Constant pressure Gibbs ensemble Monte Carlo simulations of adsorption into narrow pores

An extension to the Gibbs ensemble method for the study of adsorption of fluids into pores is proposed. Since equality of pressure is not a necessary condition for full thermodynamic equilibrium between the bulk fluid and that confined in a narrow cavity, previous studies have been performed with the volume of both simulation cells fixed. More naturally, the pressure of the bulk fluid should be constrained and the volume (and hence density) allowed to attain its equilibrium value. Thus we propose a scheme in which volume fluctuations within the bulk box are permitted; the volume of the pore remains constant. The pressure is an input parameter and the amount of adsorption, as a function of applied pressure, is obtained directly. We demonstrate that the novel moves obey microscopic reversibility. Such a method is most useful when the equation of state for the model fluid is unknown. Thus, we illustrate the method by simulating an associating model of water adsorbed into a slit-shaped carbon pore with activated sites. Good qualitative correspondence with experiment is obtained; further refinement of our model is expected to yield quantitative agreement.     

Symmetric and nonsymmetric equilibria of a rod-and-spring model

A simple rod-and-spring model is used to illustrate bifurcationin the presence of symmetry. Our aim is to demonstrate the relevanceof certain general mathematical ideas and computational techniquesin a comparatively simple physical example, a full appreciationof which can be intuitive. The model discussed here has twodistinct reflectional symmetries, i.e. Z₂Z₂ symmetry. The symmetry-grouprepresentations, invariant subspaces, projection matrices, projectedequa-tions, and extended systems used to compute loci of singularitiesare all given explicitly. A closely allied nonsymmetric modelis then developed and its behaviour is examined numerically.Connections between singularities in the symmetric and asymmetricmodels are explored.     

有点作用的抛物型方程解的控制

本文讨论状态由右端有空间点作用的抛物型偏微分方程确定的控制问题。具体地说,给定Ω(Ω为R~n的开集)中的点b,以及(0,T)上的函数v=v(t),状态y=y_(v,b)(x,t)是下列方程的解: (y/t)+Ay=v(t)δ_b(t),x∈Ω,t∈(0,T),这里假设y的初值和边值都是零,δ_b是支点为b的Dirac函数,A是x的二阶椭圆型偏微分算子.被极小化的代价泛函为 其中z给定在Ω中,N>0。 这一问题是由Lions首先提出并研究的(也参看[10]-[12],[14],[15]).本文对此又作进一步系统讨论,特别是改正了原来的一些不准确的结果.例如,引入空间 U_b={v|v∈L~2(0,T),y_v,b(·,T)∈L~2(Ω)}.本文指出而不是以前所指出的本文也指出,Green公式一般也不成立,而应该是这里Q=Ω×(0,T),∑为Q的边界,A~*为A的共轭算子,v_A是关于A的外法线方向. 同时,本文还讨论了最优性的一阶必要条件,正则性结果;引入 (b)=inf J(v,b),v∈U_b.还讨论了对b的连续性、可导性、导数在边界上的性态以及对控制问题的应用等。     

若干钠锗酸盐晶体和熔体的温致结构变化及其锗配位数的拉曼光谱研究

本文测定了Na4GeO4、Na2GeO3、Na2Ge4O9和Na4Ge9O20等晶体从273K到1413K升温及熔体的拉曼光谱,结合分析金红石型GeO2的相关结构和光谱,研究了其微结构单元在升温过程中的变化、熔体中的形态和锗的氧配位数及其温致变化。Na4GeO4和Na2GeO3晶体结构单元为GeO4四面体,在升温过程及其熔体中锗维持四配位。Na2Ge4O9和Na4Ge9O20晶体结构单元为GeO4四面体和GeO6八面体共存,升温过程中,GeO6八面体将发生结构转变,在熔融状态全部转变为GeO4四面体,并产生与钠离子等摩尔分数的非桥氧,在熔体中锗的氧配位数为4。研究还表明,桥氧的对称弯曲振动模可以反映不同微结构单元间的连接,并且随着温致结构的变化而产生特征性的变化。     

ON THE COADJOINT ORBITS OF MAXIMAL UNIPOTENT SUBGROUPS OF REDUCTIVE GROUPS

Let G be a simple algebraic group defined over an algebraically closed field of characteristic 0 or a good prime for G. Let U be a maximal unipotent subgroup of G and \( \mathfrak{u} \) its Lie algebra. We prove the separability of orbit maps and the connectedness of centralizers for the coadjoint action of U on (certain quotients of) the dual \( \mathfrak{u} \)* of \( \mathfrak{u} \). This leads to a method to give a parametrization of the coadjoint orbits in terms of so-called minimal representatives which form a disjoint union of quasi-affine varieties. Moreover, we obtain an algorithm to explicitly calculate this parametrization which has been used for G of rank at most 8, except E₈.When G is defined and split over the field of q elements, for q the power of a good prime for G, this algorithmic parametrization is used to calculate the number k(U(q); \( \mathfrak{u} \)*(q)) of coadjoint orbits of U(q) on \( \mathfrak{u} \)*(q). Since k(U(q), \( \mathfrak{u} \)*(q)) coincides with the number k(U(q)) of conjugacy classes in U(q), these calculations can be viewed as an extension of the results obtained in [11]. In each case considered here there is a polynomial h(t) with integer coefficients such that for every such q we have k(U(q)) = h(q). We also explain implications of our results for a parametrization of the irreducible complex characters of U(q).     

Flux expressions and NEMD perturbations for models of semi-flexible molecules

We derive energy and momentum flux expressions, for systems composed of a general class of semi-flexible molecules, in the Ciccotti-Ferrario-Ryckaert linear constraint formalism. According to this formalism, the whole set of Cartesian coordinates is divided into basic (independent) and secondary (dependent) subsets. It is found that energy and momentum flux vectors have a simple and general expression using both basic and secondary coordinates. In the case of non-equilibrium molecular dynamics, we give general and simple heat and shear flow algorithms, deriving the dissipative fluxes in the space of all Cartesian coordinates. In comparison with previous derivations for some models of flexible molecules, the present approach has more general applicability. Moreover, it leads to more efficient equilibrium and non-equilibrium molecular dynamics calculations of transport coefficients, and requires minimal programming effort.     

Composite optical fibre–slab waveguides: a scalar,coupled-mode analysis with vector corrections

Analytically-derived vector corrections are included as additional coupling coefficients in numerical calculations of scalar coupled-mode and compound-mode theory (SCMT) of composite fibre–slab waveguides. The slab waveguide is asymmetric, with moderate light-wave guiding and coupling assumed and the resultant polarization effects are of interest. It is found that the modifications to light propagation and coupling coefficients determined previously by first-order SCMT are dependent mainly on the strength of coupled fibre and slab modes, the thickness of the guiding layers and the ratio of refractive indices of guiding to cladding layer (asymmetry of the slab waveguide). The vector corrections observed are not significant compared with our previous SCMT results, as the optical constants defined appear to satisfy the approximations necessary for the scalar analysis. This revised version was published online in June 2006 with corrections to the Cover Date.