Hypocenter interval statistics between successive earthquakes in the two-dimensional Burridge-Knopoff model

We study statistical properties of spatial distances between successive earthquakes, the so-called hypocenter intervals, produced by a two-dimensional (2D) Burridge-Knopoff model involving stick-slip behavior. It is found that cumulative distributions of hypocenter intervals can be described by the q-exponential distributions with q<1, which is also observed in nature. The statistics depend on a friction and stiffness parameters characterizing the model and a threshold of magnitude. The conjecture which states that q_t+q_r∼2, where q_t and q_r are an entropy index of time intervals and spatial intervals, respectively, can be reproduced semi-quantitatively. It is concluded that we provide a new perspective on the Burridge-Knopoff model which addresses that the model can be recognized as a realistic one in view of the reproduction of the spatio-temporal interval statistics of earthquakes on the basis of nonextensive statistical mechanics.     

A self-adapting herding model: The agent judge-abilities influence the dynamic behaviors

We propose a self-adapting herding model, in which the financial markets consist of agent clusters with different sizes and market desires. The ratio of successful exchange and merger depends on the volatility of the market and the market desires of the agent clusters. The desires are assigned in term of the wealth of the agent clusters when they merge. After an exchange, the beneficial cluster’s desire keeps on the same, the losing one’s desire is altered which is correlative with the agent judge-ability. A parameter R is given to all agents to denote the judge-ability. The numerical calculation shows that the dynamic behaviors of the market are influenced distinctly by R, which includes the exponential magnitudes of the probability distribution of sizes of the agent clusters and the volatility autocorrelation of the returns, the intensity and frequency of the volatility.     

Non-perturbative effects in e+e− annihilation in quantum chromodynamics

We study the change of one two-point function of hadronic electromagnetic currents in the presence of background gauge fields. It is found that it has the asymptotic behavior of 1/q⁴ as compared to ln(-q²) behavior from the bare fermion loop contribution. The effects of the non-perturbative vacuum in QCD on the two-point function is studied in an explicit calculation. We obtain the same qualitative behavior as in our general discussion. The effects on the total hadronic e⁺e^? annihilation is also discussed. We find that the effect ΔR^I/R is of the order of o(1/q⁴) or O(1/q⁶). This may explain the precocious scaling in the e⁺e^? annihilation.     

X-ray binary systems and nonextensivity

We study the x-ray intensity variations obtained from the time series of 155 light curves of x-ray binary systems collected by the instrument All Sky Monitor on board the satellite Rossi X-Ray Timing Explorer. These intensity distributions are adequately fitted by q-Gaussian distributions which maximize the Tsallis entropy and in turn satisfy a nonlinear Fokker-Planck equation, indicating their nonextensive and nonequilibrium behavior. From the values of the entropic index q obtained, we give a physical interpretation of the dynamics in x-ray binary systems based on the kinetic foundation of generalized thermostatistics. The present findings indicate that the binary systems display a nonextensive and turbulent behavior.     

Distributivity and deformation of the reals from Tsallis entropy

We propose a one-parameter family R_q of deformations of the reals, which is motivated by the generalized additivity of the Tsallis entropy. We introduce a generalized multiplication which is distributive with respect to the generalized addition of the Tsallis entropy. These operations establish a one-parameter family of field isomorphisms τ_q between R and R_q through which an absolute value on R_q is introduced. This turns out to be a quasisymmetric map, whose metric and measure-theoretical implications are pointed out.     

Some remarks on Yang-Baxter algebras

We point out the existence of an alternative algebraic structure in Yang-Baxter algebra with trigonometric R-matrix, which appears to be the generalization of the Yangian in Yang-Baxter algebras with rational R-matrix and which is described most naturally by q-commutators. Some properties are presented, in particular in the case of the well-known symmetric six-vertex model. Received: 13 February 1998 / Revised: 16 March 1998 / Accepted: 17 April 1998     

Outward-inward information flux in an opinion formation model on different topologies

A simple model of opinion formation dynamics in which binary-state agents make up their opinions due to the influence of agents in a local neighborhood is studied using different network topologies. Each agent uses two different strategies, the Sznajd rule with a probability q and the Galam majority rule (without inertia) otherwise; being q a parameter of the system. Initially, the binary-state agents may have opinions (at random) against or in favor about a certain topic. The time evolution of the system is studied using different network topologies, starting from different initial opinion densities. A transition from consensus in one opinion to the other is found at the same percentage of initial distribution no matter which type of network is used or which opinion formation rule is used.     

