Cluster growth poised on the edge of break-up: Size distributions with small exponent power-laws

In many naturally occurring growth processes, cluster size distributions of power-law form n(s)∝s^−τ with small exponents 0<τ<1 are observed. We suggest here that such distributions emerge naturally from cluster growth, where size dependent aggregation is counterbalanced by size dependent break-up. The model used in the study is a simple reaction kinetic model including only monomer-cluster processes. It is shown that under such conditions power-law size distributions with small exponents are obtained. Therefore, the results suggest that the ubiquity of small exponent power-law distributions is related to the growth process, where aggregation driven cluster growth is poised on the edge of cluster break-up.     

Sandpile on directed small-world networks

We numerically investigate the avalanche dynamics of the Bak-Tang-Wiesenfeld sandpile model on directed small-world networks. We find that the avalanche size and duration distribution follow a power law for all rewiring probabilities p. Specially, we find that, approaching the thermodynamic limit (L→∞), the values of critical exponents do not depend on p and are consistent with the mean-field solution in Euclidean space for any p>0. In addition, we measure the dynamic exponent in the relation between avalanche size and avalanche duration and find that the values of the dynamic exponents are also consistent with the mean-field values for any p>0.     

Computational and experimental study of the cluster size distribution in MAPLE

A combined experimental and computational study is performed to investigate the origin and characteristics of the surface features observed in SEM images of thin polymer films deposited in matrix-assisted pulsed laser evaporation (MAPLE). Analysis of high-resolution SEM images of surface morphologies of the films deposited at different fluences reveals that the mass distributions of the surface features can be well described by a power-law, Y(N) ∝ N^−t, with exponent −t ≈ −1.6. Molecular dynamic simulations of the MAPLE process predict a similar size distribution for large clusters observed in the ablation plume. A weak dependence of the cluster size distributions on fluence and target composition suggests that the power-law cluster size distribution may be a general characteristic of the ablation plume generated as a result of an explosive decomposition of a target region overheated above the limit of its thermodynamic stability. Based on the simulation results, we suggest that the ejection of large matrix-polymer clusters, followed by evaporation of the volatile matrix, is responsible for the formation of the surface features observed in the polymer films deposited in MAPLE experiments.     

Chemical diffusion in molybdenum disulphide

Ceramic molybdenum disulphide (MoS₂) was equilibrated at an ambient sulphur vapour partial pressure p(S₂), 10 Pa<p(S₂)<1000 Pa. After the step change of p(S₂) to a new value, the equilibration kinetics was monitored by measuring electrical conductivity. The application of the solution of Fick's second law (with the initial condition: no concentration gradient in specimen and the boundary condition: surface concentration constant) to the kinetic data gave the chemical diffusion coefficient. The chemical diffusion coefficient, D_chem, determined at 1273 K, was D_chem=(3.20±0.32)*10⁻⁷ cm² s⁻¹ and was found to be independent of sulphur vapour partial pressure. The usefulness of transient electrical conductivity method for determining real values of diffusion data was discussed in terms of defect structure of the studied material.     

Crystal field energy levels of the laser crystal Gd3Ga5O12: Nd

The crystal field energy levels of laser crystal Gd₃Ga₅O₁₂: Nd³⁺ are calculated using the diagonalization (of energy matrix) method. From the calculations, the 93 observed crystal field energy levels are explained reasonably and the root-mean-square (r.m.s.) deviation σ(≈25.6 cm⁻¹) and the scalar crystal-field strength parameter Nv (≈3847 cm⁻¹) are obtained. The results are discussed.     

