Monte Carlo study of the selectivity of calcium channels: improved geometrical model

An extended model of a calcium channel is described involving a channel with a finite length. With this new geometry the channel is still selective but less so than in an infinite cylinder geometry (Boda, D., Busath, D. D., Henderson, D., and Sokolowski, S., 2000, J. phys. Chem. B, 104, 8903). The selectivity of the channel depends on the width and length of the channel filter but is not significantly affected by changes in the size of the entry vestibules. Interestingly, changes in the size of the entry vestibules do affect the details of the concentration profiles of some of the ions.     

The velocity autocorrelation function and self-diffusion coefficient of fluids with steeply repulsive potentials

We consider the velocity autocorrelation function, vacf, or C_v(t) and self-diffusion coefficients, D, of steeply repulsive inverse power fluids (SRP) in which the particles interact with a pair potential, ? (r) = ?(σ/r)ⁿ. The C_v(t) are calculated numerically by molecular dynamics simulations. Accurate expressions for the short time expansion of C_v(t) to order O(t⁴) for n large are derived for this fluid. We propose novel expressions for C_v (t) that, for n large, spans the transition from the short time regime (expandable in even powers of time) and the longer time exponential-like regime characteristic of hard spheres. Inter alia we introduce relaxation times that characterize the duration of a collision and the decay of the velocity correlation within the mean-collision or Enskog-like relaxation time, T_E.     

THE USE OF TELESCOPING SPATIAL SCALES TO CAPTURE INSHORE TO SLOPE DYNAMICS IN MARINE ECOSYSTEM MODELING

Abstract Ecosystem processes function at many scales, and capturing these processes is a challenge for ecosystem models. Nevertheless, it is a necessary step for considering many management issues pertaining to shelf and coastal systems. In this paper, we explore one method of modeling large areas with a focus at a range of scales. We develop an ecosystem model that can be used for strategic management decision support by modeling the waters off southeastern Australia using a polygon telescoping approach, which incorporates fine‐scale detail at the coastal zone, increasing in scale to a very coarse scale in the offshore areas. This telescoping technique is a useful tool for incorporating a wide range of habitats at different scales into a single model.     

Synthesis and NMR Analysis of N-Methyl-2-(4′-bromophenyl)morpholine: An Advanced Undergraduate Laboratory Experiment

Nuclear magnetic resonance spectroscopy holds a premier position as a tool for structure elucidation in organic chemistry. With the increased availability of high-field Fourier-transform spectrometers in undergraduate laboratories, there is an increased need for good instructional experiments. We describe a reliable one-step synthesis of a moderately complex structure, and a straightforward ¹H NMR spectral assignment problem that illustrates the use of coupling constants for the determination of positional relationships, geminal coupling, and correlation spectroscopy (COSY) for the identification of coupled signals [1].     

The SSA congruence theorem

Many teachers and textbooks mention ‘three and a half basic congruence theorems: SAS, ASA, SSS and HL for right triangles. Why do they neglect the SSA theorem? A recent article [1] investigated the SSA theorem, but it seems necessary to extend and, in one point, to correct the result given there.     

Analytical second derivatives for excited electronic states using the single excitation configuration interaction method: theory and application to benzo[a]pyrene and chalcone

A compact formulation and a semi-direct implementation are described of analytical second derivatives of the single excitation configuration interaction (CIS) energy. CPU time, memory usage and disc storage all scale with the same power of system size as the ground state Hartree—Fock (HF) method, with a coefficient only 2 to 3 times larger. Thus usually analytical excited state CIS frequencies are feasible when HF frequencies are feasible. As a computational example, analytical CIS/3-21G frequencies for benzo[a]pyrene are calculated more efficiently than with finite differences. As a chemical application, analytical CIS/6-31G^* frequencies are used to investigate non-planarity in the lowest π → π excited state of transchalcone.     

A new pseudospectral method with upwind features

A new pseudospectral method is presented for numerical solutionsof singular perturbation problems without turning points. Boththeoretical and numerical analyses show that this new methodis an upwind scheme. It is shown that when the perturbationparameter is fixed the computed solution converges spectrallyto the exact solution as the number of collocation points tendsto infinity. ^* Supported by a Royal Fellowship Award from the Royal Societyof London.     

Extension of Dynamic Programming to Multi-plant Renewal

Discounting formulae and dynamic programming methods have beenproposed for single machine replacement problems with and withouttechnological change. But it is often essential to considercapacity replacement collectively in terms of all the plantsowned by a company as the replacement decisions are not independent.This paper proposes a model for capacity renewal and describeshow the problem can be tackled by dynamic programming combinedwith a priority ordering system.