International Journal of Modern Physics C

It has become popular recently to apply the multifractal formalism of statistical physics (scaling analysis of structure functions and f(α) singularity spectrum analysis) to financial data. The outcome of such studies is a nonlinear shape of the structure function and a nontrivial behavior of the spectrum. Eventually, this literature has moved from basic data analysis to estimation of particular variants of multifractal models for asset returns via fitting of the empirical τ(q) and f(α) functions. Here, we reinvestigate earlier claims of multifractality using four long time series of important financial markets. Taking the recently proposed multifractal models of asset returns as our starting point, we show that the typical "scaling estimators" used in the physics literature are unable to distinguish between spurious and "true" multiscaling of financial data. Designing explicit tests for multiscaling, we can in no case reject the null hypothesis that the apparent curvature of both the scaling function and the Hölder spectrum are spuriously generated by the particular fat-tailed distribution of financial data. Given the well-known overwhelming evidence in favor of different degrees of long-term dependence in the powers of returns, we interpret this inability to reject the null hypothesis of multiscaling as a lack of discriminatory power of the standard approach rather than as a true rejection of multiscaling. However, the complete "failure" of the multifractal apparatus in this setting also raises the question whether results in other areas (like geophysics) suffer from similar shortcomings of the traditional methodology.

An effective one-dimensional model approach combining time-dependent pseudospectral method and Taylor expansion [Haoxue Qiao et al., Phys. Rev. A65, 063403 (2002)] is generalized to study a real hydrogen atom in an intense laser field. High-order harmonic generations are calculated in several cases of different laser field parameters. The ionization probability is also calculated. The influence of the strong magnetic field on harmonic generations is investigated. It is found that the plateau of high harmonics can be extended by the magnetic field and the cutoff order increases with the increase of the field intensity.

Recently, we have proposed a Euler–Lagrange transformation for cellular automata (CA) by developing new transformation formulas. Applying this method to the Burgers CA (BCA), we have succeeded in obtaining the Lagrange representation of the BCA. In this paper, we apply this method to multi-value generalized Burgers CA (GBCA) which include the Fukui–Ishibashi model and the quick-start model associated with traffic flow. As a result, we have succeeded in clarifying the Euler–Lagrange correspondence of these models. It turns out moreover that the GBCA can naturally be considered as a simple model of a multi-lane traffic flow.

In this paper we present the results of a dynamical nanotube bending study. Carbon nanotube structures under constant rate bending have been studied using classical molecular dynamics simulations method, with the inter-atomic forces described by Brenner's empirical model potential. We show that the tube diameter and the prevalent temperature play an important role in the outcome. Some of the results have been assessed by letting the most deformed part of the nanotube further relax by using a dynamical tight binding method. Significant difference was found between the empirical and the tight binding models in predicting the structure.

As the Nagel–Schreckenberg model (NaSch model) became known as a realistic approach to describe traffic flow on single-lane streets, this model was extended to two-lane traffic by several groups. On the base of our two-lane model, we will now investigate the impact of a place of obstruction, e.g., because of road works, on partial fractions, densities and mean velocities.

Phenomena on the liquid surfaces are of current importance, such as those for rivers, oceans, liquid propellant for rockets and aviation kerosene. Wave propagation on a liquid surface in the presence of surface tension is hereby investigated. Computerized symbolic computation, generalized hyperbolic-function method and Wu method are combined. Some soliton-like, exact analytic solutions are obtained for a recently-proposed (2+1)-dimensional 6th-order model. Possibly observable effects are also proposed, which certain future experiments may hopefully discover.

In city network, the state of the traffic flow which is in front of each intersection is random and disorder. It usually leads to some traffic problems. In this paper, we propose a new technique to control such dynamical state of the traffic flow on a main road. A type of the control signal has been designated at a given site (signal point) in front of each intersection. Under the effect of the control signal, the velocities of the vehicles which pass the signal point will be changed. Our method is tested for the "unified" CA traffic model which is the marriage of the NaSch model and the BML model. The simulation results demonstrate that using this control strategy, when the traffic light is green, the disorder state of the traffic flow which is in front of each intersection can be suppressed, and the periodic state of the traffic flow will occur.

A technique is presented for the identification of rule that generates a given complex pattern of linear one-dimensional cellular automata (LCA). The technique is based on the construction of a Markov transition matrix for the Markov chains that correspond to the evolution of the automaton. Such chain is generated by the evolution of a sequence of symbols representing the value of a string composed by small portion of the sites of the automaton. Excellent results are obtained for the identification of the rules that generate different complex patterns.

In the Sznajd consensus model on the square lattice, two people who agree in their opinions convince their neighbors of this opinion. We generalize it to many layers representing many age levels, and check if a consensus among all layers is possible. Advertising sometimes, but not always, produces a consensus on the advertised opinion.

We have studied the chain length dependence of folding time for proteins by implementing a novel Monte Carlo (MC) method. The physical parameters in our model are derived from the statistics for bending and torsion angles and distances between the centers of the monomers up to the fourth neighborhood. By assigning potential wells to each of the physical parameters, we are able to use a modified Metropolis algorithm to efficiently trace the later conformations of the proteins as time evolves. Our prescription for microscopic dynamics of the protein "Crambin" results in an increase of folding times with increasing chain length. The folding times are determined via Debye relaxation process.

The equilibrium thermodynamic properties of two peptide sequences of β-casein in the α-helix regions were studied by three-dimensional molecular modeling in vacuum. All the three-dimensional conformations of each peptide sequences were obtained by multicanonical simulations using ECEPP/2 force field and each simulation was started from completely random initial conformation. No a-priori information about ground-state is used in the simulations. In the present study, we calculated the average values of total energy, specific heat, fourth-order cumulant for two peptide sequences of β-casein as a function of temperature. We observed that the specific heat shows two peaks as a function of temperature for both peptides. Because our sequences have highly helical structure and two peaks in the specific heat, we have also studied the helix–coil transitions to determine these peaks. Our data indeed show these peptides have highly helical structure and better agreement with the results of spectroscopic techniques and other prediction methods.

By means of a more general ansatz and the computerized symbolic system Maple, a generalized algebraic method to uniformly construct solutions in terms of special function of nonlinear evolution equations (NLEEs) is presented. We not only successfully recover the previously-known traveling wave solutions found by Fan's method, but also obtain some general traveling wave solutions in terms of the special function for the asymmetric Nizhnik–Novikov–Vesselov equation.