The Casimir operators of inhomogeneous groups

We have found the number of invariant operators for the inhomogeneous groups IGL(n, R), ISL(n, R), ISO(p, q), IU(p, q), ISU(p, q), ISp(2n), i.e. the inhomogeneous groups with the classical homogeneous subgroups, and also for the Weyl group W(p, q). For some special cases explicit forms of the invariant operators are obtained. We also discuss the methods applied, together with problems in some cases, possible further developments and relevance for the supersymmetric theories.     

Influence of surface roughness and contact load on friction coefficient and scratch behavior of thermoplastic olefins

To study the effects of surface roughness and contact load on the friction behavior and scratch resistance of polymers, a set of model thermoplastic olefins (TPO) systems with various surface roughness (R_a) levels were prepared and evaluated. It is found that a higher R_a corresponds to a lower surface friction coefficient (μ_s). At each level of R_a, μ_s gets larger as contact load increases, with a greater increase in μ_s as R_a level increases. It is also observed that with increasing contact load and increasing R_a, the μ_s tend to level off. In evaluating TPO scratch resistance, a lower μ_s would delay the onset of ductile drawing-induced fish-scale surface deformation feature, thereby raising the load required to cause scratch visibility. However, as the contact load is further increased, the μ_s evolves to become scratch coefficient of friction (SCOF) as significant sub-surface deformation and tip penetration occur and material displacement begins, i.e., ploughing. No dependence of R_a and μ_s on the critical load for the onset of ploughing is observed. In this work, the distinction between μ_s and SCOF will be illustrated. Approaches for improving scratch resistance of polymers via control of R_a are also discussed.     

Thermal entanglement of Hubbard dimers in the nonextensive statistics

The thermal entanglement of the Hubbard dimer (two-site Hubbard model) has been studied with the nonextensive statistics. We have calculated the auto-correlation (O_q), pair correlation (L_q), concurrence (Γ_q) and conditional entropy (R_q) as functions of entropic index q and the temperature T. The thermal entanglement is shown to considerably depend on the entropic index. For q<1.0, the threshold temperature where Γ_q vanishes or R_q changes its sign is more increased and the entanglement may survive at higher temperatures than for q=1.0. Relations among L_q, Γ_q and R_q are investigated. The physical meaning of the entropic index q is discussed with the microcanonical and superstatistical approaches. The nonextensive statistics is applied also to Heisenberg dimers.     

Δ Isobar Degrees of Freedom in the 3He Transverse Electron Scattering Response Function

The importance of Δ(1232) isobar degrees of freedom is investigated for the transverse (e, e′) response of ³He in the quasi-elastic peak region and beyond (considered momentum transfer range: 500 ≤ q ≤ 1,000 MeV/c). Besides Δ isobar currents (Δ-IC) meson exchange currents and relativistic corrections to the nucleonic one-body current are included. The calculation is carried out by using the Lorentz integral transform (LIT) method. Results for the transverse response function R _T are presented up to q = 700 MeV/c, whereas for higher q only some preliminary results for the LIT of R _T are discussed. In the quasi-elastic peak region Δ-IC enhance R _T by about 5% and tend to cancel three-nucleon force effects. One observes an excellent agreement with experimental R _T results. Particularly strong Δ-IC contributions are found for transitions into the final state with isospin T = 3/2, which is only reachable in three-body break-up reactions.     

Dynamic peer-to-peer competition

The dynamic behavior of a multiagent system in which the agent size s_i is variable it is studied along a Lotka-Volterra approach. The agent size has hereby the meaning of the fraction of a given market that an agent is able to capture (market share). A Lotka-Volterra system of equations for prey-predator problems is considered, the competition factor being related to the difference in size between the agents in a one-on-one competition. This mechanism introduces a natural self-organized dynamic competition among agents. In the competition factor, a parameter σ is introduced for scaling the intensity of agent size similarity, which varies in each iteration cycle. The fixed points of this system are analytically found and their stability analyzed for small systems (with n=5 agents). We have found that different scenarios are possible, from chaotic to non-chaotic motion with cluster formation as function of the σ parameter and depending on the initial conditions imposed to the system. The present contribution aim is to show how a realistic though minimalist nonlinear dynamics model can be used to describe the market competition (companies, brokers, decision makers) among other opinion maker communities.     

