International Journal of Modern Physics C

In this paper we present a singularly P-stable exponentially — fitted four-step method for the numerical solution of the radial Schrödinger equation. More specifically we present a method that is singularly P-stable (a concept later introduced in this paper) and also integrates exactly any linear combination of the functions {1, x, x², x³, x⁴, x⁵, exp (±Ivx)}. The numerical experimentation showed that our method is considerably more efficient compared to well-known methods used for the numerical solution of resonance problem of the radial Schrödinger equation.

Genetic programming (GP) has been used to discover a function that describes pseudo-rapidity distribution of created pions from proton–proton (p-p) interactions at high and ultra-high energies. The predicted distributions from the GP-based model are compared with the experimental data. The discovered function of GP model has proven matching better for experimental data.

The dynamics of a five-dimensional nonlinear network based on the theory of Chinese traditional medicine is studied by the Lyapunov exponent spectrum, Poincaré, power spectrum and bifurcation diagrams. The result shows that this system has complex dynamical behaviors, such as chaotic ones. It also shows that the system evolves into chaos through a series of period-doubling bifurcations.

We propose a scheme to secret sharing of an unknown N-atom entangled state in driven cavity QED. The scheme needs only atomic Bell states as the quantum channels and joint Bell-state measurement is unnecessary. In addition, the scheme is insensitive to the cavity decay and the thermal field.

Genetic programming (GP) has been used to discover the function that describes the collisions of positrons with sodium, potassium, rubidium and cesium atoms at low and intermediate energies. The GP has been running based on experimental data of the total collisional cross sections to produce the total cross sections for each target atom. The incident energy and the static dipole polarizability of the alkali target atom have been used as input variables to find the discovered function. The experimental, calculated and predicted total collisional cross sections are compared. The discovered function shows a good match to the experimental data. We find that the GP technique is able to improve upon more traditional methods. To our knowledge, this is the first application of the GP technique to the data of positron collisions with alkali atoms at low and intermediate energies.

We have modified the transition probability calculations in the lattice gas model of biased-random walkers. Adopting the collision-avoided rules, a new cellular automata model of pedestrian flow which updates in parallel is established. Using this model, we have simulated and studied the evacuation process of people in a hall. The spatial configuration of people is presented, which is more consistent with the scene of reality than that presented in the lattice-gas model. It is found that the escape time t_c closely depends on the width of the door and the initial density of people, it scales as t_c ∝ W^-0.55±0.01 and t_c ∝ ρ^0.98±0.01 ≈ ρ.

It is difficult to predict the dynamics of systems which are nonlinear and whose characteristic is unknown. In order to build a model of the system from input and output data without any knowledge about the system, we try automatically to build prediction model by Genetic Programming (GP).

GP has been used to discover the function that describes nonlinear system to study the effect of wavelength and temperature on the refractive index of the fiber core. The predicted distribution from the GP based model is compared with the experimental data. The discovered function of the GP model has proved to be an excellent match to the experimental data.

In this paper, a third-order Piecewise Parabolic Method for barotropic two-fluid flows with Tait equation of state is presented. In transition layers between two different fluids, a mixture model system based on the assumption of equilibrium pressure is introduced. It conserves the mass of each fluid, the total momentum and energy of the mixture and is supplemented with an advection equation for the volume fraction of one of the two fluids. To close the model and recover the pressure, a nonbarotropic equation of state describing the thermodynamic properties of the mixture is used. However, in pure barotropic fluid regions, the isentropic version of Euler equations is employed. In addition, the third-order Piecewise Parabolic Method is employed to solve the model equations. The governing equations are first evolved in the Lagrangian coordinate system and then the computed results are mapped onto the fixed Eulerian grid in the following remapping step. As compared with other methods, a remarkable feature of our approach is that the scheme is third-order accurate in smooth regions of the solution and is able to give a steeper representation of discontinuities. Numerical results demonstrate satisfactory performances of this approach.

A fishing model is presented in this paper. A year is divided into four seasons on the basis of the Penna model. We define the rules of death, reproduction, fishing and so on for fish. And "closed fishing" in China is introduced in this model. Then we discuss the population size of fish and the fishing products in the case of "closed fishing" or not. At last the conclusion is obtained that the policy will be significant if fishing intensity is in a certain range. And reducing fishing intensity is essential policy, and "closed fishing" is just an accessorial policy.

This paper addresses the adaptive synchronization and parameters identification problem of a class of high-dimensional autonomous uncertain chaotic systems. It is proved that the controller and update rule can make the states of the drive system and the response system with unknown system parameters asymptotically synchronized, and identify the response system's unknown parameters. Chen system, coupled dynamos system and Rössler hyperchaotic system are used as examples for detailed description. The results of numerical simulations show the effectiveness of the adaptive controller.

We study the non-stationary traffic flow of the ant-trail model. The nontrivial boundary conditions are adopted. The fundamental diagram is distinctly different from that of a closed system. A shock wave is generated when the first ant reaches the food source. The shock wave propagates backward to the nest long before the first ant returns. We revise the pheromone mechanism to ensure that the ants follow the leader on a complex network. The breaking of following-the-leader is also discussed.

In this paper we present a new kind of P-stable eighteenth-order six-step method for periodic initial-value problems. We add the fourth derivatives to our previous P-stable six-step method to increase the accuracy. We apply two classes of well-known problems to our new method and compare it with the previous methods. The numerical results show that the new method is much more stable, accurate and efficient than the previous methods.