Transport and relaxation properties of isotopomeric hydrogen–helium binary mixtures. II. HD,D2, T2–He mixtures

The comprehensive comparison between calculated bulk non-equilibrium properties of hydrogen–helium isotopomeric mixtures and experiment that has previously been carried out for H₂–helium mixtures [2004, Molec. Phys., submitted] has been extended to mixtures of HD, D₂ and T₂ with ³He and ⁴He. For HD–⁴He mixtures, comparison is also made, where possible, with previous calculations of Köhler and Schaefer [1983, Physica A, 120, 185]. The phenomena examined herein include low temperature interaction second virial coefficients, binary diffusion and thermal conductivity coefficients, rotational relaxation, transport property field effects and flow birefringence. Scattering calculations have been carried out for the HD–He PES of Schaefer and Köhler [1985, Physica A, 129, 469], and for both the Köhler–Schaefer and Tao [1994, J. chem. Phys., 100, 4947] potential surfaces for the D₂–He and T₂–He interactions. Comparisons between calculated and experimental results for HD, D₂, T₂–He mixtures confirm the conclusion, reached earlier from the H₂–He comparisons, that these potential surfaces are very close to the correct one for the hydrogen–helium interaction, and that the small differences between them cannot be distinguished readily by measurements of bulk gas phenomena unless the attendant experimental uncertainties are better than ±0.3%.     

On the Ising model for the simple cubic lattice

The Ising model was introduced in 1920 to describe a uniaxial system of magnetic moments, localized on a lattice, interacting via nearest-neighbour exchange interaction. It is the generic model for a continuous phase transition and arguably the most studied model in theoretical physics. Since it was solved for a two-dimensional lattice by Onsager in 1944, thereby representing one of the very few exactly solvable models in dimensions higher than one, it has served as a testing ground for new developments in analytic treatment and numerical algorithms. Only series expansions and numerical approaches, such as Monte Carlo simulations, are available in three dimensions. This review focuses on Monte Carlo simulation. We build upon a data set of unprecedented size. A great number of quantities of the model are estimated near the critical coupling. We present both a conventional analysis and an analysis in terms of a Puiseux series for the critical exponents. The former gives distinct values of the high- and low-temperature exponents; by means of the latter we can get these exponents to be equal at the cost of having true asymptotic behaviour being found only extremely close to the critical point. The consequences of this for simulations of lattice systems are discussed at length.     

强磁场下He2++H(1s)的碰撞激发过程的态选择截面研究

强磁场下的重粒子碰撞激发过程是重要的非弹性碰撞过程, 但相关研究还几乎是空白. 应用经典蒙特卡洛的方法在得到无磁场下He²⁺+H(1s)的碰撞激发截面的基础上, 详细研究了不同强度的纵向和横向强磁场环境下到不同主量子数n和磁量子数m的碰撞激发过程的态选择截面. 同时用非微扰量子方法, 得到了强磁场下靶原子的能级, 并分析了其随磁场强度变化的原因. 对碰撞过程发现由于磁场的引入导致到不同m态的激发截面有较大的分离, 同时在较低入射能区的态选择截面变化行为与磁场方向有很大关系, 这与能级变化及横向强磁场所特有的抗磁项的相互竞争有密切联系. 通过对有关事例、径迹的分析, 解释了这些变化形成的原因. 也发现由于核的运动, 沿磁场方向的轨道角动量并非绝对守恒, 而有微小的变化. 关键词： 重粒子碰撞激发 经典蒙特卡洛模拟 强磁场 态选择截面     

The Poincaré series of the algebras of simultaneous invariants and covariants of two binary forms

Let ? _{d 1, d 2} and 𝒞 _{d 1, d 2} be the algebras of simultaneous invariants and simultaneous covariants of the two binary forms of degrees d ₁ and d ₂. Formulas for computation of the Poincaré series 𝒫? _{d 1, d 2} (z), 𝒫𝒞 _{d 1, d 2} (z) of the algebras are found. By using these formulas, we have computed the series for d ₁, d ₂ ≤ 20.     

MacMahon partition analysis and the Poincaré series of the algebras of invariants of ternary and quaternary forms

By using MacMahon partition analysis technique, the Poincaré series for the algebras of invariants of the ternary and quaternary forms of small degrees are calculated.     

Asymptotic preserving numerical schemes for a non‐classical radiation transport model for atmospheric clouds

We present numerical schemes for the P1‐moment and M1‐moment approximations of a non‐classical transport equation modeling radiative transfer in atmospheric clouds. In contrast to classical radiative transfer, the photon path‐length is introduced as an additional variable and serves as pseudo‐time in this model. Because clouds may have optically thick regions, we introduce a diffusive scaling and show that the diffusion limits of the moment models and the original equations agree. Furthermore, we show that the numerical schemes also preserve the diffusion asymptotics as well as the set of admissible and realizable states, both for the explicit and the implicit discretization of the pseudo‐time variable. A source iteration‐like method is proposed, and we observe that it converges slowly in the optical thick case, but a suitable initialization can help to overcome this problem. We validate our method in 1D and present simulation results in the 2D‐case for real cloud data. Copyright © 2013 John Wiley & Sons, Ltd.     

Bell多项式在经典Boussinesq方程中的应用

本文借助于Bell多项式研究经典Boussinesq方程,将其转换成Hirota双线性形式,构造了带参数的B(a)cklund变换,进而重新导出了其Lax表示.     

Critical behavior in inhomogeneous random graphs

We study the critical behavior of inhomogeneous random graphs in the so‐called rank‐1 case, where edges are present independently but with unequal edge occupation probabilities. The edge occupation probabilities are moderated by vertex weights, and are such that the degree of vertex i is close in distribution to a Poisson random variable with parameter w_i, where w_i denotes the weight of vertex i. We choose the weights such that the weight of a uniformly chosen vertex converges in distribution to a limiting random variable W. In this case, the proportion of vertices with degree k is close to the probability that a Poisson random variable with random parameter W takes the value k. We pay special attention to the power‐law case, i.e., the case where \begin{align*}{\mathbb{P}}(W\geq k)\end{align*} is proportional to k^‐(τ‐1) for some power‐law exponent τ > 3, a property which is then inherited by the asymptotic degree distribution. We show that the critical behavior depends sensitively on the properties of the asymptotic degree distribution moderated by the asymptotic weight distribution W. Indeed, when \begin{align*}{\mathbb{P}}(W > k) \leq ck^{-(\tau-1)}\end{align*} for all k ≥ 1 and some τ > 4 and c > 0, the largest critical connected component in a graph of size n is of order n^2/3, as it is for the critical Erd?s‐Rényi random graph. When, instead, \begin{align*}{\mathbb{P}}(W > k)=ck^{-(\tau-1)}(1+o(1))\end{align*} for k large and some τ∈(3,4) and c > 0, the largest critical connected component is of the much smaller order n^{(τ‐2)/(τ‐1)}. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 42, 480–508, 2013