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.     

Herd behavior in weight-driven information spreading models for financial market

We study two weight-driven information spreading models for financial market. In these models, we find that the activity threshold below which the ‘financial crash’ occurs can be increased by uneven distribution of information weight, compared with Eguíluz and Zimmermann model [V.M. Eguíluz, M.G. Zimmermann, Phys. Rev. Lett. 85 (2000) 5659]. We also find that below the threshold the normalized return distribution, P(Z;Δt) satisfies P(Z=0;Δt)∼exp(−Δt/b) whereas P(Z=0;Δt)∼Δt^−τ above the threshold. Here Δt is the time interval where the normalized return is defined, Z(t,Δt)=Z(t+Δt)−Z(t). By approximating the relative increase of P(Z;Δt=1) for large Z as Gaussian distribution with non-zero mean, we show that the non-zero mean of the Gaussian distribution can cause such exponentially decaying behavior of P(Z=0;Δt).     

The resonance decay function method in the determination of the pre-factor of the Néel relaxation time of single-domain nanoparticles

In its simple form, the relaxation time of the Néel relaxation process of the magnetic moment of single-domain particles is given by τ_N=τ_0Nexp(σ), σ being the ratio of anisotropy energy to thermal energy. The pre-factor, τ_0N, is normally given a value of 10⁻⁹ s, but values ranging from 10⁻⁸ to 10⁻¹² s have been reported in literature. Here, by means of the field and frequency dependence of the complex magnetic susceptibility, χ(ω,H)=χ′(ω,H)−iχ″(ω,H), of a magnetic fluid sample, in the MHz-GHz range, in conjunction with the determination of the sample decay function, b(t), the pre-factor τ_0N is determined. b(t) is readily obtained through the inverse Fourier transformation relationship, which exists between b(t) and χ″(ω).     

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.     

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)).     

Monte Carlo simulation of film growth in a phase separating binary alloy model

Using a kinetic Monte Carlo method, we simulate binary film (A_0.5B_0.5/A) growth on an L×L square lattice with the focus on the domain growth behaviour. We compute the average domain area, A(t), as a measure of domain size. For a sufficiently large system, we find that A(t) grows with a power law in time with A(t)∼t^2/3 after the initial transient time. This implies that the dynamic exponent for domain growth with non-conserved order parameter is z=3, a value which was theoretically predicted for the conserved order parameter case. Further analysis reveals that such a power-law behaviour emerges because the order parameter is approximately conserved after the early stage of growth.     

Etch front roughening in wrinkly metal

Scaling behavior of wrinkle evolution due to chemical etching of Au on stretchable substrate is studied by atomic force microscopy. The surfaces were etched with a small drop of KI solution. Scaling exponent α decreased with the etch time, from 0.93 to 0.62. For dynamic exponent β up to 30 min we find it to be 0.16 ± 0.05. Within the same time frame, the wavelength increases as ∼t^0.23+−0.05 but drops at 45 min as ∼t^{−1.22+−0.42} and saturates. At this stage, we observe percolation island type features along with some wrinkles. The measured value of α at this stage is 0.62 ± 0.02; consistent with the percolation model. The wavelength coarsening at this stage suggests the existence of chemically driven spinodal decomposition. Our obtained value of α and β is consistent with the value of z obtained from correlation length which is given by ξ = t^1/z. We find z = 4.87 ± 0.50. Our experiment suggests wrinkle formation in thin films on viscoelastic surface occurs in three stages.     

Causal particle detectors and topology

We investigate particle detector responses in some topologically non-trivial spacetimes. We extend a recently proposed regularization of the massless scalar field Wightman function in four-dimensional Minkowski space to arbitrary dimension, to the massive scalar field, to quotients of Minkowski space under discrete isometry groups and to the massless Dirac field. We investigate in detail the transition rate of inertial and uniformly accelerated detectors on the quotient spaces under groups generated by (t, x, y, z) ? (t, x, y, z + 2a), (t, x, y, z) ? (t, −x, y, z), (t, x, y, z) ? (t, −x, −y, z), (t, x, y, z) ? (t, −x, −y, z + a) and some higher dimensional generalizations. For motions in at constant y and z on the latter three spaces the response is time dependent. We also discuss the response of static detectors on the RP³ geon and inertial detectors on RP³ de Sitter space via their associated global embedding Minkowski spaces (GEMS). The response on RP³ de Sitter space, found both directly and in its GEMS, provides support for the validity of applying the GEMS procedure to detector responses and to quotient spaces such as RP³ de Sitter space and the RP³ geon where the embedding spaces are Minkowski spaces with suitable identifications.     