Thermal evolution of vacancy defects induced in sintered UO2 disks by helium implantation

A slow positron beam coupled with Doppler broadening (DB) spectrometer was used to measure the low- and high-momentum annihilation fractions, S and W, respectively, as a function of positron energy in UO₂ disks implanted with different 1 MeV ³He fluences and annealed in ArH₂ or in vacuum. The S(E) and W(E) behaviors indicate that for fluences in the range from 2 × 10¹⁴ to 2 × 10¹⁶³He cm⁻², the vacancy defects distribution evolves with the annealing temperature in the range from 264 to 700 °C under ArH₂. This evolution is found to be dependent on the ³He fluence implanted in the sintered UO₂ disks. For the lowest fluence of 2 × 10¹⁴³He cm⁻², the S(W) plot with positron energy as the running parameter suggests that only the concentration of vacancy defects decreases when annealing temperature increases. For the highest implantation fluences (from 5 × 10¹⁵ to 2 × 10¹⁶³He cm⁻²) the S(W) plot suggests that the nature of the vacancy defects changes in the annealing temperature range from 260 to 400 °C. Measurements performed in implanted UO₂ disks annealed in vacuum have revealed a partial recovery of the vacancy defects possibly due to their recombination with mobile oxygen interstitials. The role of the hydrogen infusion into the disk is also discussed.     

Second-harmonic generation in the thermal/electrical poling (100−x)GeS2·x(0.5Ga2S3·0.5CdS) chalcogenide glasses

Utilizing Maker fringe (MF) method, second-harmonic generation (SHG) has been observed within the GeS₂-Ga₂S₃-CdS pseudo-ternary glasses through thermal/electrical poling technique. The SHG phenomenon was considered to be the result of breakage of the glassy macroscopic isotropy originated from the reorientations of dipoles during the thermal/electrical poling process. Under the same poling condition conducted with 5 kV and 280 °C for 30 min, the maximum value of second-order nonlinear susceptibility χ⁽²⁾ of the poled (100−x)GeS₂·x(0.5Ga₂S₃·0.5CdS) glasses was obtained to be ≈4.36 pm/V when the value of x is equal to 30. Nonlinear dependence of χ⁽²⁾ on compositions of these glasses can be well explained according to the theory related to the reorientation of dipoles.     

Do muons interact anomalously with hadrons?

We examine the possibility that the recently observed suppression of the rate for K_L→μ⁺μ⁻ is due to the three-pion intermediate state with an anomalously large amplitude for 3π(J^P = 0⁻)→μ⁺μ⁻. We do not explicitly introduce new dynamics, but merely parameterize the empirically required enhancement in the simplest phenomenological manner. The question is then raised as to whether this interaction would be presently observable in other experiments where muons are studied in the vicinity of hadrons, in particular muon-proton scattering and muonic atoms. We also raise the same question with respect to an alternative possibility, namely that an anomalously large amplitude for ππ(J^P=0⁺)→μ⁺μ⁻ give rise to K_S→μ⁺μ⁻. The possible size and nature of effects in other experiments are thus estimated.     

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.     

On Optimal Separation of Eigenvalues for a Quasiperiodic Jacobi Matrix

We consider quasiperiodic Jacobi matrices of size N with analytic coefficients. We show that, in the positive Lyapunov exponent regime, after removing some small sets of energies and frequencies, any eigenvalue is separated from the rest of the spectrum by N ^?1(log N)^?p , with p > 15.     

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.     

DC conductivity of silver vanadium tellurite glasses

The mixed electronic-ionic conduction in 0.5[xAg₂O-(1−x)V₂O₅]-0.5TeO₂ glasses with x=0.1-0.8 has been investigated over a wide temperature range (70-425 K). The mechanism of dc conductivity changes from predominantly electronic to ionic within the 30?mol% Ag₂O?40 range; it is correlated with the underlying change in glass structure. The temperature dependence of electronic conductivity has been analyzed quantitatively to determine the applicability of various models of conduction in amorphous semiconducting glasses. At high temperature, T>θ_D/2 (where θ_D is the Debye temperature) the electronic dc conductivity is due to non-adiabatic small polaron hopping of electrons for 0.1?x?0.5. The density of states at Fermi level is estimated to be N(E_F)≈10¹⁹-10²⁰ eV⁻¹ cm⁻³. The carrier density is of the order of 10¹⁹ cm⁻³, with mobility ≈2.3×10⁻⁷-8.6×10⁻⁹ cm² V⁻¹ s⁻¹ at 300 K. The electronic dc conductivity within the whole range of temperature is best described in terms of Triberis-Friedman percolation model. For 0.6?x?0.8, the predominantly ionic dc conductivity is described well by the Anderson-Stuart model.     

