Chemical diffusion in a one dimensional lattice with two sites inequivalent2

Making use of the exact form of the Nernst-Einstein equation and an exact expression for the d.c. ionic conductivity derived by Richards, I have derived an exact expression for the chemical diffusion coefficient in a one dimensional lattice with two sites inequivalent and self-blocking by the atoms. It was found that the chemical diffusion coefficient is independent of concentration. This particular result, however, can apply only to the one dimensional lattice.     

Enhanced NMR signal from the laser-polarized129Xe produced by spin exchange at a high magnetic field

Nuclear-magnetic-resonance (NMR) measurement of laser-polarized gaseous¹²⁹Xe produced by spin-exchange optical pumping with a narrow-linewidth laser at a high magnetic field of 4.7 T is reported. The samples are contained in the glass tubes. The nuclear spin polarization of the laserpolarized¹²⁹Xe is 3.9%, and this corresponds to an enhancement of 9· 10³ compared to the equilibrium value at 311 K and at the same magnetic field. The laser-enhanced¹²⁹Xe NMR signals can be used in MR imaging.     

高电荷态离子129Xe29+与不同金属表面作用产生的X射线谱

研究了高电荷态离子129Xe29+入射金属Au、Mo、Be表面产生的特征X射线谱。实验结果表明,在入射离子的动能相同时,Au的Mα1-X射线产额比Mo的Lα1-X、Lα2-X、Lβ 1-X射线总产额高,特征X射线的产额随入射离子动能的增加而显著增加;不同动能的Xe29+入射金属Au、Mo、Be表面均未产生Xe的特征X射线。     

Local stability and hydrodynamical limit of Spitzer's one dimensional lattice model

An infinite system of ordinary differential equations is considered, the right hand side is just the negative gradient of potential energy of a one-dimensional system of unbounded spins interacting by a symmetric and convex pair potential. Constant configurations are stationary points and the mean spin is conserved. It is shown that each of these stationary points has its own domain of attraction, the initial distribution need not be translation invariant. As a consequence we obtain that the mean spin satisfies the heat equation in the hydrodynamical limit.     

A lattice Boltzmann model for coupled diffusion

Diffusion coupling between different chemical components can have significant effects on the distribution of chemical species and can affect the physico-chemical properties of their supporting medium. The coupling can arise from local electric charge conservation for ions or from bound components forming compounds. We present a new lattice Boltzmann model to account for the diffusive coupling between different chemical species. In this model each coupling is added as an extra relaxation term in the collision operator. The model is tested on a simple diffusion problem with two coupled components and is in excellent agreement with the results obtained through a finite difference method. Our model is observed to be numerically very stable and unconditional stability is shown for a class of diffusion matrices. We further develop the model to account for advection and show an example of application to flow in porous media in two dimensions and an example of convection due to salinity differences. We show that our model with advection loses the unconditional stability, but offers a straight-forward approach to complicated two-dimensional advection and coupled diffusion problems.     

Thermodynamic studies of the two dimensional Falicov-Kimball model on a triangular lattice

Thermodynamic properties of the spinless Falicov-Kimball model are studied on a triangular lattice using numerical diagonalization technique with Monte-Carlo simulation algorithm. Discontinuous metal-insulator transition is observed at finite temperature. Unlike the case of square lattice, here we observe that the finite temperature effect is not able to smear out the discontinuous metal-insulator transition seen in the ground state. Calculation of specific heat (C _v ) shows single and double peak structures for different values of parameters like on-site correlation strength (U), f-electron energy (E _f ) and temperature.     

两车道交通流耦合格子模型与数值仿真

考虑两车道耦合效应的影响和换道效应,提出了改进的两车道交通流耦合格子模型.同时,改进了换道时的流量转移率,这样更符合实际交通情况.通过线性稳定性分析,得到了改进模型的稳定性条件.数值模拟结果也表明,模型通过考虑耦合作用信息,更好地再现了换道情况,同时也表明两车道间的耦合效应对两车道交通流存在不可忽视的影响.     

A model for two dimensional orientational order

We use a generalization of Kikuchi's cluster variational method (CVM), in the pair approximation, to study anisotropic plane rotors on a square lattice as a simple model for two dimensional nematics. The system was shown to exhibit nematic ordered states at low temperature, disordering, for all anisotropies, through a continuous transition. The orientational distribution functions, order parameter, internal energy and specific heat were calculated within the CVM and compared with the results of a recent computer simulation. Estimates for the non-classical exponents were obtained using a mean field renormalization group analysis. A spin wave argument was also used to investigate the role of long range fluctuations near the isotropic fixed point. The accuracy of these different techniques is discussed within the context of our model.     

Application of129Xe 2D-EXSY NMR to intra- and interparticle exchange in zeolites

2D-EXSY NMR methods were used to explore diffusion between different domains in zeolites on two very different length scales. Measurements were made on xenon-containing samples consisting of a mixture of NaX and NaY zeolite particles which give distinct resonance lines. The cross peaks observed were interpreted in terms of interparticle exchange, and exchange rates were measured as a function of particle size. This kind of experiment with a length scale of microns to mm should be useful in model studies of diffusion in packed catalyst beds. Measurements also were made to study exchange on a much smaller length scale between the main-channel and side-pocket sites in samples of microcrystalline Na-mordenite. Exchange rates and site occupancies were measured as a function of temperature, yielding activation energies for xenon desorption and intersite diffusion. Also, information was obtained on the distribution of inequivalent side-pocket sites which leads to the large xenon NMR linewidths for this type of site.     