Impact of orientational distribution of adsorbing objects on dynamics of Random Sequential Ballistic Adsorption (RSBA) dynamics

Recently, by proposing a new variant of Random Sequential Adsorption (RSA) namely Random Sequential Ballistic Adsorption (RSBA) model [Pradip B. Shelke, A.G. Banpurkar, S.B. Ogale, A.V. Limaye, Surf. Sci. 601 (2007) 274], we addressed the issue of adsorption dynamics of extended objects where the objects, upon adsorption, protrude outside the substrate. This study brought out the role of the arriving trajectory in the adsorption dynamics. In the present work the possible role of the orientational distribution of the arriving objects in the RSBA dynamics is investigated. The dynamics of RSBA of needles (line segments) is studied analytically and by computer simulation for different types of θ distributions of arriving needles, θ being the angle made by the arriving needle with normal to the substrate. Three types of θ distributions, namely a uniform distribution over the range (0, π/2), a Gaussian distribution and a distribution uniform over the solid angle, are considered. Analytical treatment establishes that in all the three cases, the number n(t) of adsorbed objects at a late time t follows a power law n(t) ∼ t^α, and the exponent α depends on the specifics of the θ distribution. In general, for distribution f(θ) ∝ θ^β, for θ → 0, α is found to be 2/(β + 3). The simulation results are in excellent agreement with the analytical findings and together they reveal that the orientational distribution of arriving objects has significant consequences for the Random Sequential Ballistic Adsorption (RSBA) process.     

Critical parameters near the ferromagnetic-paramagnetic phase transition in La0.7A0.3(Mn1−xbx)O3 (A=Sr; B=Ti and Al; x=0.0 and 0.05) compounds

The critical parameters provide important information concerning the interaction mechanisms near the paramagnetic-to-ferromagnetic transition. In this paper, we present a thorough study for the critical behavior of La_0.7A_0.3(Mn_1−xB_x)O₃ (A=Sr; B=Ti and Al; x=0.0 and 0.05) polycrystalline samples near ferromagnetic-paramagnetic phase transition temperature by analyzing isothermal magnetization data. We have analyzed our dc-magnetization data near the transition temperature with the help of the modified Arrot plot, Kouvel-Fisher method. We have determined the critical temperature T_C and the critical parameters β, γ and δ. With the values of T_C, β and γ, we plot M×(1−T/T_C)^−β vs. H×(1−T/T_C)^−γ. All the data collapse on one of the two curves. This suggests that the data below and above T_C obey scaling, following a single equation of state. Critical parameters for x=0 and x_Ti=0.05 samples are between those predicted for a 3D-Heisenberg model and mean-field theory and for x_Al=0.05 samples the values obtained for the critical parameters are close to those predicted by the mean-field theory.     

Dependence of Néel temperature on the particle size of MnFe2O4

Mn-ferrite nanoparticles having diameter in the range 17-45 nm were synthesized by modified co-precipitation method using metal nitrate solutions. Different concentrations of NaOH were found to affect the growth of particle size. Néel temperature (T_N) was found to increase with increasing particle size. The obtained Néel temperature was higher than that of the bulk. The shift in the Néel temperature is described by the finite size-scaling theory [T_N(d)−T_N(bulk)]/T_N(bulk)=(d/d₀)^−1/v, where d is particle size, v=0.6±0.1 and d₀=1.7±0.1 nm.     

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.     

