A Moving Boundary Problem for the Sphere

A new technique is employed to solve a moving boundary problemin a sphere. A transformation is given which considerably simplifiesthe non-linearities associated with the moving boundary andenables an iterative analytic series solution to be found. Threeterms of the series expansion are obtained analytically andnumerically evaluated for comparison with results of previousauthors. Graphs of the motion of the reaction (freezing) frontand concentration (temperature) profiles behind the front aregiven. Also tabulated are the times to complete reaction (freezing)of the particle (that is the time for the moving boundary toreach the centre of the sphere).     

Multiple groups in the symmetry classification of adiabatic electronic wavefunctions

It was originally shown by Longuet-Higgins and colleagues that when the electronic Schrödinger equation is solved as a function of the nuclear coordinates the adiabatic electronic wavefunction can undergo a change of sign after completing a closed circuit. This geometric phase occurs for a circuit around a conical intersection, and in particular around a conical intersection corresponding to a linear Jahn—Teller effect. The adiabatic wavefunctions are classified here under a group called the adiabatic multiple group, which is a generalization of the ‘vibronic double group’ of C _3v introduced by Hougen, and is distinct from the familiar electron-spin double group. Although the real electronic wavefunctions can be only double-valued, the groups can have higher multiplicity because of the possibility of different circuits. For a number of symmetric- and spherical-top point groups, the adiabatic multiple group is shown to be the direct product of the point group with a phase group. The adiabatic multiple group can be applied to individual adiabatic orbitals, and so to configurations built from these orbitals. This leads to the rule that the linear Jahn—Teller effect vanishes in the single-configuration approximation for configurations containing non-degenerate electrons plus an even number of e electrons. There does not appear to be any cancellation effect for electron configurations of cubic molecules containing f electrons.     

Recreation of Wöhler’s Synthesis of Urea: An Undergraduate Organic Laboratory Exercise

An undergraduate laboratory exercise appropriate to the upper-level organic or inorganic course is presented. The objective of the laboratory is to recreate an experiment of historical significance familiar to organic chemistry students while also incorporating modern techniques of spectroscopic characterization and purification.     

Report On ‘Multimedia Instruction’

The ‘Multimedia Instruction’ workshop examined a variety of uses for multimedia in instruction. Marco Molinaro, Director of Multimedia Development for the Modular Chemistry Consortium based at the University of California at Berkeley, presided. The session consisted of developing a common language used in describing multimedia, exploring demonstration programs, and using hands-on experience to create, adapt, or critique available software.     

Stable Subharmonics of the Forced Van der Pol Equation

The Van der Pol equation with periodic forcing term is investigatednumerically for a range of values of the parameters. The equationis integrated using the fourth order Runge-Kutta method. Twodifferent types of subharmonics have been found, namely "normal"subharmonics and "abnormal" subharmonics. Finally, the criticalvalue b = is investigated.     

Report On ‘Chemistry in a Biological Context’

The American Chemical Society has started its first large-scale project related to opening up new options for undergraduate majors. Tentatively titled Chemistry in a Biological Context, the work has only just begun. Participants are invited to provide early feedback into the nature and shape of the project.     

BIOECONOMIC INTERACTIONS IN AN ESTABLISHED FISHING EXCLUSION ZONE: THE GULF OF CASTELLAMMARE,NW SICILY

ABSTRACT. Fishing exclusion zones have become a key management tool for habitat protection and species conservation within fisheries. In many instances, where overfishing or habitat destruction is taking place, they are being promoted strongly. For fisheries management, their use is widespread and their popularity growing. It is clear that in some cases marine protected areas may be crucial to sustaining resources. Most research to date has considered the biological or ecological effects of such reserves. However, little real analysis has been published that takes into account the links between the biology and the economics of the fisheries involved, making the economic benefits to fisheries less clear. This paper considers an exclusion zone which was implemented in 1990 in the Gulf of Castellammare, Sicily in the form of a trawl ban, modeling the potential effects of future policy in this area. The success of the trawl ban has far exceeded expectations, and it is simulated that it may be advantageous, under strict conditions, to relax the ban in part for some of the year.     

Time Optimal Control and the Van der Pol Oscillator

The problem considered is the control of the Van der Pol oscillator,where the control appears as a forcing term on the right-handside of the differential equation, the "goal" is the equilibriumstate and the "cost" is the time of transfer from an initialstate to the equilibrium state. Qualitative methods and some simple analytic procedures includinga Liapunov type stability theorem are used to determine domainsof controllability and switching curves.