, A.A. Moreira, L.S. Lucena, J.S. Andrade Jr., Phys. Rev. E 72 (2005) 041404] with respect to higher dimensions. The mass distribution exhibits a power-law behavior, P(m)∝m^−α. It has been found that the index α for p_e<p_c, p_c being the percolation threshold of a regular percolation, appears to be independent of the value of p_e and is also independent of the lattice dimensionality. When p_e=p_c, α appears to depend marginally on the lattice dimensionality, and the relation α=τ−1, τ being the exponent associated with cluster size distribution of a regular percolation via n_s∝s^−τ, appears to be valid.     

Spatial fluctuations in reaction-limited aggregation

A general method is used for describing reaction-diffusion systems, namely van Kampen's method of compounding moments, to study the spatial fluctuations in reaction-limited aggregation processes. The general formalism used here and in subsequent publications is developed. Then a particular model is considered that is of special interest, since it describes the occurrence of a phase transition (gelation). The corresponding rate constants for the reaction between two clusters of sizei and sizej areK _ij=ij (i, j=1, 2,). For thediffusion constants D _j of clusters of sizej the following class of models is considered:D _j=D if 1Js andD _j=0 ifj>s. The casess= ands< are studied separately. For the models= the equal-time and the two-time correlation functions are calculated; this modelbreaks down at the gel point. The breakdown is characterized by a divergence of the density fluctuations, and is caused by the large mobility of large clusters. For all models withs< the density fluctuations remain finite att _c, and the equal-time correlation functions in the pre- and in the post-gel stage are calculated. Many explicit and asymptotic results are given. From the exact solution the upper critical dimension in this gelling model isd _c=2.     

Spectral methods and cluster structure in correlation-based networks

We investigate how in complex systems the eigenpairs of the matrices derived from the correlations of multichannel observations reflect the cluster structure of the underlying networks. For this we use daily return data from the NYSE and focus specifically on the spectral properties of weight W_ij=|C|_ij−δ_ij and diffusion matrices D_ij=W_ij/s_j−δ_ij, where C_ij is the correlation matrix and s_i=∑_jW_ij the strength of node j. The eigenvalues (and corresponding eigenvectors) of the weight matrix are ranked in descending order. As in the earlier observations, the first eigenvector stands for a measure of the market correlations. Its components are, to first approximation, equal to the strengths of the nodes and there is a second order, roughly linear, correction. The high ranking eigenvectors, excluding the highest ranking one, are usually assigned to market sectors and industrial branches. Our study shows that both for weight and diffusion matrices the eigenpair analysis is not capable of easily deducing the cluster structure of the network without a priori knowledge. In addition we have studied the clustering of stocks using the asset graph approach with and without spectrum based noise filtering. It turns out that asset graphs are quite insensitive to noise and there is no sharp percolation transition as a function of the ratio of bonds included, thus no natural threshold value for that ratio seems to exist. We suggest that these observations can be of use for other correlation based networks as well.     

Reconnection dynamics for quantized vortices

By analyzing trajectories of solid hydrogen tracers in superfluid ⁴He, we identify tens of thousands of individual reconnection events between quantized vortices. We characterize the dynamics by the minimum separation distance δ(t) between the two reconnecting vortices both before and after the events. Applying dimensional arguments, this separation has been predicted to behave asymptotically as δ(t)≈A(κ|t−t₀|)^1/2, where κ=h/m is the quantum of circulation. The major finding of the experiments and their analysis is strong support for this asymptotic form with κ as the dominant controlling feature, although there are significant event to event fluctuations. At the three-parameter level the dynamics may be about equally well-fit by two modified expressions: (a) an arbitrary power-law expression of the form δ(t)=B|t−t₀|^α and (b) a correction-factor expression δ(t)=A(κ|t−t₀|)^1/2(1+c|t−t₀|). The measured frequency distribution of α is peaked at the predicted value α=0.5, although the half-height values are α=0.35 and 0.80 and there is marked variation in all fitted quantities. Accepting (b) the amplitude A has mean values of 1.24±0.01 and half height values of 0.8 and 1.6 while the c distribution is peaked close to c=0 with a half-height range of −0.9 s⁻¹ to 1.5 s⁻¹. In light of possible physical interpretations we regard the correction-factor expression (b), which attributes the observed deviations from the predicted asymptotic form to fluctuations in the local environment and in boundary conditions, as best describing our experimental data. The observed dynamics appear statistically time-reversible, which suggests that an effective equilibrium has been established in quantum turbulence on the time scales (≤0.25 s) investigated. We discuss the impact of reconnection on velocity statistics in quantum turbulence and, as regards classical turbulence, we argue that forms analogous to (b) could well provide an alternative interpretation of the observed deviations from Kolmogorov scaling exponents of the longitudinal structure functions.     

