Theoretical calculation of the shock compression properties of liquid H2 + D2 mixtures

Based on liquid variational perturbation theory with quantum mechanics correction, the effective exp-6 potential is adopted to compute the shock Hugoniot of liquid H₂ + D₂ mixtures at different molar rations. An examination of the confidence of the above computation is performed by comparing experiments and calculations, in which similar calculation procedure used for H₂ + D₂ is adopted for H₂ and D₂ each, since no experimental data are available to conduct this kind of comparison. Good agreement in both comparisons is found. This fact may look as if an indirect positive verification of calculation procedure was used here at least in the pressure and temperature domain covered by the experimental data of H₂ and D₂ used for comparison, numerically nearly up to 20 GPa and 10⁴ K. Project supported by the Science and Technology Foundation of China Academy of Engineering Physics (Grant No. 97Z011).     

Systematic study for grey particles in relativistic nucleus + emulsion (Ag) interactions

The hadronic and string cascade model and the corresponding event generator LUCIAE are used to study systematically the production of the grey particles in (14.6, 60 and 200A GeV)0 + Em, (2004 GeV)Si + Em, (200A GeV)S + Em and (11.6A GeV)Au + Em reactions. The dependences of the mean multiplicity, the multiplicity distributions and the polar angular distributions of the grey particles on the incident energy, the projectile mass and the collision centrality observed in emulsion experiments, respectively, are all reproduced by LUCIAE calculations. In addition the effects of the rescattering on the grey particle production are also investigated. Project supported by the National Natural Science Foundation of China (Grant Nos. 19575071 and 19875019) and DFG of Germany.     

Willmore Functionals

We prove some integral inequalities for immersed tori in the three sphere. The functionals considered are generalizations of the Willmore functional.

     

Hyperbolic metric and normal family

In this paper, we study the normality of the family of meromorphic functions from the viewpoint of hyperbolic metric. Then, a new sufficient and necessary condition is obtained, which can determine a given family of meromorphic functions is normal or not.     

Asymptotic properties of the MLE for the autoregressive process coefficients under stationary Gaussian noise

In this paper we study the Maximum Likelihood Estimator (MLE) of the vector parameter of an autoregressive process of order p with regular stationary Gaussian noise. We prove the large sample asymptotic properties of the MLE under very mild conditions. We do simulations for fractional Gaussian noise (fGn), autoregressive noise (AR(1)) and moving average noise (MA(1)).     

Spatiotemporal dynamics of a Leslie–Gower predator–prey model incorporating a prey refuge

In this paper, we investigate the spatiotemporal dynamics of a two-dimensional predator–prey model, which is based on a modified version of the Leslie–Gower scheme incorporating a prey refuge. We establish a Lyapunov function to prove the global stability of the equilibria with diffusion and determine the Turing space in the spatial domain. Furthermore, we perform a series of numerical simulations and find that the model dynamics exhibits complex Turing pattern replication: stripes, cold/hot spots-stripes coexistence and cold/hot spots patterns. The results indicate that the effect of the prey refuge for pattern formation is tremendous. This may enrich the dynamics of the effect of refuge on the predator-prey systems.