Localized interface phonon polaritons in superlattice with a structural defect consisting of ternary mixed crystal

Using a transfer matrix method, we investigate the existence and characteristics of the localized interface phonon-polariton modes (IPPMs) in superlattice (SL) with a structural defect consisting of ternary mixed crystal (Al_xGa_1−xAs). The results show that the introduction of two-mode behavior of the ternary mixed crystal leads to the rich and varied localized IPPMs spectra with new features. The characteristics and positions of the localized IPPMs in the Reststrahlen region are strongly dependent on the concentration x of the ternary mixed crystal. Moreover, it is found that the localized IPPMs are sensitive to the thicknesses of the defect and constituent layers as well as to the transverse wavenumber q_∥.     

High-performance distribution of limited resources via a dynamical reallocation scheme

Using the context of routing efficiency in a complex scale-free network, we study the problem of how a limited amount of resources should be distributed to the nodes in a network so as to achieve a better performance, without imposing a certain pre-determined distribution. A dynamical reallocation scheme, based on the willingness of sharing resources with a busy neighboring node, is proposed as a tool for allowing an initially uniform distribution of resource to evolve to a high-performance distribution. The resulting distribution gives a critical packet generation rate R_c that is significantly enhanced when compared with evenly distributing the same amount of resources on the nodes. There emerges a relation between the resource allocated to a node and the degree of the node in the form of . The exponent γ is found to vary with the packet generation rate R. For R<R_c, γ takes on a high value and shows a weak dependence on R; for R>R_c, γ drops with R; and for R?R_c, γ saturates. For good performance, the values of γ indicate a behavior different from that linear in k, as often assumed in previous studies. The resource distribution is also analyzed in terms of the betweenness of the nodes.     

The dual (p,q)-Alexander-Conway Hopf algebras and the associated universal ℐ-matrix

The dually conjugate Hopf algebrasFun _p,q (R) andU _p,q (R) associated with the two-parametric (p,q)-Alexander-Conway solution (R) of the Yang-Baxter equation are studied. Using the Hopf duality construction, the full Hopf structure of the quasitriangular enveloping algebraU _p,q (R) is extracted. The universal ?-matrix forsFun _p,q (R) is derived. While expressing an arbitrary group element of the quantum group characterized by the noncommuting parameters in a representation independent way, the ?-matrix generalizes the familiar exponential relation between a Lie group and its Lie algebra. The universal ?-matrix and the FRT matrix generators,L ^(±), forU _p,q (R) are derived from the ?-matrix.     

Effects of low frequency near metal-insulator transition temperatures on polycrystalline La0.65Ca0.35Mn1−yFeyO3 (where y=0.05-0.10) ceramic oxides

The ac electrical properties of 5-10% Fe doped polycrystalline sample have been investigated by complex impedance analysis over the frequency and temperature ranges of 1-100 kHz and 77-300 K, respectively. The average normalized change (ΔZ′/Δf)/Z₀ has been deduced for these Fe doped CMR samples which shows an increasing trend with iron doping. The most pronounced effect of frequencies is at T_c, with the increase of Fe doping it is observed that not only T_c is lowered substantially but also the height of the peaks of real part of impedance (Z′) is increased which in turn decreases considerably with the increase of the ac field. An equivalent circuit model, R_g(R_gbC_gb), i.e. a resistor-capacitor network, has been proposed to explain the impedance results at different temperatures. The plot between τ and 1/T gives a straight line from where relaxation time (τ₀) has been deduced. The correlated barrier hopping (CBH) model has been employed and the binding energy of the defect states is estimated to be between 0.39 and 0.25 eV while the minimum hoping distance varies within the range of 2.93-5.21 Å for these 5-10% Fe doped LCM samples.     