Green function theory of Curie and order—order transitions in ferromagnetic systems

Dipolar critical temperatures in ferromagnetic systems with isotropic bilinear and biquadratic exchange are investigated by means of the Green function technique. Expressions are found for both the familiar Curie temperature, T_c, and the less well known order-order transition temperature, T_o, at which, under appropriate conditions, the magnetic ordering undergoes a change between fully aligned and canted ferromagnetism. At T = 0, a fully aligned state has <s_i^z = s for spin s and all lattice sites i, while a canted state has 〈s_i^z〉<s. It is shown independently of the Green function analysis that the T = 0 ground state is fully aligned if α, the ratio of biquadratic to bilinear exchange integrals, obeys ?[2s(s?1)]^?1<α< [2s²?2s+1]^?1. The region below the lower limit is identified as the range in which canted ferromagnetism can occur and is a range that does not appear to have been considered previously via the Green function formalism.The temperature dependence of the magnetic ordering is investigated by means of the double-time temperature-dependent Green function formalism. A new decoupling scheme is derived and used to reduce higher order Green functions to lowest order. It is found that a canted state, occuring at low temperatures, undergoes a transition to a fully aligned state at a temperature T₀ and subsequently becomes disordered at temperature T_c. Transitions to paramagnetism are found to be second order for α<α_c and first order for α?α_c where α_c is a critical value that depends on the atomic spin and weakly on the lattice structure. A phase diagram is given to illustrate the results, and a comparison is made with the corresponding results found in mean field theory.     

An analytic approach to the measurement of nestedness in bipartite networks

We present an index that measures the nestedness pattern of bipartite networks, a problem that arises in theoretical ecology. Our measure is derived using the sum of distances of the occupied elements in the incidence matrix of the network. This index quantifies directly the deviation of a given matrix from the nested pattern. In the simplest case the distance of the matrix element a_i,j is d_i,j=i+j, the Manhattan distance. A generic distance is obtained as d_i,j=(i^χ+j^χ)^1/χ. The nestedness index is defined by ν=1−τ, where τ is the “temperature” of the matrix. We construct the temperature index using two benchmarks: the distance of the complete nested matrix that corresponds to zero temperature and the distance of the average random matrix where the temperature is defined as one. We discuss an important feature of the problem: matrix occupancy ρ. We address this question using a metric index χ that adjusts for matrix occupancy.     

Iron isotope effect on Tc in optimally-doped (Ba,K)Fe2As2 (Tc = 38 K) and SmFeAsO1−y (Tc = 54 K) superconductors

We report the iron isotope effect on a transition temperature (T_c) in an optimally-doped (Ba,K)Fe₂As₂ (T_c = 38 K) and SmFeAsO_1−y (T_c = 54 K) superconductors. In order to obtain the reliable isotope shift in T_c, twin samples with different iron isotope mass are synthesized in the same conditions (simultaneously) under high-pressure. We have found that (Ba,K)Fe₂As₂ shows an inverse iron isotope effect α_Fe = −0.18 ± 0.03 while SmFeAsO_1−y shows a small iron isotope effect α_Fe = −0.02 ± 0.01, where the isotope exponent α is defined by T_c ∼ M^−α (M is the isotopic mass). The results show that α_Fe changes in the iron-based superconductors depending on the system. The distinct iron isotope effects imply the exotic coupling mechanism in the iron-based superconductors.     

