On Non-Linear Ordinary Differential Equations of Boundary Layer Type

A numerical method previously applied to linear two-point boundary value problems of boundary layer type is extended to some non-linear problems. Discretization of the differential equation leads to a set of non-linear algebraic equations, which is solved by a modified Newton's method; both the mesh spacing and the boundary layer parameter are iteratively adjusted during the solution process. Several examples are discussed; one of these concerns the problem of shock wave formation in a supersonic nozzle.     

Evaluating Experiment with Computation in Physical Chemistry: The Particle-In-A-Box Model with Cyanine Dyes

The results from a classic experiment in the undergraduate physical chemistry laboratory, the particle-in-a-box model for spectroscopic transitions of conjugated dyes, is compared to computational results obtained using a molecular mechanics structural approach and the extended Hückel molecular orbital picture. The goal of this exercise is to help students to think critically about their experimental data and to use comparisons of mathematical and computational models to try to understand departures of an experiment from expectations.     

Molecular dynamics simulations of a flexible liquid crystal

Molecular dynamics simulations have been performed for a liquid crystal composed of a Gay—Berne core site with two alkyl chains of different length (C₇ and C₃) at either end of the molecule. Calculations have been carried out for 512 molecules in the NVT ensemble for simulation times of up to 8.0ns at two distinct densities. The liquid crystal phases of the material have been fully characterized by measurements of orientational order parameters and radial distribution functions in each phase. Results are also presented for conformational distributions and effective torsional potentials of the system. We conclude that models of this nature represent a powerful approach to the study of flexibility in mesogenic systems and open up possibilities for predicting both the phase behaviour and bulk properties of liquid crystals based solely on a prior knowledge of intermolecular interactions.     

On Namias's Fractional Fourier Transforms

The objective of this paper is to make rigorous a formal study(Namias, 1980) of fractional powers for the Fourier transform.To make the theory unambiguous, it is found necessary to modifyNamias's fractional operators. Some theorems are then provedfor the modified operators and an operational calculus is developed.Finally, an application to an ordinary differential equationis considered.     

Edge Effects in Composites by Moiré Interferometry

Many aspects of the physical behavior of composite materials can be observed and quantified by moiré interferometry. While rapid progress is being made in the mathematical analysis of composite members, experimental measurements are essential to guide and verify the theoretical work. Moiré interferometry reveals in-plane displacement fields on the surface of a specimen, as caused by external loading or other source of deformation. It responds to geometric changes of the specimen only, and thus it is effective for diverse engineering materials, including anisotropic and nonlinear materials. Its sensitivity is as much as two orders of magnitude higher than classical coarse moiré methods for in-plane measurements.     

Three-dimensional Contact of a Rigid Roller Traversing a Viscoelastic Half Space

In this paper, the authors consider a nontrivial three-dimensionalviscoelastic contact problem which has some physical significance.(Although the subject of the analysis is an elliptical roller,it is only a small step onward to the consideration of a crownedcylindrical roller.) Generally, it is the intractability of the mathematics whichhinders analytic solution of true three-dimensional problemsin (visco)elasticity. The traditional method of surmountingthis difficulty is to reduce the problem to two dimensions,either by choosing a suitable geometry, or by using an appropriateco-ordinate system. The elastic line integral theory representsanother approach; certain approximations are used to simplifythe governing equations, thus allowing the solution of the problem. After the development of a viscoelastic analogue of the Boussinesqequation valid for the solution of quasi-steady state viscoelasticcontact problems, analysis proceeds making use of near fieldand extended line integral approximations. Results are generatedshowing the velocity dependence of several physical parameters,including the size and shape of the contact zone. One additionalpoint of interest is uncovered, namely the presence of a pressurepeak near the leading edge of the contact zone.     

Synthesis and Inclusion Properties of a Novel Thiacalix[4]arene-Based Hard–Soft Receptor with 1,3-Alternate Conformation

A novel ditopic receptor possessing two complexation sites and bearing 1,3-alternate conformation based on thiacalix[4]arene was prepared. The binding behaviors with alkali metals and silver ion have been examined by ¹H NMR titration experiment. Although the formation of the heterogeneous dinuclear complexes was not observed, the exclusive formation of mononuclear complexes of 1,3-alternate-3 with metal cations is of particular interest in negative allosteric effect in the thiacalix[4]arene family. These findings demonstrate that preorganization, subtle conformational changes and affinity have a pronounced effect on the complexation process between the two different arms placed at the two edges of the thiacalix[4]arene cavity.