Variable-order fractional mean square displacement function with evolution of diffusibility

It is a challenging issue to characterize the evolution of diffusibility, which causes some complex diffusion. For the clear physical significance in some parameters of the existing fractional diffusion models, we present a modified fractional diffusion model and then establish the fractional mean square displacement (MSD) functions using a variable-order integration with memory of the order. The comparative analysis and numerical simulation demonstrate that the variable-order MSD function can characterize the evolution of the diffusibility without losing the advantage of fewer parameters.     

On the Einstein model for EXAFS parallel and perpendicular mean‐square relative displacements

The correlated Einstein model for EXAFS parallel and perpendicular mean‐square relative displacements (MSRDs) is discussed. By means of dynamical simulations on different crystalline structures, the error owing to the Einstein‐fit model on the EXAFS MSRDs is estimated as a function of the standard deviation of the density of vibrational states. This error should be taken into account to improve the accuracy of the MSRDs.     

纳弧度分辨力角位移传感器及平均灵敏度标定

给出了基于六次临界反射棱镜的精密角位移传感器,采用的是差动式结构。实验结果表明,传感器灵敏度高,量程为500μrad,具有5nrad的分辨力。提出了适合于小量程角位移传感器的平均灵敏度的标定方法,可以快速标定平均灵敏度,降低标定过程中标定系统及传感器自身漂移对标定精度的影响。     

On the limit distribution of layer block spin variables in the mean spherical model

The limit distribution of the layer block spin variables of the mean spherical model under Neumann–Dirichlet boundary conditions is investigated in the presence of an inhomogeneous external field which changes sign at distance Lx (0x1) from the Neumann boundary. The behaviour of the equation of state is studied in different temperature and field regimes: high-temperature bulk limit, critical finite-size scaling regime, and low-temperature moderate-field regime. A new classes of critical behaviour for the characteristic function of the limit distributions are obtained and studied in the three different regimes.     

Solutions of fractional nonlinear diffusion equation and first passage time: Influence of initial condition and diffusion coefficient

We investigate the solutions and the first passage time for anomalous diffusion processes governed by the fractional nonlinear diffusion equation with diffusion coefficient separable in time and space, D(t,x)=D(t)|x|^−θ, subject to absorbing boundary condition and the conventional initial condition p(x,0)=δ(x−x₀). We obtain explicit analytical expressions for the probability distribution, the first passage time distribution, the mean first passage time and the mean squared displacement, and discuss their behavior corresponding to different time dependent diffusion coefficients.     

Impact of colored cross-correlated noises on stochastic resonance and mean extinction rate for a metapopulation system with a multiplicative periodic signal

In this paper, we aim to explore the mean extinction rate and the phenomena of the stochastic resonance (SR) for a metapopulation system induced by a multiplicative periodic signal, colored cross-correlated multiplicative and additive Gaussian noises. By use of the fast descent method and the adiabatic approximation theory for the signal-to-noise ratio, we obtain the expression of the signal-to-noise ratio (SNR). Numerical results indicate that the various SR phenomena occur in the metapopulation system due to the variation of the noise terms and the correlation time. Specifically, the noise correlation always plays a critical role in motivating the SR phenomenon, while the multiplicative noise exerts the inhibition effect on the SR. Interestingly, the weak additive noise can stimulate the resonant peak of the SNR, while the further increase of the noise intensity will lead to the reduction of the SR effect. On the other hand, the noise correlation time τ plays antipodal roles in motivating the SR phenomenon under different circumstances. With regard to the mean extinction rate of the population from the boom state to the extinction one, by performing the numerical calculations, it is found that the additive noise always accelerate the extinction of the population, while the correlation noise will slow down the decline for the population. The role that the noise correlation time plays in the population extinction depends on the values that λ takes.     