Rotational band crossings in the actinides

In the actinides bothi _13/2 protons andj _15/2 neutrons are close to the Fermi surface. At rapid rotation these high-j particles will unpair and align their orbital angular momentum along the axis of rotation giving rise tos-bands that cross the ground-state band. Coulomb excitation of the odd nuclei ₂₃₇ ⁹³ Np (established up to the 45/2⁺ state) and ₂₃₅ ⁹² U (established up to the 51/2^? state) provides specific information about these band crossings: From the saturating alignment of the odd high-j particle in both nuclei at intermediate rotational frequencies we find the aligned angular momentum of thei _13/2 protons-band to be 6.6? while the corresponding value for thej _15/2 neutrons-band is 5.5?. At more rapid rotation above ?ω=0.18 MeV we observe additional alignment in²³⁵U. This is ascribed to the interaction of the protons-band. From the gradual onset of the additional alignment we deduce that forZ=92 the protons-band interacts strongly with the ground-state band and from a comparison of the actual amount of alignment with the full value of 6.6? we estimate the crossing to occur around ?gw _c ^p =0.25 MeV.     

The effect of Cu substitution on the A1g mode of La0.7Sr0.3MnO3 manganites

We report on the first Raman data of Cu substituted La_1−ySr_yMn_1−xCu_xO₃ (0≤x≤0.10 and 0.17≤y≤0.3, accordingly in order to have the same Mn⁴⁺/[Mn⁴⁺+Mn³⁺] ratio), collected in the frequency range 100-900 cm⁻¹ and at room temperature, with parallel (e_i∥e_s) and crossed (e_i⊥e_s) polarizations of the incident (e_i) and scattered (e_s) light. Spectra were fitted with a Drude-Lorentz model, and peaks at 190-220 and 430 cm⁻¹, together with two broad structures centered at near 500 and 670 cm⁻¹, have been found. We also have observed that the A_1g mode is substantially shifted with increasing Cu substitution. The A_1g phonon shift is a linear function of the tolerance factor t and the rhombohedral angle α_r, thus following the structural changes of the MnO₆ octahedra in the system.     

Edge-based-attack induced cascading failures on scale-free networks

Most previous existing works on cascading failures only focused on attacks on nodes rather than on edges. In this paper, we discuss the response of scale-free networks subject to two different attacks on edges during cascading propagation, i.e., edge removal by either the descending or ascending order of the loads. Adopting a cascading model with a breakdown probability p of an overload edge and the initial load (k_ik_j)^α of an edge ij, where k_i and k_j are the degrees of the nodes connected by the edge ij and α is a tunable parameter, we investigate the effects of two attacks for the robustness of Barabási-Albert (BA) scale-free networks against cascading failures. In the case of α<1, our investigation by the numerical simulations leads to a counterintuitive finding that BA scale-free networks are more sensitive to attacks on the edges with the lowest loads than the ones with the highest loads, not relating to the breakdown probability. In addition, the same effect of two attacks in the case of α=1 may be useful in furthering studies on the control and defense of cascading failures in many real-life networks. We then confirm by the theoretical analysis these results observed in simulations.     

SUSY-QCD corrections to scalar quark pair production in e+e− annihilation

We calculate the supersymmetric O(α_s) QCD corrections to the cross section e⁺e⁻ → q̃_iq̃_j (i, j = 1,2) within the Minimal Supersymmetric Standard Model. We pay particular attention to the case of the left-right squark mixing and to the renormalization of the mixing angle. The corrections due to gluino exchange turn out to be smaller than those due to gluon exchange, but they can be significant at higher energies, even for a gluino mass of a few hundred GeV.     

Mass distribution in n—polymer stochastic aggregation and large—mass behaviour

The exact solutions of the rate equations of the n-polymer stochastic aggregation involving two types of clusters, active and passive for the kernel \dprⁿ_k=1s_(ik)(s_(ik)=i_k) and \dsumⁿ_k=1s_(ik)(s_(ik)=i_k), are obtained. The large-mass behaviours of the final mass distribution of the active and passive clusters have scaling-like forms, although the models exhibit different properties. Respectively, they have different decay exponents γ=\dfrac{2n+1}{2(n-1)} and γ=q+\dfrac{2n+1}{2(n-1)} for \dprⁿ_{k=1}s(ik)(s(ik)=ik) and γ=\dfrac 3{2(n-1)} and γ=q+\dfrac 3{2(n-1)} for \dsumⁿk=1}s(ik)(s(ik)=ik), which include exponents of two-polymer stochastic aggregation. We also find that gelation is suppressed for kernel \dprⁿk=1s(ik)(s(ik)=ik) which is different from the deterministic aggregation.}     

Structure and high pressure behaviour of organic crystals based on aromatically substituted 1,3,4-oxadiazoles

