Structure indices for multidimensional systems

The structure indices of a one-dimensional system are an importantset of invariants. In this paper we examine a generalizationof this concept to multidimensional linear systems, which correspondsto the algebraic concept of a Hilbert series. We use the standardtheory of the Hilbert series to explain some of the previousID system-theoretic results. We discuss the computation of nDstructure indices from an initial condition set, and the invariantswhich can be derived from these indices.     

Molecular dynamics study of the mobility in poly(butyl methacrylate) isomers

Molecular mobility is studied in poly(butyl methacrylate) isomers with molecular dynamics simulations in order to understand the role of the side chain steric hindrance on the β and δ relaxation mechanisms. The simulations suggest that in the temperature range studied the δ process is weakly influenced by the α process. Conversely, the β process seems to be significantly changed as compared with the low frequency regime. The results exposed also show evidence that the intramolecular cooperativity is higher in PnBMA than in PtBMA, which, could be related to the distance to the α-β crossover.     

Testing Ten Theories

Using the most comprehensive data set now available, this investigation tests the precision of all exchange theories that now contend. Beyond precision, the investigation focuses on broad issues of effectiveness including consistency, parsimony, and whether the theories can be applied to structures larger than normally studied in the lab. Seeking greater parsimony, this investigation introduces a new model by combining parts of two contending theories. We find that all ten theories have scientific merit for all can predict with some effectiveness for the exchange structures experimentally investigated. Nevertheless, the ten vary in precision. Elementary Theory is the most precise. The new Expected-value Resistance model ranks second in precision and is the simplest. Both apply to large networks as well as the best of the other theories.     

A Side-by-Side Single Sex Age-Structured Human Population Dynamic Model: Exact Solution and Model Validation

A side-by-side single sex age-structured population dynamic model is presented in this paper. The model consists of two coupled von Foerster-McKendrick-type quasi-linear partial differential equations, two initial conditions, and two boundary conditions. The state variables of the model are male and female population densities. The solutions of these partial differential equations provide explicit time and age dependence of the variables. The initial conditions define the male and female population densities at the initial time, while the boundary conditions compute the male and female births at zero-age by using fertility rates. The assumptions of the nontime-dependence of the death and fertility rates and a specific factorization of the migratory balances allow us to obtain exact solutions for male and female population densities. In addition, the hypotheses about the mathematical structure of the input variables are formulated, and the exact solution of the model is obtained. Next, the model is applied to the case study of Spain for the time period 1996–2004. Model validation demonstrates that this approach is a powerful prediction tool. Code and data are available upon request.     

Theoretical study of rearrangements in water dimer and trimer

The global minimum and transition states for the acceptor-tunnelling, donor-acceptor interchange and bifurcation tunnelling rearrangements of the water dimer, and the single-flip, bifurcation and concerted proton transfer processes in the water trimer have been reinvestigated. Our analysis of the tunnelling splittings and spectroscopy is based on ab initio calculations at the computational level of second-order M?ller-Plesset (MP2) theory with basis sets of aug-cc-pVXZ quality (X = D, T, Q for the dimer; X = D, T for the trimer). In both water dimer and trimer, the binding energy, barrier heights, intermonomer distances, and harmonic frequencies converge smoothly as the size of the basis set increases. In the water dimer, the binding energy was evaluated as 5.09kcal mol^?1, while the activation energies are 0.52 (acceptor-tunnelling) 0.79 (donor-acceptor interchange), and 1.94 kcal mol^?1 (bifurcation tunnelling) at the MP2/aug-cc-pVQZ level. In the water trimer, the binding energy was evaluated as 16.29 kcal mol^?1, while the activation energies are 0.28 (single-flip), 2.34 (bifurcation), and 26.36 (proton transfer) kcal mol^?1 at the MP2/aug-cc-pVTZ level.     

Single-file motion of polyatomic molecules in one-dimensional nanoporous materials

In a continuation of the study of the mobility of fluids adsorbed in nanoporous materials, molecular dynamics simulations are used to investigate the behaviour of polyatomic ethane molecules adsorbed in AlPO₄-5. The current work is based on the use of the united atom approach as a better model than the single-centre ethane used to date. Ethane molecules are modelled as rigid diatoms, and as a result the molecules have more degrees of freedom in the form of the rotational components that are absent in the single-centre ethane model. This represents a more sophisticated model for ethane and is used in the simulations to test earlier findings. Simulations with binary mixtures of methane and ethane also have been conducted with three mixture compositions. The transition from ordinary diffusion to single-file motion for a finite residence time is found to occur at a methyl group diameter of 4.75 Å. This is identical to the ethane diameter in the earlier study. Thus, only the minimum dimension determines the transition size. Also it is shown that the diatomic molecules undergo free rotation within the channel even when they are in the single-file mode of motion. In the case of binary mixtures, the methane molecules still undergo ordinary diffusion. Ethane molecules exhibit single-file motion at a methyl group diameter of 4.75 Å. The diffusion coefficient of methane decreases with increasing ethane size, while the trends in the single-file mobility of ethane as a function of methyl group diameter are nonlinear.     

Structure,rearrangements and evaporation of rotating atomic clusters

Eigenvector-following techniques are used to explore the classical effective potential energy surface of rotating clusters composed of identical rare gas atoms. Precise determination of transition states reveals the mechanisms for atomic rearrangements and allows us to calculate rate constants for the evaporation of an atom from the cluster surface using RRK theory. We examine the variation in the effective potential energy surface with the magnitude of the angular momentum, with particular reference to centrifugal distortion and the resulting spectroscopic constants, the Hessian index of the stationary points, and the centrifugal barriers to evaporation. Most of the calculations are performed using a pairwise additive Lennard-Jones potential, but comparisons are made with the accurate Aziz potential augmented by a three-body Axilrod-Teller term.     

Polarization effects in liquid metals and charge stabilized colloidal dispersions

The induced polarization contributions to the effective interionic potentials are derived for liquid metals, liquid alloys and charge stabilized colloidal dispersions. These contributions have been obtained within a perturbative scheme that includes up to three-body terms. The formalism is illustrated by calculating the static structure factor S(k) of liquid Ga near melting. It is found that the main effects due to the induced polarization in S(k) are first lowering the height of the principal diffraction peak, and second sharpening the subsidiary peak present in liquid Ga.     

A simulation study of the pore size dependence of transport selectivity in cylindrical pores

The equilibrium adsorption and transport properties of mixtures of methane and carbon dioxide, modelled as spherical molecules, have been studied in cylindrical model pores with graphitic properties over a range of cylinder radii. The equilibrium isotherms exhibit packing transitions similar to those observed for single adsorbates; as a consequence, optimum separation factors are found at particular radii, depending on the fugacity (or pressure) in the system. The equations of non-equilibrium thermodynamics have been developed so as to represent the flux of each component in a Fickian form, as a coefficient multiplying the gradient of the total density. Diffusion coefficients were calculated from streaming velocity correlations and NEMD was used to obtain the ‘apparent’ viscous component. The results show that diffusion coefficients from equilibrium molecular dynamics and viscous diffusion coefficients from non-equilibrium calculations are identical within the errors of the calculation. It follows that equilibrium and dynamic separation factors have the same values over a range of pore sizes.