FORECASTING MINERAL SUPPLY FROM MINERAL RENT DATA

An optimal control model of exhaustible resources is used to clarify the long run relationship between mineral rent and depletion cost at the industry level. A standard first order condition of the time rate of change of rents is reformulated to reveal that rent data may be used to help forecast the rise in extraction costs resulting from resource depletion. This application of the theory of exhaustible resources is illustrated using historical mineral industry rent and extraction cost data. A forecast of U.S. coal extraction costs, following the method proposed in this paper, suggests that future rates of extraction cost increases will be similar to rates experienced in the past.     

Real-time recursive estimation of statistical parameters

Recursive algorithms for the computation of standard deviation and average deviation are derived and their applications in data acquisition are discussed. The relative speeds and accuracies of the two algorithms are compared for synthetic data. The performance of recursive estimation under shot and proportional noise limitations is also described. As an example of the utility of these algorithms, absorbance data with constant confidence intervals are collected regardless of incident and transmitted intensities. The desired precision is specified prior to data acquisition and used to control signal-averaging of the data in real time.     

Diffusion from sessile droplets through membranes

We analyze diffusion from a periodic array of hemispherical droplets through a membrane. We find that the multiple sources do not interact strongly, even when the droplets are closely spaced, so that the flux through the membrane appears nearly additive.     

Vibrational dynamics of fullerene molecules adsorbed on metal surfaces studied with synchrotron infrared radiation

Infrared (IR) spectroscopy of chemisorbed C₆₀ on Ag (111), Au (110) and Cu (100) reveals that a non-IR-active mode becomes active upon adsorption, and that its frequency shifts proportionally with the charge transferred from the metal to the molecule by about 5 cm^-1 per electron. The temperature dependence of the frequency and the width of this IR feature have also been followed for C₆₀/Cu (100) and were found to agree well with a weak anharmonic coupling (dephasing) to a low-frequency mode, which we suggest to be the frustrated translational mode of the adsorbed molecules. Additionally, the adsorption is accompanied by a broadband reflectance change, which is interpreted as due to the scattering of conduction electrons of the metal surface by the adsorbate. The reflectance change allows determination of the friction coefficient of the C₆₀ molecules, which results in rather small values (∼2×10⁹ s^-1 for Ag and Au, and ∼1.6×10⁹ s^-1for Cu), consistent with a marked metallic character of the adsorbed molecules. Pre-dosing of alkali atoms onto the metal substrates drastically changes the IR spectra recorded during subsequent C₆₀ deposition: anti-absorption bands, as well as an increase of the broadband reflectance, occur and are interpreted as due to strong electron–phonon coupling with induced surface states. Received: 6 June 2001 / Accepted: 23 October 2001 / Published online: 3 April 2002     

On Congruence of Complex Matrices

For each of a standard set of normal forms for (n × n) complex matrices under the relation of congruence, explicit matrices are exhibited which transform, via congruence, the normal form to its transpose.     

Optimization of in-vacuo template-stripped Pt surfaces via UHV STM

A recently demonstrated [1] in-vacuo template-stripping process is applied to the study of platinum films stripped from ultra-flat silicon-oxide surfaces. Template-stripped (TS) Pt surfaces, prepared with a range of post-deposition annealing times prior to being stripped from the templating surface in an ultra-high vacuum (UHV) environment, are examined by UHV scanning tunneling microscopy (STM). These studies reveal that without post-deposition annealing, TS Pt surfaces are largely made up of poorly-ordered, granular nanostructures undesirable for many applications. The post-deposition annealing treatments explored in the study result in the emergence and continuous growth of large smooth crystallites. Issues with crystallite orientation relative to the TS surface and artefacts arising as a result of the epoxy used in the template-stripping process are presented and discussed in relation to optimizing the template-stripping procedure for specific applications such as self-assembled monolayer (SAM) formation for molecular electronics. PACS 68.37.Ef; 68.47.De; 68.55.Jk; 81.05.Bx; 81.15.Ef     

Mode beating in spot-size converter lasers

An anomalous modulation in the wavelength spectrum has been observed in lasers with spot-size converters. This intensity modulation is shown to be caused by beating between the fundamental lasing mode and radiation modes in the taper. This results in a periodic modulation in the net gain spectrum, which causes wavelength jumps between adjacent net gain maxima, and a drive current dependent spectral width that is expected to affect system performance. The amplitude of this spectral modulation is reduced significantly by either using an angled rear-facet which reflects the beating radiation modes away from the laser axis, or by using a nonlinear, adiabatic taper.