The crystalline structure of a new compound containing the 1,3,4-oxadiazole moiety, 4-(5-methyl-1,3,4-oxadiazole-2yl-)-N,N′-dimethyl-phenylamine (MODPA) was determined. It shows a monoclinic structure with space group P2₁/c and lattice parameters: a=1.02997(6), b=0.64840(4), c=1.58117(10) nm and β=99.4820(10)°. To study the intermolecular interactions in oxadiazole containing organic crystals, X-ray studies on MODPA and 2,5-diphenyl-1,3,4-oxadiazole (DPO) were performed up to 5 GPa at room temperature. The Murnaghan equation of state is used to describe the compression behaviour of both substances. From these results, the bulk modulus and its pressure derivative were determined. The values obtained are: K₀=6.3 GPa and K′₀=6.8 for MODPA and K₀=7.3 GPa and K′₀=6.7 for DPO. Additionally, measurements under increasing temperature at ambient pressure were carried out to evaluate the thermal expansion coefficient: α=1.8×10⁻⁴ K⁻¹ for MODPA and α=1.9×10⁻⁴ K⁻¹ for DPO.     

2D-to-3D percolation crossover of metal-insulator composites

Percolation properties and d.c. conductivity were determined for an L²×h-random resistor network model of metal-insulator composite films. The effects of the thickness h on the percolation threshold and conductivity were studied numerically in the limit of an infinite size of the L²-plane parallel to the film. For thicknesses ranging from h/L=0.01 to h/L=0.24, a crossover between a finite-size regime and a saturation regime was observed at h/L≈0.1. In the finite-size regime (h/L?0.01), the percolation threshold scales as pc(h)−pc3∝h−1/x, the exponent x being compatible with that of the critical exponent of the 3D correlation length, ν₃. The conductivity exponent t appeared to depend linearly on the ratio h/L with a slope νD compatible with 2+ν₂, where ν₂ is the 2D correlation length exponent. In the saturation regime, a scaling correction for the percolation threshold was found with an exponent 1+1/ν₃. In this regime we also observed a logarithmic dependence of the conductivity exponent on h/L.     

Magnetic properties of (Nd,Pr)–Fe–B nanocomposite over quenched and annealed ribbons

The base alloys of nominal composition (Nd_0.75Pr_0.25)_yFe_balanceB_x (y=10−9.2 and x=6−19.2) were chosen to study the influence of RE/B ratio, smaller than stochiometric composition on magnetic properties of over quenched and annealed ribbons. From X-ray diffraction analysis of these ribbons, the α-Fe and Fe₃B phases were observed along with (Nd,Pr)₂Fe₁₄B major phase. The average grain size was calculated using these patterns as: 35 nm for α-Fe, 45 nm for (Nd,Pr)₂Fe₁₄B and 22 nm for Fe₃B particles. TEM analysis also supported the nano distribution of the above phases. These X-ray graphs support the idea of exchange coupling between hard and soft phases responsible for the observed magnetic properties. In these ribbons the saturation magnetization J_s and remnant magnetization J_r increases from 1.19 T to 1.66 T and from 0.65 T to 0.91 T, respectively as RE/B ratio increases. The increase in J_s and J_r may be attributed to the presence of exchange coupling between these phases. The corresponding coercivity _jH_c decreases from 673.33 to 271.33 k Am⁻¹. The maximum energy product (BH)_max initially increases from 72.42 kJ m⁻³to 109.85 kJ m⁻³ up to RE/B≈1 and then decreases to 58.5 kJ m⁻³, depending on the shape of second quadrant B–H loop. The coercivity mechanism observed from initial hysteresis curve was considered to be nucleation of domain wall.     

Evolutionary prisoner’s dilemma game on weighted scale-free networks

This paper investigates the evolutionary prisoner’s dilemma on weighted scale-free networks. The weighted networks are generated by adopting Barabási-Albert scale-free network and assigning link weight with w_ij=(k_i×k_j)^β. Simulation results show that the cooperation frequency has a strong dependence on β. The value of β which is associated with the maximal cooperation frequency has been sought out. Moreover, Gini coefficient and Pareto exponent of the system’s wealth distribution are investigated. The inequality of wealth distribution is minimized at β≈−1.     