Intermittency in the atmospheric surface layer: Unresolved or slowly varying?

We present streamwise velocity structure functions 〈δv_L(τ)〉=〈|v(t+τ)−v(t)|^p〉 (with p=1:5) obtained in the near neutral atmospheric surface layer at the Utah SLTEST site at the highest terrestrial Reynolds number Re_τ=O(10⁶). We show that the occurrence of very large scale coherent oscillations in the streamwise velocity throughout the wall region, interpreted as genuine structural features of the canonical turbulent boundary layer, affects the scaling exponents of the p>3 order structure functions. This results in a slight alteration of the intermittent behavior of the velocity field. It was found that for positive (fast) large scale oscillation of the low-pass filtered velocity signal, deviations from the Kolmogorov K41 prediction (absence of multiscaling) are more marked, as compared to negative (slow) excursion. The results are discussed in terms of convergence of statistics from atmospheric boundary layer measurements.     

Phase transitions and molecular motions in [Zn(NH3)4](BF4)2 studied by nuclear magnetic resonance, infrared and Raman spectroscopy

Middle infrared absorption, Raman scattering and proton magnetic resonance relaxation measurements were performed for [Zn(NH₃)₄](BF₄) in order to establish relationship between the observed phase transitions and reorientational motions of the NH₃ ligands and BF₄⁻ anions. The temperature dependence of spin-lattice relaxation time (T₁(¹H)) and of the full width at half maximum (FWHM) of the bands connected with ρ_r(NH₃), ν₂(BF₄) and ν₄(BF₄) modes in the infrared and in the Raman spectra have shown that in the high temperature phase of [Zn(NH₃)₄](BF₄)₂ all molecular groups perform the following stochastic reorientational motions: fast (τ_R≈10⁻¹² s) 120° flips of NH₃ ligands about three-fold axis, fast isotropic reorientation of BF₄⁻ anions and slow (τ_R≈10⁻⁴ s) isotropic reorientation (“tumbling”) of the whole [Zn(NH₃)₄]²⁺ cation. Mean values of the activation energies for uniaxial reorientation of NH₃ and isotropic reorientation of BF₄⁻ at phases I and II are ca. 3 kJ mol⁻¹ and ca. 5 kJ mol⁻¹, respectively. At phases III and IV the activation energies values for uniaxial reorientation of both NH₃ and of BF₄⁻ equal to ca. 7 kJ mol⁻¹. Nearly the same values of the activation energies, as well as of the reorientational correlation times, at phases III and IV well explain existence of the coupling between reorientational motions of NH₃ and BF₄⁻. Splitting some of the infrared bands at T_C2=117 K suggests reducing of crystal symmetry at this phase transition. Sudden narrowing of the bands connected with ν₂(BF₄), ν₄(BF₄) and ρ_r(NH₃) modes at T_C3=101 K implies slowing down (τ_R?10⁻¹⁰ s) of the fast uniaxial reorientational motions of the BF₄⁻ anions and NH₃ ligands at this phase transition.     

Order parameter and barrier height in LaSrMnO cluster glasses

Using the results of magnetization measurements of LaSrMnO cluster glasses, it is shown that the concentration of frozen magnetic moments exponentially decreases with the increase of temperature. We find that temperature dependence of the order parameter q, of the form q−q(T)∼T−5/2, is universal characteristic of the investigated cluster glasses and that the barrier height Δ closely follows the quadratic relation to the temperature, Δ≈BT².     

