In this work, we study the Cauchy problem for the radially symmetric spatially homogeneous Boltzmann equation with Debye-Yukawa potential. We prove that this Cauchy problem enjoys the same smoothing effect as the Cauc...In this work, we study the Cauchy problem for the radially symmetric spatially homogeneous Boltzmann equation with Debye-Yukawa potential. We prove that this Cauchy problem enjoys the same smoothing effect as the Cauchy problem defined by the evolution equation associated to a fractional logarithmic harmonic oscillator. To be specific, we can prove the solution of the Cauchy problem belongs to Shubin spaces.展开更多
Thermodynamic properties of a Debye-Yukawa system of particles are explored by using molecular dynamics simulation in the canonical ensemble. The excess free energy f of the Debye-Yukawa system is calculated by using ...Thermodynamic properties of a Debye-Yukawa system of particles are explored by using molecular dynamics simulation in the canonical ensemble. The excess free energy f of the Debye-Yukawa system is calculated by using two different approaches for the liquid phase, and the energy is obtained in a coupling parameter range of 0 ≤ F ≤100 and a wide range of the screening parameter κ. Simulation measurements for excess internal energy and pressure of the system over dimensionless parameters （κ, F） are also presented and compared with previous theoretical and simulated results. A F-expansion-fitting approach for the liquid phase is introduced with the expansion coefficients, which are functions of the screening parameter κ. The fitting coefficients are obtained by directly comparing them with the simulation measurements with a relative deviation of 1% or less. It is shown that the computational results provide a relatively simple method to calculate the excess internal energy and free energy in certain cases, which depend strongly on Г.展开更多
基金supported by the Natural Science Foundation of China(11701578)
文摘In this work, we study the Cauchy problem for the radially symmetric spatially homogeneous Boltzmann equation with Debye-Yukawa potential. We prove that this Cauchy problem enjoys the same smoothing effect as the Cauchy problem defined by the evolution equation associated to a fractional logarithmic harmonic oscillator. To be specific, we can prove the solution of the Cauchy problem belongs to Shubin spaces.
文摘Thermodynamic properties of a Debye-Yukawa system of particles are explored by using molecular dynamics simulation in the canonical ensemble. The excess free energy f of the Debye-Yukawa system is calculated by using two different approaches for the liquid phase, and the energy is obtained in a coupling parameter range of 0 ≤ F ≤100 and a wide range of the screening parameter κ. Simulation measurements for excess internal energy and pressure of the system over dimensionless parameters （κ, F） are also presented and compared with previous theoretical and simulated results. A F-expansion-fitting approach for the liquid phase is introduced with the expansion coefficients, which are functions of the screening parameter κ. The fitting coefficients are obtained by directly comparing them with the simulation measurements with a relative deviation of 1% or less. It is shown that the computational results provide a relatively simple method to calculate the excess internal energy and free energy in certain cases, which depend strongly on Г.
