Scaling Laws for the Multidimensional Burgers Equation with Quadratic External Potential

The reordering of the multidimensional exponential quadratic operator in coordinate-momentum space (see X. Wang, C.H. Oh and L.C. Kwek (1998). J. Phys. A.: Math. Gen. 31:4329–4336) is applied to derive an explicit formulation of the solution to the multidimensional heat equation with quadratic external potential and random initial conditions. The solution to the multidimensional Burgers equation with quadratic external potential under Gaussian strongly dependent scenarios is also obtained via the Hopf-Cole transformation. The limiting distributions of scaling solutions to the multidimensional heat and Burgers equations with quadratic external potential are then obtained under such scenarios. AMS Subject Classifications: 60G60, 60G15, 62M15, 60H15     

On the existence of a variational principle for an operator equation with second derivative with respect to “ time”

Using methods of nonlinear functional analysis, we define the structure of an evolution operator equation of second order that can be formulated in direct variational terms.     

Electrokinetic Response of Double Layers

Based on electrokinetic equations, we calculate the dynamic response of the thin double layer of a charged surface. The double layer response acts as effective boundary conditions for the ion concentrations, flow field, and potential outside the double layer. The results can be used to further calculate the electrophoresis or the dielectric spectrum of the deformable charged suspensions.     

46.8MeV的 ~(12)C非弹性散射

在Glauber多重散射理论框架下,使用跃迁密度方法和三种N-N湮没势,计算了46·8MeV的反质子在~(12)C上的非弹性散射微分截面.理论曲线与实验数据符合得较好.     

Influence of surface modification adopting thermal treatments on dispersion of detonation nanodiamond

In order to improve the dispersion of detonation nanodiamonds (ND) in aqueous and non-aqueous media, a series of thermal treatments have been conducted in air ambient to modify ND surface. Small angle X-ray scattering (SAXS) technique and high resolution transmission electron microscopy (HRTEM) were introduced to observe the primary size of ND. Differential thermal analysis (DTA), X-ray diffraction (XRD) methodology, X-ray photoelectron spectroscopy (XPS) and Fourier transform infrared (FTIR) spectroscopy were adopted to analyze the structure, bonds at surfaces of the treated ND. Malvern instrument Zetasizer3000HS was used for measuring the surface electric potential and the size distribution of ND. As thermal treatments can cause graphitization and oxidization of functional groups at the surface, ND treated at high temperature is correspondingly more negatively charged in an aqueous medium, and the increased absolute value of zeta potential ensures the electrostatic stability of ND particles. Specially, after being treated at a temperature more than 850 K, ND can be well dispersed in various media.     

Molecular field theory for nematic liquid crystal film with finite layers

The nematic liquid crystal film composed of n molecular layers is studied based upon a spatially anisotropic pair potential, which reproduces approximately the elastic free energy density. On condition that the system has perfect nematic order, as in the Lebwohl—Lasher model, the director in the film is isotropic. The effect of the temperature is investigated by means of molecular field theory. Some new results are obtained. Firstly, symmetry breaking takes place when taking account of the temperature, and the state with the director along the normal of the film has the lowest free energy. Secondly, the N—I phase transition temperature increases as an effect of finite sizes instead of decreasing as in the Lebwohl—Lasher model. Thirdly, the nematic order is induced in the layers near the surface in the isotropic phase.     

Molecular Dynamics Study of gases H2,D2 and T2

The classical Molecular dynamics simulation has been used to study the equation of state of gas H2,D2 and T2.It has also been investigated that the isotope mass affects on the accuracy of equation of state.Our calculated Iesults show that the classical effect is principal and the isotope mass effects on the equation of state are obvious for the much light gases.At the same time,some useful theoretical data of equation of state for these gases have been provided.It is found that the classical simulation is still effective to the quantum gas.However,the quantum mechanics simulation and the improvement of intermolecular interaction potential are necessary if more accurate computational results are expected.     

Nonadiabatic collision model calculations of ion-pair formation cross sections of Cs+O2→Cs++O

This paper has improved Hickman's nonadiabatic collision model by substituting Hickman's constant velocity classical straight line trajectory approximation with the solution of motion equation mR=?dV(R)/dR, and has calculated the cross sections of ion-pair formation Cs+O₂→Cs⁺+O^?₂ with the improved nonadiabatic collision model (INCM). A comparison of our results with other theoretical and experimental results has been made.     

Spin polarization effect for Os2 molecule

Density functional Theory （DFT） （B3p86） of Gaussian03 has been used to optimize the structure of Os2 molecule. The result shows that the ground state for Os2 molecule is 9-multiple state and its electronic configuration is ^9∑^＋g, which shows spin polarization effect of Os2 molecule of transition metal elements for the first time. Meanwhile, we have not found any spin pollution because the wavefunction of the ground state does not mingle with wavefunctions with higher energy states. So, the fact that the ground state for Os2 molecule is a 9-multiple state is indicative of spin polarization effect of Os2 molecule of transition metal elements. That is, there exist 8 parallel spin electrons. The non-conjugated electron is greatest in number. These electrons occupy different spacious tracks, so that the energy of Os2 molecule is minimized. It can be concluded that the effect of parallel spin of Os2 molecule is larger than the effect of the conjugated molecule, which is obviously related to the effect of electron d delocalization. In addition, the Murrell-Sorbie potential functions with the parameters for the ground state ^9∑^＋g and other states of Os2 molecule are derived. Dissociation energy De for the ground state of Os2 molecule is 3.3971eV, equilibrium bond length Re is 0.2403nm, vibration frequency ωe is 235.32cm^-1. Its force constants f2, f3, and f4 are 3.1032×10^2aJ·nm^-2, -14.3425×10^3aJ·nm^-3 and 50.5792×10^4aJ·nm^-4 respectively. The other spectroscopic data for the ground state of Os2 molecule ωexe, Be and ae are 0.4277cm^- 1, 0.0307cm^- 1 and 0.6491 × 10^-4cm^-1 respectively.     

Smolukhovsky problem for electrons in a metal

We find an analytic solution of the Smolukhovsky problem of the temperature and electric potential jumps in a metal under the action of the temperature gradient normal to the surface. We take the character of the electron energy accommodation on the surface into account. We find the analytic expressions for the electric field generated by heat processes, for the temperature distribution, and for the electric potential.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 142, No. 1, pp. 93–111, January, 2005.