Precursory phenomena associated with large avalanches in the long-range connective sandpile (LRCS) model

Reduction in b-values before a large earthquake is a very popular topic for discussion. This study proposes an alternative sandpile model being able to demonstrate reduction in scaling exponents before large events through adaptable long-range connections. The distant connection between two separated cells was introduced in the sandpile model. We found that our modified long-range connective sandpile (LRCS) system repeatedly approaches and retreats from a critical state. When a large avalanche occurs in the LRCS model, accumulated energy dramatically dissipates and the system simultaneously retreats from criticality. The system quickly approaches the critical state accompanied by the increase in the slopes of the power-law frequency-size distributions of events. Afterwards, and most interestingly, the power-law slope declines before the next large event. The precursory b-value reduction before large earthquakes observed from earthquake catalogues closely mimics the evolution in power-law slopes for the frequency-size distributions of events derived in the LRCS models. Our paper, thus, provides a new explanation for declined b-values before large earthquakes.     

Critical properties of island perimeters in the flooding transition of stochastic and rotational sandpile models

Critical properties of external perimeters of islands that appear at the flooding transition in the toppling surfaces, defined by the toppling number _Si$S_i$ of each sand column, of stochastic and rotational sandpile models are studied. A set of new critical exponents are estimated by extensive numerical simulation and finite size scaling analysis. The values of the critical exponents are found different for these sandpile models. Several scaling relations among the critical exponents and the Hurst exponent describing the self-affinity of the toppling surfaces are established and verified. The critical exponents obtained here are also found connected to the exponents describing the avalanche size distribution.     

The15N(p,α 0)12C reaction at stellar energies

The¹⁵N(ρ, α₀)¹²C reaction has been investigated in the energy range ofE _p (lab)=78-810keV. The measurement of the excitation functions and α-particle angular distributions involved solid targets as well as a quasi-point supersonic jet gas target. The determination of absolute cross sections has been carried out with the gas target. The observed energy dependence of the total cross sections can be described in terms of two-level Breit-Wigner shapes including the resonances atE _p (J ^π)=335(1^?) and 1,028(1^?)keV. The data lead to a zero-energy intercept of the astrophysicalS(E) factor ofS(0)= 65±4MeV-b. The angular distributions are asymmetric around 90° and require an additional amplitude in the reaction mechanism, which interferes predominantly with the 335 keV resonance. The origin of this background amplitude is discussed.     

Extracting d-orbital occupancy from magnetic Compton scattering in bilayer manganites

We consider the shape of the magnetic Compton profile (MCP), J_mag(p_z), in La_1.2Sr_1.8Mn₂O₇ for momentum transfer p_z along the [110] direction and the associated reciprocal form factor B(r) defined by taking the one-dimensional Fourier transform of J_mag(p_z). B(r) is shown to contain a prominent dip at r≈1 Å, where the minimum value B_min of B(r) can be related to the occupancies of the e_g orbitals of dx²−y² and d3z²−r² symmetry in the system. We illustrate our procedure in detail by analyzing the measured MCP at 5 K and the MCP computed within the framework of the local spin density approximation (LSDA) and comment on the differences between the measured and computed e_g occupancies as a reflection of the limitations of the LSDA in treating electron correlation effects.     

Sandpile Dynamics Driven by Degree on Scale-Free Networks

We introduce a sandpile model driven by degree on scale-free networks, where the perturbation is triggered at nodes with the same degree. We numerically investigate the avalanche behaviour of sandpile driven by different degrees on scale-free networks. It is observed that the avalanche area has the same behaviour with avalanche size. When the sandpile is driven at nodes with the minimal degree, the avalanches of our model behave similarly to those of the original Bak-Tang-Wiesenfeld （BTW） model on scale-free networks. As the degree of driven nodes increases from the minimal value to the maximal value, the avalanche distribution gradually changes from a clean power law, then a mixture of Poissonian and power laws, finally to a Poisson-like distribution. The average avalanche area is found to increase with the degree of driven nodes so that perturbation triggered on higher-degree nodes will result in broader spreading of avalanche propagation.