Evolution of cooperation among mobile agents

We study the effects of mobility on the evolution of cooperation among mobile players, which imitate collective motion of biological flocks and interact with neighbors within a prescribed radius R. Adopting the the prisoner’s dilemma game and the snowdrift game as metaphors, we find that cooperation can be maintained and even enhanced for low velocities and small payoff parameters, when compared with the case that all agents do not move. But such enhancement of cooperation is largely determined by the value of R, and for modest values of R, there is an optimal value of velocity to induce the maximum cooperation level. Besides, we find that intermediate values of R or initial population densities are most favorable for cooperation, when the velocity is fixed. Depending on the payoff parameters, the system can reach an absorbing state of cooperation when the snowdrift game is played. Our findings may help understanding the relations between individual mobility and cooperative behavior in social systems.     

From trees to galaxies: The Potts model on a random surface

The matrix model of random surfaces with c = ∞ has recently been solved and found to be identical to a random surface coupled to a q-states Potts model with q = ∞. The mean field-like solution exhibits a novel type of tree structure. The natural question is, down to which—if any—finite values of c and q does this behavior persist? In this work we develop, for the Potts model, an expansion in the fluctuations about the q = ∞ mean field solution. In the lowest—cubic—non-trivial order in this expansion the corrections to mean field theory can be given a nice interpretation in terms of structures (trees and “galaxies”) of spin clusters. When q drops below a finite q_c, the galaxies overwhelm the trees at all temperatures, thus suppressing mean field behavior. Thereafter the phase diagram resembles that of the Ising model, q = 2.     

Mean-Field Analysis of the q-Voter Model on Networks

We present a detailed investigation of the behavior of the nonlinear q-voter model for opinion dynamics. At the mean-field level we derive analytically, for any value of the number q of agents involved in the elementary update, the phase diagram, the exit probability and the consensus time at the transition point. The mean-field formalism is extended to the case that the interaction pattern is given by generic heterogeneous networks. We finally discuss the case of random regular networks and compare analytical results with simulations.     

Competing magnetic structures in the DySi FeB-type phase diagram

The temperature magnetic phase diagrams, of the dimorphic DySi compound, have been studied in terms of wave vectors in the range 1.5-45 K, by neutron diffraction. The polycrystalline sample consists of 26% of CrB-type (Cmcm no. 63, all atoms at 4c site: (0, y, 1/4)) and of 74% of FeB-type (Pnma no. 62, all atoms at 4c site: (x, 1/4, z)). The CrB-ordering is described by the wave vector: q₁=(0, 0, 1/2) over the entire magnetically ordered regime with a uniaxial magnetic structure along the shortest axis c. The FeB-type magnetic phase diagram reveals three distinct regions of magnetic ordering below T_N and one first order transition at T₂=23.5 K (on heating). The ordering is described by two symmetry independent magnetic vectors q₂=(0, 1/2, 1/6) and q₃=(0, q_3y, q_3z) with a temperature variable length. At 1.5 K q_3y≈1/2 and q_3z≈1/11. The two phases coexist in the form of domains. They differ in the moment orientation of the q₃ phase that deviates by ∼22° from the b-axis in the (0, 0, 1) plane. The low temperature range (LT) 1.5 K—T₂ subdivides into two regions: (i) LT-1, between 1.5 K—T₁ where the relative amount of the two phases remains unchanged and in (ii) LT-2: T₁-T₂ where the amount of the incommensurate q₃ phase increases at the cost of the commensurate q₂ amplitude modulated structure which remains unchanged but fully disappears at the first order transition at T₂=23.5 K. The q₃ phase undergoes minor changes until 22 K and gets destabilised at T₂ where the q_3z component jumps from the LT value q_3z≈1/11 to the HT value ≈1/7 and the q_3y component increases from 0.484(1) to 0.495(1). (iii) The high temperature (HT) range T₂-T_N (T_N=40±1 K) is described by a single wave vector q₃. The disproportionation of the HT magnetic phase q₃ below T₂ into two coexisting distinct phases q₂, q₃ down to 1.5 K is an unusual phenomenon, to our knowledge observed for the first time. Various mechanisms are discussed.