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.     

Experimental investigation and numerical simulation of the influence of resonator-length detuning on the output power,pulse duration and spectral width of a cw mode-locked picosecond optical parametric oscillator

We report on a cw mode-locked non-critically phase matched KTP optical parametric oscillator synchronously pumped by a picosecond Ti:Sapphire laser. High average signal output power of up to 950 mW over a large tuning range has been achieved. For this OPO the influence of resonator-length detuning on the output power, pulse duration and spectral bandwidth has been investigated. The measured data are in good agreement with the results of a numerical simulation using a split-step Fourier method which considers the group-velocity mismatch, the group-velocity dispersion and the self-phase modulation. The numerical simulation also describes the measured strong pump depletion and its influence on the OPO output and efficiency.     

On Kauffman invariants for 6-valent graphs

An explicit way for producing invariants for 6-valent graphs with rigid vertices within the framework of Kauffman's approach to graph invariants is presented. These invariants can be used to detect the chirality of a 6-valent graph with rigid vertices. A relevant example is considered. Bibliography: 19 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 223, 1995, pp. 251–262. Translated by A. M. Nikitin     

Normalization and averaging on compact lie groups in nonlinear mechanics

We consider the method of normal forms, the Bogolyubov averaging method, and the method of asymptotic decomposition proposed by Yu. A. Mitropol’skii and the author of this paper. Under certain assumptions about group-theoretic properties of a system of zero approximation, the results obtained by the method of asymptotic decomposition coincide with the results obtained by the method of normal forms or the Bogolyubov averaging method. We develop a new algorithm of asymptotic decomposition by a part of the variables and its partial case — the algorithm of averaging on a compact Lie group. For the first time, it became possible to consider asymptotic expansions of solutions of differential equations on noncommutative compact groups.     

Alloying by high dose ion implantation of iron into magnesium and aluminium

Alloys of the systems Fe–Al (mixable over the whole concentration range) and Fe–Mg (insoluble with each other) were produced by implantation of Fe ions into Al and Mg, respectively. The implantation energy was 200 keV and the ion doses ranged from 1 × 10₁₄ to 9 × 10₁₇cm^-2The obtained implantation profiles were determined by Auger electron spectroscopy depth profiling. Maximum iron concentrations reached were up to 60 at.% for implantation into Al and 94 at.% for implantation into Mg. Phase analysis of the implanted layers was performed by conversion electron Mössbauer spectroscopy and X‐ray diffraction. For implantation into Mg, two different kinds of Mössbauer spectra were obtained: at low doses paramagnetic doublets indicating at least two different iron sites and at high doses a dominant ferromagnetic six‐line‐pattern with a small paramagnetic fraction. The X‐ray diffraction pattern concluded that in the latter case a dilated αiron lattice is formed. For implantation into Al, the Mössbauer spectra were doublet structures very similar to those obtained at amorphous Fe–Al alloys produced by rapid quenching methods. They also indicated at least two different main iron environments. For the highest implanted sample a ferromagnetic six‐line‐pattern with magnetic field values close to those of Fe₃Al appeared.     

Logarithmic temperature dependence of the conductivity of the two-dimensional metal

We report on the first observation and studies of a weak delocalizing logarithmic temperature dependence of the conductivity, which causes the conductivity of the 2D metal to increase as T decreases down to 16 mK. The prefactor of the logarithmic dependence is found to decrease gradually with density, to vanish at a critical density n _c , 2∼2×10¹² cm⁻², and then to have the opposite sign at n>n _c ,2. The second critical density sets the upper limit on the existence region of the 2D metal, whereas the conductivity at the critical point, G _c ,2∼120e ²/h, sets an upper (low-temperature) limit on its conductivity. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 6, 497–501 (25 September 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Investigation of the chemical state of copper in Cu/SiO2 composite films by x-ray photoelectron spectroscopy

The concentration and chemical state of copper in the subsurface region of Cu/SiO₂ composite films obtained by simultaneous magnetron sputtering from two sources (Cu and SiO₂) are determined by x-ray photoelectron spectroscopy (XPS). It is established that copper in the as-grown film is primarily in the form of unoxidized atoms dispersed in a SiO₂ matrix. Annealing of the film results in practically no oxidation, but about 70% of the copper atoms condense into metallic clusters with sizes below 10 Å in the subsurface region and about 50 Å in the bulk of the film. The changes in the binding energy of core electrons, and especially in the energies of Auger electrons, are so large in this situation that photoelectron and Auger spectroscopy are efficient methods for monitoring the chemical state of this composite material.     

High quantum efficiency of intersubband transitions in coherent tunneling of electrons through asymmetric double-barrier structures

A converging perturbation series that can be summed analytically has been obtained for intersubband transitions of electrons coherently tunneling through the middle of a dimensionally quantized level in an asymmetric double-barrier structure in a high-frequency terahertz electric field. The possibility of a substantial increase in tunneling current accompanied by either absorption or emission of a photon has been demonstrated. The quantum efficiency of radiative transitions between dimensionally quantized levels can be up to 66%. Zh. éksp. Teor. Fiz. 112, 237–245 (July 1997)     

Temperature and field dependences of photo-induced changes in the magnetization in yttrium iron garnet

The changes in the magnetization of yttrium iron garnet (YIG) when irradiated by a pulsed neodymium laser beam with wavelength λ=1.06 μm are investigated. Measurements are performed in the temperature range from 100 K to 600 K in various external magnetic fields. YIG single crystals grown along the crystallographic (100), (110), and (111) directions are chosen so that the external anisotropy of the indicated processes can be determined. Characteristic temperature intervals dominated by different mechanisms of variation of the magnetization under the influence of a laser pulse are discussed. Fiz. Tverd. Tela (St. Petersburg) 39, 1263–1266 (July 1997)