A variance formula related to a quantum conductance problem

Let t be a block of an Haar-invariant orthogonal (β=1), unitary (β=2) or symplectic (β=4) matrix from the classical compact groups O(n), U(n) or Sp(n), respectively. We obtain a close form for Var(tr(t^∗t)). The case for β=2 is related to a quantum conductance problem, and our formula recovers a result obtained by several authors. Moreover, our result shows that the variance has a limit ⁻¹(8β) for β=1,2 and 4 as the sizes of t go to infinity in a special way. Although t in our formulation comes from a block of an Haar-invariant matrix from the classical compact groups, the above limit is consistent with a formula by Beenakker, where t is a block of a circular ensemble.     

The electronic structure and properties of Fe6(N1−xCx)2 carbonitrides by first-principles calculations

Electronic structure and properties of Fe₆(N_1−xC_x)₂ carbonitrides with 0≤x≤1, i.e. the concentrations of N and C elements are respectively in range of 0∼7.69 wt% and 0∼6.67 wt%, have been studied by first-principles calculations based on density functional theory (DFT) implemented in the Cambridge Serial Total Energy Package (CASTEP) code. The calculated results show that the Fe₆(N_1−xC_x)₂ carbonitrides are thermodynamically and mechanically stable. Lattice parameters and stability of the carbonitrides increase when C atoms replace N atoms in Fe₆N₂ unit cell. In Fe₆(N_1−xC_x)₂ unit cell, the hybridization effect between C-2p and Fe-3d states is stronger than that between N-2p and Fe-3d states. Elastic properties and melting points of the carbonitrides change slightly with the substitution of C atoms for N atoms in Fe₆(N_1−xC_x)₂ carbonitrides.     

Exact solutions for a forced Burgers equation with a linear external force

We investigate the solutions of the Burgers equation , where F(x,t) is an external force and Φ(x,t) represents a forcing term. This equation is first analyzed in the absence of the forcing term by taking F(x,t)=k₁(t)−k₂(t)x into account. For this case, the solution obtained extends the usual one present in the Ornstein-Uhlenbeck process and depending on the choice of k₁(t) and k₂(t) it can present a stationary state or an anomalous spreading. Afterwards, the forcing terms Φ(x,t)=Φ₁(t)+Φ₂(t)x and Φ(x,t)=Φ₃x−Φ₄/x³ are incorporated in the previous analysis and exact solutions are obtained for both cases.     

High-pressure Raman spectroscopic studies on orthophosphates Ba3(PO4)2 and Sr3(PO4)2

By using diamond anvil cell (DAC), high-pressure Raman spectroscopic studies of orthophosphates Ba₃(PO₄)₂ and Sr₃(PO₄)₂ were carried out up to 30.7 and 30.1 GPa, respectively. No pressure-induced phase transition was found in the studies. A methanol:ethanol:water (16:3:1) mixture was used as pressure medium in DAC, which is expected to exhibit nearly hydrostatic behavior up to about 14.4 GPa at room temperature. The behaviors of the phosphate modes in Ba₃(PO₄)₂ and Sr₃(PO₄)₂ below 14.4 GPa were quantitatively analyzed. The Raman shift of all modes increased linearly and continuously with pressure in Ba₃(PO₄)₂ and Sr₃(PO₄)₂. The pressure coefficients of the phosphate modes in Ba₃(PO₄)₂ range from 2.8179 to 3.4186 cm⁻¹ GPa⁻¹ for ν₃, 2.9609 cm⁻¹ GPa⁻¹ for ν₁, from 0.9855 to 1.8085 cm⁻¹ GPa⁻¹ for ν₄, and 1.4330 cm⁻¹ GPa⁻¹ for ν₂, and the pressure coefficients of the phosphate modes in Sr₃(PO₄)₂ range from 3.4247 to 4.3765 cm⁻¹ GPa⁻¹ for ν₃, 3.7808 cm⁻¹ GPa⁻¹ for ν₁, from 1.1005 to 1.9244 cm⁻¹ GPa⁻¹ for ν₄, and 1.5647 cm⁻¹ GPa⁻¹ for ν₂.     