Linking electromagnetic precursors with earthquake dynamics: An approach based on nonextensive fragment and self-affine asperity models

Understanding the earthquake (EQ) preparation process in terms of precursory electromagnetic (EM) emissions has been an evolving field of multi-disciplinary research. EM emissions in a wide frequency spectrum ranging from kHz to MHz are produced by opening cracks, which can be considered as precursors of general fracture. An important feature, observed on both laboratory and geophysical scale, is that the MHz radiation systematically precedes the kHz one. Yet, the link between an individual EM precursor and a distinctive stage of the EQ preparation comprises a crucial open question. A recently proposed two-stage model on preseismic EM activity suggests that the MHz EM emission is due to the fracture of the highly heterogeneous system that surrounds the fault. The finally emerged kHz EM emission is rooted in the final stage of EQ generation, namely, the fracture of entities sustaining the system. In this work we try to further penetrate and elucidate the link of the precursory kHz EM activity with the last stage of EQ generation building on two theoretical models for EQ dynamics. First, the self-affine model states that an EQ is due to the slipping of two rough and rigid fractional Brownian profiles, one over the other, when there is an intersection between them. Second, the fragment-asperity model, rooted in a nonextensive Tsallis framework starting from first principles, consists of two rough profiles interacting via fragments filling the gap. In the latter approach, the mechanism of triggering EQ is established through the interaction of the irregularities of the fault planes and the fragments between them. This paper shows that these models of EQ dynamics can be linked with the detected kHz EM emission. In this framework of analysis of preseismic EM activity, we identify sufficient criteria that offer the possibility to discriminate whether a seismic shock is sourced in the fracture of fragments filling the gap between the rough profiles or in the fracture of “teeth” distributed across the fractional Brownian profiles that sustain the system.     

The exact solution of the diffusion trapping model of defect profiling with variable energy positrons

We report an exact analytical solution of so-called positron diffusion trapping model. This model have been widely used for the treatment of the experimental data for defect profiling of the adjoin surface layer using the variable energy positron (VEP) beam technique. However, up to now this model could be treated only numerically with so-called VEPFIT program. The explicit form of the solutions is obtained for the realistic cases when defect profile is described by a discreet step-like function and continuous exponential-like function. Our solutions allow to derive the analytical expressions for typical positron annihilation characteristics including the positron lifetime spectrum. Latter quantity could be measured using the pulsed, slow positron beam. Our analytical results are in good coincidence with both the VEPFIT numerics and experimental data. The presented solutions are easily generalizable for defect profiles of other shapes and can be well used for much more precise treatment of above experimental data.     

A fractal comparison of real and Austrian business cycle models

Rescaled range and power spectral density analysis are applied to examine a diverse set of macromonetary data for fractal character and stochastic dependence. Fractal statistics are used to evaluate two competing models of the business cycle, Austrian business cycle theory and real business cycle theory. Strong evidence is found for antipersistent stochastic dependence in transactions money (M1) and components of the monetary aggregates most directly concerned with transactions, which suggests an activist monetary policy. Savings assets exhibit persistent long memory, as do those monetary aggregates which include savings assets, such as savings money (M2), M2 minus small time deposits, and money of zero maturity (MZM). Virtually all measures of economic activity display antipersistence, and this finding is invariant to whether the measures are adjusted for inflation, including real gross domestic product, real consumption expenditures, real fixed private investment, and labor productivity. This strongly disconfirms real business cycle theory.     

Lyapunov exponents and anomalous diffusion of a Lorentz gas with infinite horizon using approximate zeta functions

We compute the Lyapunov exponent, the generalized Lyapunov exponents, and the diffusion constant for a Lorentz gas on a square lattice, thus having infinite horizon. Approximate zeta functions, written in terms of probabilities rather than periodic orbits, are used in order to avoid the convergence problems of cycle expansions. The emphasis is on the relation between the analytic structure of the zeta function, where a branch cut plays an important role, and the asymptotic dynamics of the system. The Lyapunov exponent for the corresponding map agrees with the conjectured limit _map = -2 log(R) + C + O(R) and we derive an approximate value for the constantC in good agreement with numerical simulations. We also find a diverging diffusion constantD(t)logt and a phase transition for the generalized Lyapunov exponents.     

