International Journal of Modern Physics C

A generalized optimal velocity model is analyzed, where the optimal velocity function depends not only on the headway of each car but also the headway of the immediately preceding one. The stability condition of the model is derived by considering a small perturbation around the homogeneous flow solution. The effect of the generalized optimal velocity function is also confirmed with numerical simulations, by examining the hysteresis loop in the headway-velocity phase space, and the relation between the flow and density of cars. In the model with a specific parameter choice, it is found that an intermediate state appears for the movement of cars, where the car keeps a certain velocity whether the headway is short or long. This phenomenon is different from the ordinary stop-and-go state.

Gene expression programming is applied to find one-dimensional maps. A survey on gene expression programming is also given.

We study a variant of the Cont–Bouchaud model, which utilizes the percolation approach of multi-agent simulations of the stock market fluctuations. Here, instead of considering the relative price change as the difference of the total demand and total supply, we consider the relative price change to be proportional to the "relative" difference of demand and supply (the ratio of the difference in total demand and total supply to the sum of the total demand and total supply). We then study the probability distribution of the price changes.

In last years several mathematical methods were successfully used for financial time series modeling. The main problem is to check whether irregularities of data are generated by a stochastic process or they are due to some deterministic chaos and to the presence of low-dimensional strange attractor. We focus on a test based on the correlation dimension. In particular we examine the time series of the daily closure prices of the Italian car industry "FIAT" shares.

The train model of two blocks with stick-slip dynamics (M. de Sousa Vieira, 1995) is believed to be the simplest spring-block system, which displays chaos. Here we simplify it even more by linearizing the velocity dependence of the friction force. In this way, the nonlinearity of the equations of motion is reduced to the time moments, when a block starts to move or stops, and when the analytical solutions are to be sewn together. We demonstrate, that for small values of the velocity of blocks, the character of motion is not changed. This is observed on the bifurcation diagrams, the Lyapunov exponents, the phase portraits and the power spectra.

Standard Cellular Automata (CA) are ahistoric (memoryless), i.e., the new state of a cell depends on its neighborhood configuration only at the preceding time step. The effect of keeping ahistoric memory of all past iterations in two-dimensional CA, featuring each cell by its most frequent state is analyzed in this work.

In this paper a finite-difference lattice Boltzmann method is introduced, discretizing the lattice Boltzmann equation by centered-time and centered-space finite differences. It is well known from numerical analysis that such discretization of the derivatives results in numerical dispersion and dissipation. The numerical dispersion is eliminated perfectly by using a fictitious absorption term in the master equation and the dissipation is compensated by solving a second, reference equation and the method of division. As a test problem, the evolution of a decaying Taylor vortex in a 2π periodic domain is studied.

We present the algorithms necessary for the implementation of a quantum neural network with learning and classification tasks. A complete implementation for the classification and learning algorithms is given in terms of unitary quantum gates. Such a quantum neural network can be used to perform complex classification tasks or to solve the general problem of binary mapping.

We present results of an extension of the market model introduced by Bornholdt to high dimensions. Three and four dimensions are shown to behave similar to two, for suitable parameters.

The relation between dislocation velocity and resolved shear stress is studied computationally at the atomic scale using Molecular Dynamics simulations in a two-dimensional Lennard–Jones system. Mimicking a well known experimental technique, we apply a calibrated stress pulse to a system with a single dislocation and follow with a run-time graphics tool and displacement-field based tracking method, the dislocation motion caused by momentum transfer from an externally generated stress pulse. The empirically suggested power law relation between dislocation velocity and resolved shear stress seems to hold also in the atomic scale.

The Nagel–Schreckenberg-model (NaSch-model) describes macroscopic features of real traffic very well. However, the characterization of a single car driver's behavior in some details is not realistic, e.g., the NaSch-driver calculates his/her distance to the car in front from the position this car has just in the very moment and ignores that it could move further in the next time step. This behavior is rarely found in real traffic. Normally, a driver estimates the speed of the car in front, takes as well a certain braking distance into consideration and keeps distance accordingly. As an answer to this demand, the second rule of the NaSch-model is modified in the following.

A simple Ising spin model, which can describe the mechanism of price formation in financial markets is proposed. In contrast to other agent-based models, the influence does not flow inward from the surrounding neighbors to the center site, but spreads outward from the center to the neighbors. The model thus describes the spread of opinions among traders. It is shown via standard Monte Carlo simulations that very simple rules lead to dynamics that duplicate those of asset prices.