Diagrams of electrochemical equilibria of the system copper-potassium ethylxanthate-water at 25°C

On the basis of thermodynamic calculations, diagrams of metastable electrochemical equilibria of the system copper-potassium ethylxanthate-water, at 25°C were constructed. The equilibria equations and diagrams for the total activity of [EtX^?] + [HEtX] + 2 [(EtX)₂] (equalling 10^?1, 10^?4 and 10^?7 mol/dm³), are presented. The practical conclusions resulting from these diagrams for the flotation of native copper are discussed.     

Non-integrability of the three-body problem

We consider the planar problem of three bodies which attract mutually with the force proportional to a certain negative integer power of the distance between the bodies. We show that such generalisation of the gravitational three-body problem is not integrable in the Liouville sense.     

Diffuse Interstellar Band at 862 nm as a Reddening Tracer for GAIA

We investigate the plausibility of using diffuse interstellar band at862 nm for tracing interstellar extinction with the ESA's astrometric space mission GAIA. For this purpose we perform numerical tests to simulate the conditions of real observations, covering a wide range of stellar parameters and different amounts of interstellar extinction. Our simulations indicate that with the present Radial Velocity Spectrometer setup the uncertainty in color excess of σ_E(B-V)≤ 0.05 can be achieved only for the interstellar reddening tracers brighter than V ∼ 13. None of the plausible tracers can provide accurate color excesses (σ _E(B-V) ≤ 0.05) at the distances beyond 2 kpc. We therefore conclude that with the currently planned instrumentation onboard GAIA this method can not be used as a stand-alone approach for probing interstellar extinction on the Galactic distance scales within the framework of the GAIA mission. This revised version was published online in July 2006 with corrections to the Cover Date.     

Pure cross-anisotropy for geotechnical elastic potentials

The pure cross-anisotropy is understood as a special scaling of strain (or stress). The scaled tensor is used as an argument in the elastic stiffness (or compliance). Such anisotropy can be overlaid on the top of any elastic stiffness, in particular on one obtained from an elastic potential with its own stress-induced anisotropy. This superposition does not violate the Second Law. The method can be also applied to other functions like plastic potentials or yield surfaces, wherever some cross-anisotropy is desired. The pure cross-anisotropy is described by the sedimentation vector and at most two constants. Scaling with more than two purely anisotropic constants is shown impossible. The formulation was compared with experiments and alternative approaches. Static and dynamic calibration of the pure anisotropy is also discussed. Graphic representation of stiffness with the popular response envelopes requires some enhancement for anisotropy. Several examples are presented. All derivations and examples were accomplished using the algebra program Mathematica.

     

Energy-dependent variability from accretion flows

We develop a formalism to calculate energy-dependent fractional variability (rms) in accretion flows. We consider rms spectra resulting from radial dependences of the level of local variability (as expected from the propagation of disturbances in accretion flows) assuming the constant shape of the spectrum emitted at a given radius. We consider the cases when the variability of the flow is either coherent or incoherent between different radial zones. As an example of local emission, we consider blackbody, Wien and thermal Comptonization spectra. In addition to numerical results, we present a number of analytical formulae for the resulting rms. We also find an analytical formula for the disc Wien spectrum, which we find to be a very good approximation to the disc blackbody. We compare our results to the rms spectrum observed in an ultrasoft state of GRS 1915+105.     

Mechanics of a sandy subsoil subjected to cyclic loadings

A simple model for compaction of a sand, that may be useful in various geotechnical applications is presented. The model has been formulated in terms of the cyclic stress and strain amplitudes. The compaction properties of a dry sand are characterized by a common compaction curve described by two coefficients. The second aim of this paper is to show some applications of the theory proposed. The attention has been restricted to the two extreme cases of practical importance, namely to the behaviour of a dry sand (or a saturated sand but in free draining conditions), and to the behaviour of saturated sand in undrained conditions. Some numerical algorithms showing how to deal with those problems are presented and illustrated on the following examples: settlement and pore pressure generation in a soil stratum subjected to an earthquake, settlement of a foundation, pore pressure generation and liquefaction in a sea-bed. The results obtained suggest that the model proposed, as well as a method of dealing with boundary value problems can serve as a useful tool for the analysis of a sandy subsoil subjected to cyclic loadings.     

Dynamic ray tracing on Lagrangian manifolds

Summary. We show that Maslov's extension of the WKBJ method allows an extension of the dynamic ray tracing to wavefields involving caustics of arbitrary form. If the receiver lies off the caustics, then the synthetic seismogram can be obtained by integrating the DRT system along a single ray joining the receiver to the source which may touch caustics. If the receiver-lies in the vicinity of a caustic then DRT has to be carried out along a bunch of rays covering a neighbourhood of the receiver. Our approach encompasses pre-stressed and/or anisotropic media. Initial boundary conditions for a point source embedded in an anisotropic elastic medium are also presented.