Beyond Scaling and Locality in Turbulence

An analytic perturbation theory is suggested in order to find finite-size corrections to the scaling power laws. In the frame of this theory it is shown that the first order finite-size correction to the scaling power laws has following form , where η is a finite-size scale (in particular for turbulence, it can be the Kolmogorov dissipation scale). Using data of laboratory experiments and numerical simulations it is shown shown that a degenerate case with α ₀=0 can describe turbulence statistics in the near-dissipation range r > η, where the ordinary (power-law) scaling does not apply. For moderate Reynolds numbers the degenerate scaling range covers almost the entire range of scales of velocity structure functions (the log-corrections apply to finite Reynolds number). Interplay between local and non-local regimes has been considered as a possible hydrodynamic mechanism providing the basis for the degenerate scaling of structure functions and extended self-similarity. These results have been also expanded on passive scalar mixing in turbulence. Overlapping phenomenon between local and non-local regimes and a relation between position of maximum of the generalized energy input rate and the actual crossover scale between these regimes are briefly discussed. PACS: 47.27.-i, 47.27.Gs.     

Quantifying bid-ask spreads in the Chinese stock market using limit-order book data

The statistical properties of the bid-ask spread of a frequently traded Chinese stock listed on the Shenzhen Stock Exchange are investigated using the limit-order book data. Three different definitions of spread are considered based on the time right before transactions, the time whenever the highest buying price or the lowest selling price changes, and a fixed time interval. The results are qualitatively similar no matter linear prices or logarithmic prices are used. The average spread exhibits evident intraday patterns consisting of a big L-shape in morning transactions and a small L-shape in the afternoon. The distributions of the spread with different definitions decay as power laws. The tail exponents of spreads at transaction level are well within the interval (2,3) and that of average spreads are well in line with the inverse cubic law for different time intervals. Based on the detrended fluctuation analysis, we found the evidence of long memory in the bid-ask spread time series for all three definitions, even after the removal of the intraday pattern. Using the classical box-counting approach for multifractal analysis, we show that the time series of bid-ask spread do not possess multifractal nature.     

Stylized facts from a threshold-based heterogeneous agent model

A class of heterogeneous agent models is investigated where investors switch trading position whenever their motivation to do so exceeds some critical threshold. These motivations can be psychological in nature or reflect behaviour suggested by the efficient market hypothesis (EMH). By introducing different propensities into a baseline model that displays EMH behaviour, one can attempt to isolate their effects upon the market dynamics. The simulation results indicate that the introduction of a herding propensity results in excess kurtosis and power-law decay consistent with those observed in actual return distributions, but not in significant long-term volatility correlations. Possible alternatives for introducing such long-term volatility correlations are then identified and discussed.     

Percolation processes in monomer-polyatomic mixtures

In this paper, the percolation of mixtures of monomers and polyatomic species (k$k$-mers) on a square lattice is studied. By means of a finite-size scaling analysis, the critical exponents and the scaling collapsing of the fraction of percolating lattices are found. A phase diagram separating a percolating from a non-percolating region is determined. The main features of the phase diagram are discussed in order to predict its evolution for larger k$k$-mer sizes.     

Implementation of divide-and-conquer method including Hartree-Fock exchange interaction

The divide-and-conquer (DC) method, which is one of the linear-scaling methods avoiding explicit diagonalization of the Fock matrix, has been applied mainly to pure density functional theory (DFT) or semiempirical molecular orbital calculations so far. The present study applies the DC method to such calculations including the Hartree-Fock (HF) exchange terms as the HF and hybrid HF/DFT. Reliability of the DC-HF and DC-hybrid HF/DFT is found to be strongly dependent on the cut-off radius, which defines the localization region in the DC formalism. This dependence on the cut-off radius is assessed from various points of view: that is, total energy, energy components, local energies, and density of states. Additionally, to accelerate the self-consistent field convergence in DC calculations, a new convergence technique is proposed.     