Heat treatment effects on microstructure and magnetic properties of Mn-Zn ferrite powders

Mn-Zn ferrite powders (Mn_0.5Zn_0.5Fe₂O₄) were prepared by the nitrate-citrate auto-combustion method and subsequently annealed in air or argon. The effects of heat treatment temperature on crystalline phases formation, microstructure and magnetic properties of Mn-Zn ferrite were investigated by X-ray diffraction, thermogravimetric and differential thermal analysis, scanning electron microscopy and vibrating sample magnetometer. Ferrites decomposed to Fe₂O₃ and Mn₂O₃ after annealing above 550 °C in air, and had poor magnetic properties. However, Fe₂O₃ and Mn₂O₃ were dissolved after ferrites annealing above 1100 °C. Moreover, the 1200 °C annealed sample showed pure ferrite phase, larger saturation magnetization (M_s=48.15 emu g⁻¹) and lower coercivity (H_c=51 Oe) compared with the auto-combusted ferrite powder (M_s=44.32 emu g⁻¹, H_c=70 Oe). The 600 °C air annealed sample had the largest saturation magnetization (M_s=56.37 emu g⁻¹) and the lowest coercivity (H_c=32 Oe) due to the presence of pure ferrite spinel phase, its microstructure and crystalline size.     

Thermal isomerization and cyclization of 1-naphthylacetylene: Experimental results, quantum chemical and transition state theory calculations

The isomerization of 1-naphthylacetylene diluted in argon was studied behind reflected shock waves in a 2 in i.d. single pulse shock tube over the temperature range 1000-1250 K and overall densities of ∼3 × 10⁻⁵ mol/cm³. The only reaction product found in the post shock mixtures was acenaphthylene. The first order rate constant of the isomerization was found to be k = 2.08 × 10¹² exp(−54.2 × 10³/RT) s⁻¹, where R is expressed in units of cal/K mol. Potential energy surfaces of the cyclization reaction 1-naphthylacetylene → acenaphthylene and the isomerization 1-naphthylacetylene → 2-naphthylacetylene were calculated using the Becke three-parameter hybrid method with Lee-Yang-Parr correlation functional approximation (B3LYP). Structure, energy and frequency calculations were carried out with the Dunning correlation consistent polarized double ζ (cc-pVDZ) basis set. The rate constant (k_∞) for the 1-naphthylacetylene → acenaphthylene cyclization was calculated using transition state theory, the value obtained is k_∞ = 3.52 × 10¹² exp(−55.9 × 10³/RT) s⁻¹, where R is expressed in units of cal/K mol. The agreement between the experiment and the calculations is very good. RRKM calculations were done to transfer k_∞ to the pressure of the single pulse shock tube experiments. In view of high temperature and the large molecule involved the deviation from k_∞ is very small. The isomerization 1-naphthylacetylene → 2-naphthylacetylene proceeds via the formation of an unstable intermediate 1,2-naphthalenocyclobutene and has a high barrier of ∼83.5 kcal/mol. In view of this high barrier, the isomerization cannot compete with the cyclization that proceeds with a barrier of ∼56 kcal/mol.     

Lorentz contracted geometrical model

The model assumes that when two high energy particles collide each behaves as a geometrical object which has a Gaussian density and is spherically symmetric except for the Lorentz-contraction in the incident direction. Folding the two spatial distribution together we obtain the slope (b) of the elastic diffraction peak in terms of the c.m. velocities (β_i and β_j) and the sizes (A_i and A_j) of the two incident particles. These sizes are assumed to have the experimental s-dependence of σ_tot ∝ πA² for each reaction. The combined s-dependence of the σ_tot's and the β's gives the s-dependence of the elastic slope $\text{b}{}_{\mathrm{ij}}\text{(s) =}\text{1}\text{2}\text{(A}{}_{\mathrm{i}}{}^2\text{β}{}_{\mathrm{i}}{}^2\text{+ A}{}_{\mathrm{j}}{}^2\text{β}{}_{\mathrm{j}}{}^2\text{)}\text{σ}{}^{\mathrm{ij}}{}_{\mathrm{<mtext>tot</mtext>}}\text{(s)}\text{σ}{}^{\mathrm{ij}}{}_{\mathrm{<mtext>tot</mtext>}}\text{(∞)}$. This formula agrees with the experimental slope for p-p, $\text{p}$-p, K⁺-p, K^?-p and π^±-p elastic scattering from 3 to 1500 GeV/c, with only 3 parameters: A_π² = 6.1, A_K² = 3.3 and A_p² = 10.5 (GeV/c)^?2.