On evolution of open dynamical systems: Some algebraic methods

Open dynamical systems which are governed by a finite number of ordinary differential equations with controls (time-dependent control parameters) constitute a large and important class of models for practical purposes. In the last few years, there has been considerable interest and progress in algebraic methods for solving the equations of the form (*) $$\dot x\left( t \right) = L_0 x\left( t \right) + \sum\limits_{j = 1}^r {u\left( t \right)L_i x\left( t \right)} ,$$ i.e. bilinear models. In this paper, intended as an expository introduction to the main results of system-theoretic approach to the modelling of open systems, a new “polynomial” representation of solutions to (*) is discussed.     

Comparison of hydrogeologic parameters evaluated by deep well testing programs to assess nuclear waste repository feasibility

Hydrogeologic parameters evaluated for rocks investigated in deep well testing projects for nuclear waste repository feasibility are transmissivity, hydraulic conductivity and storativity. Such studies have been carried out in rock formations of different geologic types, origins and ages for nuclear waste management agencies in North America and Europe. From transient pressure testing, an assessment of static pressure in selected fracture zones was measured from which a profile with depth was developed using modelling techniques. As well, temperatures of formation fluids and hence thermal gradients have also been provided. Hydrogeologic parameters are commonly used in risk analysis for repositories with respect to the possible escape of contaminants and worst case scenarios. The parameters are related to the rate of possible radionuclide migration into the biosphere. The techniques of the investigation and analysis methods of this work have been fully described in the literature. This paper is the first to date, however, to compare results from testing in differen geologic environments. High transmissivity zones have been observed in the upper few hundred metres of granite formations. Below that depth, the rock is more competent and discrete zones of higher permeability occur less frequently. Our studies show, however, that in these rocks, zones of high hydraulic conductivity do not always correspond to zones of high fracture frequency. Most formation pressure profiles have a vertical gradient of about 10 kPa/m. In discrete zones, deviations from this trend can occur due to vertical inhomogeneity in the rock. Thermal gradients vary considerably from one investigation site to another. For example, in the Canadian Shield, gradients are of the order of 1.0 degree C per 100 m, whereas in similar rock types in Europe, the gradient is up to 4.0 degrees C per 100 m.     

Thermal studies of Cr2O3 doped CaCO3-SiO2 (2∶1) system

Mixtures of CaCO₃SiO₂ in 21 molar ratio were subjected separated to thermal analysis with varying concentration of Cr₂O₃ (0.1 to 5%) as dopant. The activation energy (E _a) and enthalpy (H) shows a decreasing trend with 0.1 to 1% Cr₂O₃ and attains a minimum value with 1% dopant. 0.1 to 0.5% Cr₂O₃ helps in the formation of and C₂S, (Cement Chemistry notations, C = CaO, S = SiO₂) phases at 1400° C and above but 1% Cr₂O₃ stabilizes -C₂S phase along with a little free lime and CaCrO₄. A small quantity of CaCrO₄, Cr₂SiO₂ and -C₂S are also formed along with the major phases with 5% Cr₂O₃ indicating that Cr³⁺ can substitute both Ca²⁺ and Si⁴⁺ ions in the C₂S lattice.     

Effect of stress-strain-law transients on formability

The effect of work-hardening changes, of the type that follow a rapid change of strain state or strain rate, on formability has been investigated using finite element modeling (FEM). A standard sheet tensile test was chosen as an arbitrary forming operation and a rigid-viscoplastic FEM program was employed for analysis. In each case, a transitional region of true strains between 0.1 and 0.2 was modeled. Transients involving lowered work-hardening rates (negative value of An) promoted increased strain localization and premature failure while transients with increased work-hardening rates enhanced formability. Total engineering elongations (50 mm gage length) varied between 20 pct and 46 pct, illustrating the importance of the transient far beyond the transient region. The controlling factor is the effective work-hardening rate in the transient region rather than the change in strength coefficient or flow stressper se. A direct stress offset of the flow curve { } also affects strain localization through a change in effective work-hardening rate.