Frequency-selective laser optical pumping and spin exchange of cesium with129Xe and131Xe in a high magnetic field

We report the experimental results of frequency-selective laser optical pumping and spin exchange of Cs with¹²⁹Xe and¹³¹Xe in a high magnetic field of 11.74 T. Our results show that hyperpolarized¹²⁹Xe and¹³¹Xe nuclear magnetic resonance (NMR) signals exhibit alternating phases when the laser frequency for pumping the cesium atoms is changed, which is explained on the basis of the high-field optical pumping of Cs. We obtain about 3% polarization of the¹²⁹Xe. The electron-spin polarization of the Cs atoms has been measured to be about 22% with a simple NMR method.     

A new search for the atomic EDM of 129Xe at FRM-II

Permanent electric dipole moments (EDMs) arise due to the breaking of time-reversal or, equivalently, CP-symmetry. Although EDM searches have so far only set upper limits, which are many orders of magnitude larger than Standard Model (SM) predictions, the motivation for more sensitive searches is stronger than ever. A new effort at FRM-II incorporating ¹²⁹Xe and ³He as a co-magnetometer can potentially improve the current limit. The noble gas mixture of ¹²⁹Xe and ³He is simultanously polarized by spin-exchange optical pumping and then transferred into a high-performance magnetically shielded room. Inside, both species can freely precess in the presence of applied magnetic and electric fields. The precession signals are detected by LTc SQUID sensors. In EDM cells with silicon electrodes we observed spin lifetimes in excess of 2500 s without and with high-voltage applied. This meets one requirement to achieve our goal of improving the EDM limit on ¹²⁹Xe by several orders of magnitude.     

A model for cluster confinement in one dimensional many-body systems

A variant of the one-dimensional “toy model” for QCD of Horowitz et al. is presented, which uses a density dependent rather than the many-body force originally proposed by Lenz et al. Our approach suggests, already within the RPA framework, the occurrence of a phase transition simulating the one from quark to hadronic matter, similar to the transition foreseen by Horowitz et al. However our force is easy to handle in three dimensions as well, but in such a case, of course, the correspondence between our and the “toy model” remains to be verified.     

A two scale nonlinear fractal sea surface model in a one dimensional deep sea

Using the theory of nonlinear interactions between long and short waves,a nonlinear fractal sea surface model is presented for a one dimensional deep sea.Numerical simulation results show that spectra intensity changes at different locations(in both the wave number domain and temporal-frequency domain),and the system obeys the energy conservation principle.Finally,a method to limit the fractal parameters is also presented to ensure that the model system does not become ill-posed.     

A boundary value problem for the two dimensional Broadwell model

It is shown that a certain boundary value problem for the steady two-dimensional Broadwell model on a rectangle has a solution. The boundary conditions specify the ingoing particle densities on each side of the rectangle.Research supported by the Natural Science and Engineering Research Council Canada under Grants A7847 and A8560     

Lagrangian of the most probable path for one dimensional nonlinear diffusion processes

Using a Lagrangian density of the Fokker-Planck equation and the Kolmogoroff backward equation we construct a Lagrangian of the most probable path for one dimensional nonlinear diffusion processes.     

A quasiharmonic model calculation for non-markovian far-infrared spectra of HCl in Kr and Xe liquids

The far-infrared spectra (0–200 cm^?1) of dilute solutions of HCl in liquid Kr and Xe have been calculated by applying of a non-markovian spectral theory called PTOC (partial time ordering cumulants) and by using a quasiharmonic model for the liquid structure recently reported by us (A. Calvo Hernández et al., 1987, J. chem. Phys., 86, 4597) and successfully applied to HCl?Ar solution (Ibid., 86, 4607). The bath correlation functions which appear in the spectral theory involve a reduced set of parameters regarding both the HCl?Kr and HCl?Xe interactions and the liquid structure. From comparison between theoretical and experimental spectra it is possible to deduce quantitative values for the above parameters. The pronounced rotational fine structure of the experimental spectra for HCl in Kr and Xe liquids is quite well explained by the actual model.     

Exact results for the one dimensional asymmetric exclusion model

The asymmetric exclusion model describes a system of particles hopping in a preferred direction with hard core repulsion. These particles can be thought of as charged particles in a field, as steps of an interface, as cars in a queue. Several exact results concerning the steady state of this system have been obtained recently. The solution consists of representing the weights of the configurations in the steady state as products of non-commuting matrices.     

Multiple-relaxation-time lattice Boltzmann model for the convection and anisotropic diffusion equation

A lattice Boltzmann model with a multiple-relaxation-time (MRT) collision operator for the convection–diffusion equation is presented. The model uses seven discrete velocities in three dimensions (D3Q7 model). The off-diagonal components of the relaxation-time matrix, which originate from the rotation of the principal axes, enable us to take into account full anisotropy of diffusion. An asymptotic analysis of the model equation with boundary rules for the Dirichlet and Neumann-type (specified flux) conditions is carried out to show that the model is first- and second-order accurate in time and space, respectively. The results of the analysis are verified by several numerical examples. It is also shown numerically that the error of the MRT model is less sensitive to the variation of the relaxation-time coefficients than that of the classical BGK model. In addition, an alternative treatment for the Neumann-type boundary condition that improves the accuracy on a curved boundary is presented along with a numerical example of a spherical boundary.