A lattice Boltzmann model for miscible viscous fingering in porous media is proposed. Stable displacement between two fluids with same viscosity is simulated. Good agreement with analytical solution is obtained. Specifically,effects of viscosity contrast and Peclet number are investigated. It shows that great viscosity contrast makes fingers grow faster. As viscosity contrast is given,there exists a critical Peclet number above which tip-splitting happens. Study on transversely averaged concentration profile indicates that mixing length first goes as t^1/2,then shifts into a linear dependence in t.

The Monte Carlo Method has been applied to study the properties of the ground state of the four nucleon system. The wave function of the nucleon is assumed to contain the Jastrow factor, which Is due to the correlation of the other nucleons in the system. The variational constants of the wave function have been calculated by Zabolitzky and Kalos.Jn this article, we have used the wave function quoted above to calculate the binding energy of the system, its root mean square radius, the density distribution of the nucleon and the form factor.The result of our calculation indicates that the Monte Carlo Method can be used to study the properties of the ground state of the nuclear system. It requires to do further work to ensure that this method can be used to study other properties of the nucleus such as the properties of the excited states, the nuclear transitions, etc.