Improved DOSY NMR data processing by data enhancement and combination of multivariate curve resolution with non-linear least square fitting

The quality of DOSY NMR data can be improved by careful pre-processing techniques. Baseline drift, peak shift, and phase shift commonly exist in real-world DOSY NMR data. These phenomena seriously hinder the data analysis and should be removed as much as possible. In this paper, a series of preprocessing operations are proposed so that the subsequent multivariate curve resolution can yield optimal results. First, the baseline is corrected according to a method by Golotvin and Williams. Next, frequency and phase shift are removed by a new combination of reference deconvolution (FIDDLE), and a method presented by Witjes et al. that can correct several spectra simultaneously. The corrected data are analysed by the combination of multivariate curve resolution with non-linear least square regression (MCR-NLR). The MCR-NLR method turns out to be more robust and leads to better resolution of the pure components than classic MCR.     

On the exact solutions of nonlinear diffusion-reaction equations with quadratic and cubic nonlinearities

Attempts have been made to look for the soliton content in the solutions of the recently studied nonlinear diffusion-reaction equations [R S Kaushal, J. Phys. 38, 3897 (2005)] involving quadratic or cubic nonlinearities in addition to the convective flux term which renders the system nonconservative and the corresponding Hamiltonian non-Hermitian.     

Application of the Stoner-Wohlfarth model with interaction for the determination of the saturation magnetisation, anisotropy field, and mean field interaction in bulk amorphous ferromagnets

Magnetic hysteresis curves of bulk amorphous ferromagnet alloys of composition Nd₆₀Fe₃₀Al₁₀, Nd₆₀Fe₂₀Co₁₀Al₁₀ and Pr₅₈Fe₂₄Al₁₈ have been measured in applied magnetic fields up to 9 T at temperatures in the range 10-350 K. The behaviour of the demagnetisation curve in the first quadrant is interpreted using a mean field interaction model as proposed by Callen et al. [Phys. Rev. B 16 (1977) 263], which extends the Stoner-Wohlfarth model [Philos. Trans. Roy. Soc. A 240 (1948) 599] for a random distribution of non-interacting uniaxial grains. Application of the mean field interaction model enables the determination of the saturation magnetisation M_s, anisotropy field H_a, and interaction parameter d, and from these other magnetic parameters, such as the anisotropy constant, K, are deduced. For the three alloys, the temperature dependent behaviour of M_s, H_a, d and K over the range 20-350 K are found to be qualitatively similar, though there are quantitative differences. In all cases M_s increases with decreasing temperature, both H_a and K increase with decreasing temperature, reaching a peak in the range 75-120 K, and then decreasing, and d decreases approximately linearly as the temperature decreases. The physical mechanisms responsible for coercivity in these materials are discussed in the context of random anisotropy and a strong pinning model of domain walls.     

On the critical behavior of the Ising model with mixed two- and three-spin interactions

A study is made of a two-dimensional Ising model with staggered three-spin interactions in one direction and two-spin interactions in the other. The phase diagram of the model and its critical behavior are explored by conventional finite-size scaling and by exploiting relations between mass gap amplitudes and critical exponents predicted by conformal invariance. The model is found to exhibit a line of continuously varying critical exponents, which bifurcates into two Ising critical lines. This similarity of the model with the Ashkin-Teller model leads to a conjecture for the exact critical indices along the nonuniversal critical curve. Earlier contradictions about the universality class of the uniform (isotropic) case of the model are clarified.     

On the theoretical description of the chemisorption of the hydrogen atom on the metallic surface. Calculation of energy interaction of H with hcp Co and Ni surface clusters

A model, based on the generalized valence bond theory, capable of describing the interaction of hydrogen atom (H) with large molecular systems is proposed. The accuracy of the model has been checked by calculating the and H₂ systems. Atomic spin densities for clusters having 1243 atoms have been obtained. The surface magnetic and chemisorption property differences between the Ni and Co metals have been analyzed. An extrapolation scheme suitable to obtain H chemisorption energies on infinite systems from the finite ones has been proposed. Size-converged results have been obtained for the Co. Potential energy surfaces of hydrogen, on and below, the Co surface have been provided.