Discrete path sampling

A theoretical framework is developed for the calculation of rate constants by sampling connected pathways composed of local minima and transition states that link them together. The theory is applicable to two-state or effective two-state systems and is applied to permutational or morphological isomerization in a two-dimensional cluster of seven Lennard-Jones atoms, water clusters containing eight and nine molecules, and a cluster of 38 Lennard-Jones atoms, which exhibits a double funnel energy landscape.     

Conformations and thermodynamic properties of sulphur homocycles. II. The fluxional S+ 8 radical cation

According to both UB3LYP/6-311G* and UMP2/6-311G* calculations, the lowest energy conformer of the S⁺ ₈ radical cation possesses C_s symmetry. However, there are three other structures with low relative energies that do not exceed 6.5 kcal mol^?1. These conformers, which are found to be very prone to pseudorotation, are predicted to interconvert readily. The fluxional nature of S⁺ ₈ is expected to facilitate its reactions with organic species where a specific conformation is demanded by steric constraints, which may explain its high reactivity towards PAHs with crowded hydrogen atoms.     

Experimental verification of the Stokes-Einstein relation in liquid Fe—FeS at 5 GPa

Experiments have been performed at 5 GPa on liquid Fe-FeS in order to determine Fe and S self-diffusivity as a function of temperature. The viscosity of the sample was then obtained using the Stokes-Einstein relation. The results are in excellent agreement with previous experiments where the viscosity of a material of the same composition under similar conditions was measured directly. These results support high, near-metallic, values of diffusivity and low viscosity in liquid Fe-S up to a few hundred K above the eutectic temperature, in contrast with some previous studies. Moreover, these results fully confirm the validity of the Stokes-Einstein relation between viscosity and diffusion coefficients for Fe_0.61S_0.39.     

Numerical Solution of Volterra Integral Equations with Continuous or Discontinuous Terms

Convergence criteria are given for the numerical solution ofVolterra integral equations with and without discontinuous terms.Several numerical methods are compared.     

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.