The generalized exponential-integral V(x,y)=∫1∞ exp(−xt)ln(t+y)dtt and computer algorithms for y = 0, 1

The generalized exponential-integral function V(x, y) defined here includes as special cases the function E⁽²⁾₁(x) = V(x, 0) introduced by van de Hulst and functions M₀(x) = V(x, 1) and N₀(x) = V(x, -1) introduced by Kourganoff in connection with integrals of the form ∫ E_n)t)E_m(t±x), which play an important role in the theory of monochromatic radiative transfer. Series and asymptotic expressions are derived and, for the most important special cases, y = 0 and y = 1, Chebyshev expansions and rational approximations are obtained that permit the function to be evaluated to at least 10 sf on 0<x<∞ using 16 sf arithmetic.     

The effect of gamma irradiation on electrical and dielectric properties of Al-TiW-Pd2Si/n-Si Schottky diode at room temperature

The effects of ⁶⁰Co (γ-ray) irradiation on the electrical and dielectric properties of Al-TiW-Pd₂Si/n-Si Schottky diodes (SDs) have been investigated by using capacitance-voltage (C-V) and conductance-voltage (G/ω-V) measurements at room temperature and 500 KHz. The corrected capacitance and conductance values were obtained by eliminating the effect of series resistance (R_s) on the measured capacitance (C_m) and conductance (G_m) values. The high-low frequency capacitance (CHF-CLF) method given in [12] as N_ss = (1/qA) [((1/C_LF) − (1/C_ox))⁻¹ −  ((1/C_HF) − (1/C_ox))⁻¹] was successfully adapted to the before-after irradiation capacitance given in this report as N_ss = (1/qA) [((1/C_bef) − (1/C_ox))⁻¹ − ((1/C_after) − (1/C_ox))⁻¹] for the analyzing the density of interface states. The N_ss-V plots give a distinct peak corresponding to localized interface states regions at metal and semiconductor interface. The experimental values of the ac electrical conductivity (σ_ac), the real (M′) and imaginary (M″) parts of the electrical modulus were found to be strong functions of radiation and applied bias voltage, especially in the depletion and accumulation regions. The changes in the dielectric properties in the depletion and accumulation regions stem especially from the restructuring and reordering of the charges at interface states and surface polarization whereas those in the accumulation region are caused by series resistance effect.     

Dynamical theory for photon and photoelectric pulse distributions in single molecule fluorescence

A single two-level molecule driven by CW-laser field and a photomultiplier tube (PMT) are considered as two parts of the united dynamical system connected with each other by photons of molecular fluorescence. Each PMT is characterized by a rate α of photo-effect and by a rate β of PMT recovery. A theory for the photon distribution function w_N(t) and for the photoelectric pulse distribution function f_n(t) for such a system is built up. If times 1/ α and 1/ β characterizing PMT are much shorter as compared to the average time interval 1/ k between two successively emitted photons of fluorescence, the photon and the photoelectron distribution functions coincide with each other, i.e. f_n(t) ≅ w_N(t). A relation between w_N(t) and f_n(t) is studied in detail for the case in which PMT works slower as compared to the rate k of photon emission, i.e. at 1/ α, 1/ β ≥ 1/ k.     

The rule for a subdiffusive particle in an extremely diverse environment

We consider a subdiffusive continuous time random walker in an inhomogeneous environment. Each microscopic random time is drawn from a waiting time probability density function (WT-PDF) of the form: , 0<β?1. The parameter k is a random quantity also, and is drawn from a PDF, , 0?γ<1, for a cutoff parameter . We show that the effective WT-PDF, ψ(t), obtained by averaging φ(t;k) with p(k), exhibits a transition in the rule that governs the power of ψ(t). ψ(t) obeys, , and μ is given by two different formula. When, 1−γ>β, μ=β, but otherwise, μ=1−γ. The rule for the scaling of ψ(t) reflects the competition between two different mechanisms for subdiffusion: subdiffusion due to the heavily tailed φ(t;k) for individual jumps, and subdiffusion due to the collective effect of an environment made of many slow local regions. These two different mechanisms for subdiffusion are not additive, and compete each other. The reported transition is dimension independent, and disappears when the power β is also distributed, in the range, 0<β?1. Simulations exemplified the transition, and implications are discussed.