Increase of YBa2Cu3O7 critical currents by Mo substitution and high-pressure oxygen annealing

We have previously shown for powders that Mo substitution into the CuO chains of YBa₂Cu₃O₇ can create effective pinning centres which significantly increase the critical current density (j_c) in 7 T field by a factor of 4 and 10 at 50 and 60 K, respectively (Rogacki et al., 2006) [1]. The present work reports on the influence of the Mo substitution and high-pressure oxygen annealing on the pinning properties and critical currents of YBa₂Cu_3-xMo_xO_7-d by comparing pure (x = 0, d > 0) and substituted (x = 0.03, d < 0) single crystals. Pinning properties have been investigated by measurements of magnetization loops and calculations of j_c in the ab-plane, in the temperature range from 2 to 90 K and in fields up to 14 T. Depending on the Mo substitution and the oxygen treatment, several types of pinning centres increasing j_c have been revealed and analysed in the frame of Dew-Hughes’ and Kramer's models.     

Conductivity of heavily doped Si:P under uniaxial stress

Barely insulating, uncompensated Si:P samples have been tuned through the metal‐insulator transition applying uniaxial stress along the [100] direction. We find a critical exponent μ ≈︂ 1 of the electrical conductivity extrapolated to temperature T = 0, i.e. σ(T → 0,S) ∼ |S — S_c|^μ, in disagreement with earlier stress tuning studies along [123‐] where μ ≈︂ 0.5 was reported. Varying the stress or the concentration leads to a different T dependence of σ(T). Our stress‐tuning measurements obey finite‐T scaling with a dynamic exponent z = 3.     

High-frequency dielectric and conductometric properties of poly-l-lysine aqueous solutions at the crossover between semidilute and entangled regime

The dielectric and conductometric properties of poly-l-lysine aqueous solutions have been investigated in the frequency range from 1 MHz to 1.8 GHz, where micro-Brownian dynamics and internal motion of side-chain polar groups result in a well-defined relaxation process, intermediate between that caused by counterion polarization (characteristic of the polyelectrolyte nature of the polyion investigated) and that associated with the orientational polarization of the aqueous phase. The polymer concentration has been varied in a wide interval in order to investigate the influence of different chain conformations on the dielectric parameters as a consequence of the different concentration regimes occurring in these systems. With the help of polymer scaling theories, scaling relations for the dielectric strength and the relaxation time are presented, predicting, as the polymer concentration is increased, a transition from semidilute-unentangled to semidilute-entangled regimes. We compare these predictions with the experimental findings over the whole concentration range investigated, with a qualitative agreement. Deviations from the scaling behavior related to a crossover regime between unentangled and entangled regions are briefly discussed. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 3123–3130, 1999     

Multifractal analysis of foreign exchange data

In this paper we perform multifractal analyses of five daily Foreign Exchange (FX) rates. These techniques are currently used in turbulence to characterize scaling and intermittency. We show the multifractal nature of FX returns, and estimate the three parameters in the universal multifactal framework, which characterize all small and medium intensity fluctuations, at all scales. For large fluctuations, we address the question of hyperbolic (fat) tails of the distributions which are characterized by a fourth parameter, the tail index. We studied both the prices fluctuations and the returns, finding no systematic difference in the scaling exponents in the two cases. We discuss and compare our results with several recent studies, and show how the additive models are not compatible with data: Brownian, fractional Brownian, Lévy, Truncated Lévy and fractional Lévy models. We analyse in this framework the ARCH(1), GARCH(1,1) and HARCH (7) models, and show that their structure functions scaling exponents are undistinguishable from that of Brownian motion, which means that these models do not adequately describe the scaling properties of the statistics of the data. Our results indicate that there might exist a multiplicative ‘flux of financial information’, which conditions small‐scale statistics to large‐scale values, as an analogy with the energy flux in turbulence. Copyright © 1999 John Wiley & Sons, Ltd.     

Complete one‐ and two‐center partitioning scheme for the total energy in the Hartree–Fock theory

We proposed a complete calculation scheme for attributing the total energy by the Hartree–Fock theory to atoms (E_A) and the region between two atoms (E_AB). It was pointed out that the conventional method using the Fock matrix includes a large amount of mutual contamination in both E_A and E_AB. The new scheme was derived from the basic expression of the total energy. Calculated results by the new scheme satisfy the theoretical requirements. The scaling effect on partitioned energies was also examined. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 35–46, 1999